2.04:_Atomic_Mass

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<div class="box-objectives">
<span id="Learning_Objectives"></span><span id="Learning_Objectives"></span><h5 class="box-legend"><span class="lt-icon-default">Learning Objectives</span></h5>

<ul>
    <li class="lt-chem-21700" style="background-color: unset;">to know the meaning of isotopes and atomic masses.</li>
</ul>
</div>

<span id="Atomic_and_Molecular_Weights"></span><span id="Atomic_and_Molecular_Weights"></span><h2 style="background-color: unset;" class="lt-chem-21700">Atomic and Molecular Weights</h2>

<p class="lt-chem-21700" style="background-color: unset;">The subscripts in chemical formulas, and the coefficients in chemical equations represent <em>exact </em>quantities. <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="98" style="font-size: 85%; position: relative;" data-semantic-locale="en" data-semantic-domain="clearspeak" data-semantic-style="default" data-semantic-domain2style="mathspeak:default,clearspeak:default" data-semantic-collapsible="collapsible" data-semantic-expandable="expandable" data-semantic-level="Level" data-semantic-speech-none="normal H of sub 2 normal O" data-semantic-speech="&lt;mark name=&quot;0&quot;/&gt; normal &lt;prosody pitch=&quot;+30%&quot;&gt; &lt;mark name=&quot;0&quot;/&gt; &lt;say-as interpret-as=&quot;character&quot;&gt;H&lt;/say-as&gt; &lt;/prosody&gt; &lt;break time=&quot;250ms&quot;/&gt; &lt;mark name=&quot;6&quot;/&gt; of &lt;mark name=&quot;3&quot;/&gt; sub &lt;mark name=&quot;2&quot;/&gt; 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The following equation:</p>

<p class="lt-chem-21700" style="background-color: unset;">not only tells us that propane reacts with oxygen to produce carbon dioxide and water, but that <strong><em>1</em></strong> molecule of propane reacts with <strong><em>5</em></strong> molecules of oxygen to produce <strong><em>3</em></strong> molecules of carbon dioxide and <strong><em>4</em></strong> molecules of water. Since counting individual atoms or molecules is a little difficult, quantitative aspects of chemistry rely on knowing the <em>masses</em> of the compounds involved.</p>

<p class="lt-chem-21700" style="background-color: unset;">Atoms of different elements have different masses. Early work on the separation of water into its constituent elements (hydrogen and oxygen) indicated that 100 grams of water contained 11.1 grams of hydrogen and 88.9 grams of oxygen:</p>

<p class="lt-chem-21700" style="background-color: unset;">Later, scientists discovered that water was composed of <strong><em>two atoms</em></strong> of hydrogen <strong><em>for each atom</em></strong> of oxygen. Therefore, in the above analysis, <em>in the 11.1 grams of hydrogen there were twice as many atoms as in the 88.9 grams of oxygen.</em> Therefore, an oxygen atom must weigh about 16 times as much as a hydrogen atom:</p>

<p class="lt-chem-21700" style="background-color: unset;">Hydrogen, the lightest element, was assigned a relative mass of '1', and the other elements were assigned 'atomic masses' relative to this value for hydrogen. Thus, oxygen was assigned an atomic mass of 16. We now know that a <strong>hydrogen</strong> atom has a mass of <strong>1.6735 x 10<sup>-24</sup></strong> grams, and that the <strong>oxygen</strong> atom has a mass of <strong>2.6561 X 10<sup>-23</sup></strong> grams. As we saw earlier, it is convenient to use a reference unit when dealing with such small numbers: the <strong>atomic mass unit</strong>. The atomic mass unit (<strong><em>amu</em></strong>) was not standardized against hydrogen, but rather, against the <sup>12</sup>C isotope of <strong>carbon</strong> (<strong><em>amu</em> = 12</strong>).</p>

<p class="lt-chem-21700" style="background-color: unset;">Thus, the mass of the <strong>hydrogen atom</strong> (<sup>1</sup>H) is 1.0080 <em>amu</em>, and the mass of <strong>an oxygen atom</strong> (<sup>16</sup>O) is 15.995 <em>amu</em>. Once the masses of atoms were determined, the <strong><em>amu</em></strong> could be assigned an actual value:</p>

<p class="lt-chem-21700" style="background-color: unset;">1 <strong><em>amu</em></strong> = 1.66054 x 10<sup>-24</sup> <strong>grams</strong> conversely: 1 <strong>gram</strong> = 6.02214 x 10<sup>23</sup> <strong><em>amu</em></strong></p>

<p class="lt-chem-21700 mt-align-center" style="background-color: unset;">Mass Numbers and Atomic Mass of Elements: <a target="_blank" href="https://youtu.be/Bg8yBFSBuqs" rel="external noopener nofollow" class="link-https">Mass Numbers and Atomic Mass of Elements, YouTube(opens in new window)</a><span> [youtu.be]</span></p>

<span id="Average_Atomic_Mass"></span><span id="Average_Atomic_Mass"></span><h2 style="background-color: unset;" class="lt-chem-21700">Average Atomic Mass</h2>

<p class="lt-chem-21700" style="background-color: unset;">Although the masses of the electron, the proton, and the neutron are known to a high degree of precision (<span class="external">Table 2.3.1</span>), the mass of any given atom is not simply the sum of the masses of its electrons, protons, and neutrons. For example, the ratio of the masses of <sup>1</sup>H (hydrogen) and <sup>2</sup>H (deuterium) is actually 0.500384, rather than 0.49979 as predicted from the numbers of neutrons and protons present. Although the difference in mass is small, it is extremely important because it is the source of the huge amounts of energy released in nuclear reactions.</p>

<p class="lt-chem-21700" style="background-color: unset;">Because atoms are much too small to measure individually and do not have charges, there is no convenient way to accurately measure absolute atomic masses. Scientists can measure relative atomic masses very accurately, however, using an instrument called a mass spectrometer. The technique is conceptually similar to the one Thomson used to determine the mass-to-charge ratio of the electron. First, electrons are removed from or added to atoms or molecules, thus producing charged particles called ions. When an electric field is applied, the ions are accelerated into a separate chamber where they are deflected from their initial trajectory by a magnetic field, like the electrons in Thomson&rsquo;s experiment. The extent of the deflection depends on the mass-to-charge ratio of the ion. 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href="#MJX-103-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-103-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="2" 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data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container></span>). Thus it is not possible to calculate absolute atomic masses accurately by simply adding together the masses of the electrons, the protons, and the neutrons, and absolute atomic masses cannot be measured, but relative masses can be measured very accurately. It is actually rather common in chemistry to encounter a quantity whose magnitude can be measured only relative to some other quantity, rather than absolutely. We will encounter many other examples later in this text. In such cases, chemists usually define a standard by arbitrarily assigning a numerical value to one of the quantities, which allows them to calculate numerical values for the rest.</p>

<figure><img alt="Diagram illustrating light propagation through an optical fiber, with a graph plotting related data." class="internal" loading="lazy" src="https://chem.libretexts.org/@api/deki/files/30351/ce4e100228e41595807a2be40259746f.jpg?revision=3" />
<figcaption>Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="103" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.532ex" role="img" focusable="false" viewbox="0 -677 2056 677" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-104-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-104-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-104-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 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data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-104-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>: Determining Relative Atomic Masses Using a Mass Spectrometer. 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162 654 127 631C88 605 68 571 68 528C68 495 90 472 122 472C154 472 176 495 176 527C176 560 157 578 119 580C145 615 186 633 242 633C302 633 332 598 332 527C332 485 324 450 309 421C282 373 245 364 183 364C171 362 165 357 165 348C165 333 172 333 192 333L235 333C310 333 348 280 348 173C348 88 317 14 241 14C176 14 128 36 99 80C134 79 160 105 160 139C160 173 135 198 101 198C62 198 42 178 42 137C42 88 64 49 108 18C147-9 193-22 244-22C301-22 350-3 393 34C436 71 457 117 457 173C457 267 383 332 303 353Z"></path><path id="MJX-106-NCM-N-37" d="M475 604C482 613 485 626 485 644L243 644C174 644 135 648 128 657C125 660 122 667 120 676L89 676L55 464L88 464C98 520 106 550 112 555C115 558 146 560 205 560L401 560L295 410C214 295 174 171 174 36C174-3 190-22 223-22C256-22 272-3 272 36L272 87C272 239 296 349 343 416Z"></path><path id="MJX-106-NCM-N-2062" d=""></path><path id="MJX-106-NCM-I-1D436" d="M148 218C148 346 204 476 267 548C318 607 406 666 505 666C609 666 660 587 660 479C660 470 657 438 657 429C657 420 663 415 676 415C681 415 685 416 688 417C693 424 696 431 698 438L760 691C760 700 755 705 745 705C741 705 735 701 727 692L662 619C623 676 568 705 497 705C442 705 388 692 333 667C222 615 141 533 89 421C63 366 50 310 50 253C50 173 75 108 126 56C177 4 242-22 322-22C401-22 473 7 538 64C565 87 588 115 607 146C634 191 648 222 648 241C648 250 643 255 632 255C623 255 618 251 616 242C595 177 562 125 517 88C460 41 400 17 338 17C218 17 148 98 148 218Z"></path><path id="MJX-106-NCM-I-1D459" d="M173 632L49 119C46 105 44 93 44 84C44 31 83-11 136-11C185-11 220 41 241 145C241 154 236 159 225 159C217 159 211 152 208 138C188 59 165 19 138 19C121 19 113 33 113 60C113 75 115 91 119 107L258 679L258 683C255 690 249 694 242 694C210 694 136 685 124 684C109 682 102 674 102 659C102 650 111 645 130 645C147 645 173 645 173 632Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="^{37}Cl" data-semantic-type="infixop" 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data-latex="{37}"><g data-mml-node="mn" data-latex="37" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="1" data-semantic-parent="2" data-semantic-attributes="latex:{37};texclass:ORD" data-semantic-level-number="2" data-speech-node="true"><use data-c="33" href="#MJX-106-NCM-N-33"></use><use data-c="37" href="#MJX-106-NCM-N-37" transform="translate(500,0)"></use></g></g></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="5" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="1" data-speech-node="true" transform="translate(790.1,0)"><use data-c="2062" href="#MJX-106-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="C" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="3" data-semantic-parent="7" data-semantic-attributes="latex:C" data-semantic-level-number="1" data-speech-node="true" transform="translate(790.1,0)"><use data-c="1D436" href="#MJX-106-NCM-I-1D436"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="6" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="1" data-speech-node="true" transform="translate(1550.1,0)"><use data-c="2062" href="#MJX-106-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="4" data-semantic-parent="7" data-semantic-attributes="latex:l" data-semantic-level-number="1" data-speech-node="true" transform="translate(1550.1,0)"><use data-c="1D459" href="#MJX-106-NCM-I-1D459"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="^{37}Cl" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="2,3,4" data-semantic-content="5,6" data-semantic-attributes="latex:^{37}Cl" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(7 (2 0 1) 5 3 6 4)"><msup data-latex="^{37}" data-semantic-type="superscript" data-semantic-role="unknown" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="0,1" data-semantic-parent="7" data-semantic-attributes="latex:^{37}" data-semantic-owns="0 1" data-semantic-level-number="1" data-speech-node="true"><mi data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="2" data-semantic-level-number="2" data-speech-node="true"></mi><mrow data-mjx-texclass="ORD" data-latex="{37}"><mn data-latex="37" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:{37};texclass:ORD" data-semantic-level-number="2" data-speech-node="true">37</mn></mrow></msup><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="1" data-speech-node="true">&#8290;</mo><mi data-latex="C" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:C" data-semantic-level-number="1" data-speech-node="true">C</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="1" data-speech-node="true">&#8290;</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:l" data-semantic-level-number="1" data-speech-node="true">l</mi></math></mjx-assistive-mml></mjx-container>, in approximately a 3:1 ratio. (a) When a sample of elemental chlorine is injected into the mass spectrometer, electrical energy is used to dissociate the Cl<sub>2</sub> molecules into chlorine atoms and convert the chlorine atoms to Cl<sup>+</sup> ions. The ions are then accelerated into a magnetic field. The extent to which the ions are deflected by the magnetic field depends on their relative mass-to-charge ratios. Note that the lighter <sup>35</sup>Cl<sup>+</sup> ions are deflected more than the heavier <sup>37</sup>Cl<sup><sub>+</sub></sup> ions. By measuring the relative deflections of the ions, chemists can determine their mass-to-charge ratios and thus their masses. (b) Each peak in the mass spectrum corresponds to an ion with a particular mass-to-charge ratio. The abundance of the two isotopes can be determined from the heights of the peaks.</figcaption>

<figcaption>A: Diagram of a mass spectrometer, showing analysis of gaseous chlorine. B: Mass spectrum of chlorine.</figcaption>
</figure>

<p class="lt-chem-21700" style="background-color: unset;">The arbitrary standard that has been established for describing atomic mass is the atomic mass unit (amu or u), defined as one-twelfth of the mass of one atom of <sup>12</sup>C. Because the masses of all other atoms are calculated relative to the <sup>12</sup>C standard, <sup>12</sup>C is the only atom listed in <span class="external">Table 2.3.2</span> whose exact atomic mass is equal to the mass number. Experiments have shown that 1 amu = 1.66 &times; 10<sup>&minus;24</sup> g.</p>

<p class="lt-chem-21700" style="background-color: unset;">Mass spectrometric experiments give a value of 0.167842 for the ratio of the mass of <sup>2</sup>H to the mass of <sup>12</sup>C, so the <strong>absolute mass</strong> of <sup>2</sup>H is</p>

<p class="lt-chem-21700" style="background-color: unset;">The masses of the other elements are determined in a similar way.</p>

<p class="lt-chem-21700" style="background-color: unset;">The <a title="Periodic Table of the Elements" href="https://chem.libretexts.org/Ancillary_Materials/Reference/Periodic_Table_of_the_Elements">periodic table</a> lists the atomic masses of all the elements. Comparing these values with those given for some of the isotopes in <span class="external">Table 2.3.2</span> reveals that the atomic masses given in the periodic table never correspond exactly to those of any of the isotopes. Because most elements exist as mixtures of several stable isotopes, the atomic mass of an element is defined as the weighted average of the masses of the isotopes. For example, naturally occurring carbon is largely a mixture of two isotopes: 98.89% <sup>12</sup>C (mass = 12 amu by definition) and 1.11% <sup>13</sup>C (mass = 13.003355 amu). The percent abundance of <sup>14</sup>C is so low that it can be ignored in this calculation. The average atomic mass of carbon is then calculated as follows:</p>

<p class="lt-chem-21700" style="background-color: unset;">Carbon is predominantly <sup>12</sup>C, so its average atomic mass should be close to 12 amu, which is in agreement with this calculation.</p>

<p class="lt-chem-21700" style="background-color: unset;">The value of 12.01 is shown under the symbol for C in the periodic table, although without the abbreviation amu, which is customarily omitted. Thus the tabulated atomic mass of carbon or any other element is the weighted average of the masses of the naturally occurring isotopes.</p>

<div class="box-example">
<span id="Example_.5C(.5CPageIndex.7B1.7D.5C):_Bromine"></span><span id="Example_.5C(.5CPageIndex.7B1.7D.5C):_Bromine"></span><h5 class="box-legend"><span class="lt-icon-default">Example <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="108" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.532ex" role="img" focusable="false" viewbox="0 -677 2056 677" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-109-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-109-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-109-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path><path id="MJX-109-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true"><use data-c="32" href="#MJX-109-NCM-N-32"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(500,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-109-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="34" href="#MJX-109-NCM-N-34"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-109-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-109-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>: Bromine</span></h5>

<p class="lt-chem-21700" style="background-color: unset;">Naturally occurring bromine consists of the two isotopes listed in the following table:</p>

<table class="mt-responsive-table" align="center" border="1" cellpadding="1" cellspacing="1">
    <caption>Solutions to Example 2.4.1</caption>
    <thead>
        <tr>
            <th scope="col" style="text-align:center;"><strong>Isotope</strong></th>
            <th scope="col" style="text-align:center;"><strong>Exact Mass (amu)</strong></th>
            <th scope="col" style="text-align:center;"><strong>Percent Abundance (%)</strong></th>
        </tr>
    </thead>
    <tbody>
        <tr>
            <td class="lt-chem-21700" data-th="Isotope" style="text-align: center; background-color: unset;"><sup>79</sup>Br</td>
            <td class="lt-chem-21700" data-th="Exact Mass (amu)" style="text-align: center; background-color: unset;">78.9183</td>
            <td class="lt-chem-21700" data-th="Percent Abundance (%)" style="text-align: center; background-color: unset;">50.69</td>
        </tr>
        <tr>
            <td class="lt-chem-21700" data-th="Isotope" style="text-align: center; background-color: unset;"><sup>81</sup>Br</td>
            <td class="lt-chem-21700" data-th="Exact Mass (amu)" style="text-align: center; background-color: unset;">80.9163</td>
            <td class="lt-chem-21700" data-th="Percent Abundance (%)" style="text-align: center; background-color: unset;">49.31</td>
        </tr>
    </tbody>
</table>

<p class="lt-chem-21700" style="background-color: unset;">Calculate the atomic mass of bromine.</p>

<p class="lt-chem-21700" style="background-color: unset;"><strong>Given</strong>: exact mass and percent abundance</p>

<p class="lt-chem-21700" style="background-color: unset;"><strong>Asked for</strong>: atomic mass</p>

<p class="lt-chem-21700" style="background-color: unset;"><strong>Strategy</strong>:</p>

<ol start="1" style="list-style-type: upper-alpha;">
    <li class="lt-chem-21700" style="background-color: unset;">Convert the percent abundances to decimal form to obtain the mass fraction of each isotope.</li>
    <li class="lt-chem-21700" style="background-color: unset;">Multiply the exact mass of each isotope by its corresponding mass fraction (percent abundance &divide; 100) to obtain its weighted mass.</li>
    <li class="lt-chem-21700" style="background-color: unset;">Add together the weighted masses to obtain the atomic mass of the element.</li>
    <li class="lt-chem-21700" style="background-color: unset;">Check to make sure that your answer makes sense.</li>
</ol>

<p class="lt-chem-21700" style="background-color: unset;"><strong>Solution</strong>:</p>

<p class="lt-chem-21700" style="background-color: unset;"><strong>A</strong> The atomic mass is the weighted average of the masses of the isotopes. In general, we can write</p>

<p class="lt-chem-21700" style="background-color: unset;">atomic mass of element = [(mass of isotope 1 in amu) (mass fraction of isotope 1)] + [(mass of isotope 2) (mass fraction of isotope 2)] + &hellip;</p>

<p class="lt-chem-21700" style="background-color: unset;">Bromine has only two isotopes. Converting the percent abundances to mass fractions gives</p>

<p class="lt-chem-21700" style="background-color: unset;"><strong>B</strong> Multiplying the exact mass of each isotope by the corresponding mass fraction gives the isotope&rsquo;s weighted mass:</p>

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\times 0.5069 = 40.00\; amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{79}Br}: 79.9183 \\0003Bamu \times 0.5069 = 40.00\\0003B amu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:2" data-semantic-id="37" data-semantic-children="32,36" data-semantic-content="22" data-semantic-parent="38" data-semantic-owns="32 22 36" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" 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data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-id="17" data-semantic-parent="31" data-semantic-attributes="latex:a" data-semantic-level-number="4" data-speech-node="true" transform="translate(278,0)"><use data-c="1D44E" href="#MJX-112-NCM-I-1D44E"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="29" data-semantic-parent="31" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true" transform="translate(807,0)"><use data-c="2062" href="#MJX-112-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-id="18" data-semantic-parent="31" data-semantic-attributes="latex:m" data-semantic-level-number="4" data-speech-node="true" transform="translate(807,0)"><use data-c="1D45A" href="#MJX-112-NCM-I-1D45A"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="30" data-semantic-parent="31" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true" transform="translate(1685,0)"><use data-c="2062" href="#MJX-112-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="u" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-id="19" data-semantic-parent="31" data-semantic-attributes="latex:u" data-semantic-level-number="4" data-speech-node="true" transform="translate(1685,0)"><use data-c="1D462" href="#MJX-112-NCM-I-1D462"></use></g></g></g></g></g></g></svg><mjx-break size="3"> </mjx-break><svg width="8.548ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 3778.2 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ce{^{79}Br}: 79.9183 \;amu \times 0.5069 = 40.00\; amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{79}Br}: 79.9183 \\0003Bamu \times 0.5069 = 40.00\\0003B amu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:2" data-semantic-id="37" data-semantic-children="32,36" data-semantic-content="22" data-semantic-parent="38" data-semantic-owns="32 22 36" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-id="32" data-semantic-children="31,21" data-semantic-content="20" data-semantic-parent="37" data-semantic-owns="31 20 21" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mo" data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="20" data-semantic-parent="32" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,&times;" data-semantic-level-number="3" data-speech-node="true"><use data-c="D7" href="#MJX-112-NCM-N-D7"></use></g><g data-mml-node="mn" data-latex="0.5069" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="21" data-semantic-parent="32" data-semantic-attributes="latex:0.5069" data-semantic-level-number="3" data-speech-node="true" transform="translate(1000.2,0)"><use data-c="30" href="#MJX-112-NCM-N-30"></use><use data-c="2E" href="#MJX-112-NCM-N-2E" transform="translate(500,0)"></use><use data-c="35" href="#MJX-112-NCM-N-35" transform="translate(778,0)"></use><use data-c="30" href="#MJX-112-NCM-N-30" transform="translate(1278,0)"></use><use data-c="36" href="#MJX-112-NCM-N-36" transform="translate(1778,0)"></use><use data-c="39" href="#MJX-112-NCM-N-39" transform="translate(2278,0)"></use></g></g></g></g></g></svg><mjx-break size="4"> </mjx-break><svg width="7.542ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 3333.8 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ce{^{79}Br}: 79.9183 \;amu \times 0.5069 = 40.00\; amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{79}Br}: 79.9183 \\0003Bamu \times 0.5069 = 40.00\\0003B amu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:2" data-semantic-id="37" data-semantic-children="32,36" data-semantic-content="22" data-semantic-parent="38" data-semantic-owns="32 22 36" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="22" data-semantic-parent="37" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="2" data-speech-node="true"><use data-c="3D" href="#MJX-112-NCM-N-3D"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-id="36" data-semantic-children="23,25,26,27" data-semantic-content="33,34,35" data-semantic-parent="37" data-semantic-owns="23 33 25 34 26 35 27" data-semantic-level-number="2" data-speech-node="true" transform="translate(1055.8,0)"><g data-mml-node="mn" data-latex="40.00" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:4" data-semantic-id="23" data-semantic-parent="36" data-semantic-attributes="latex:40.00" data-semantic-level-number="3" data-speech-node="true"><use data-c="34" href="#MJX-112-NCM-N-34"></use><use data-c="30" href="#MJX-112-NCM-N-30" transform="translate(500,0)"></use><use data-c="2E" href="#MJX-112-NCM-N-2E" transform="translate(1000,0)"></use><use data-c="30" href="#MJX-112-NCM-N-30" transform="translate(1278,0)"></use><use data-c="30" href="#MJX-112-NCM-N-30" transform="translate(1778,0)"></use></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:4" data-semantic-id="33" data-semantic-parent="36" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="3" data-speech-node="true" transform="translate(2278,0)"></g></g></g></g></g></svg><mjx-break size="0"> </mjx-break><svg width="5.106ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 2257 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ce{^{79}Br}: 79.9183 \;amu \times 0.5069 = 40.00\; amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{79}Br}: 79.9183 \\0003Bamu \times 0.5069 = 40.00\\0003B amu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:2" data-semantic-id="37" data-semantic-children="32,36" data-semantic-content="22" data-semantic-parent="38" data-semantic-owns="32 22 36" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-id="36" data-semantic-children="23,25,26,27" data-semantic-content="33,34,35" data-semantic-parent="37" data-semantic-owns="23 33 25 34 26 35 27" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:4" data-semantic-id="33" data-semantic-parent="36" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="3" data-speech-node="true"></g><g data-mml-node="mi" data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="25" data-semantic-parent="36" data-semantic-attributes="latex:a" data-semantic-level-number="3" data-speech-node="true" transform="translate(278,0)"><use data-c="1D44E" href="#MJX-112-NCM-I-1D44E"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="34" data-semantic-parent="36" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="3" data-speech-node="true" transform="translate(807,0)"><use data-c="2062" href="#MJX-112-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="26" data-semantic-parent="36" data-semantic-attributes="latex:m" data-semantic-level-number="3" data-speech-node="true" transform="translate(807,0)"><use data-c="1D45A" href="#MJX-112-NCM-I-1D45A"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="35" data-semantic-parent="36" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="3" data-speech-node="true" transform="translate(1685,0)"><use data-c="2062" href="#MJX-112-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="u" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="27" data-semantic-parent="36" data-semantic-attributes="latex:u" data-semantic-level-number="3" data-speech-node="true" transform="translate(1685,0)"><use data-c="1D462" href="#MJX-112-NCM-I-1D462"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ce{^{79}Br}: 79.9183 \;amu \times 0.5069 = 40.00\; amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{79}Br}: 79.9183 \\0003Bamu \times 0.5069 = 40.00\\0003B amu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:2" data-semantic-="" data-semantic-children="10,11" data-semantic-content="12" data-semantic-parent="38" data-semantic-attributes="latex:{{\vphantom{A}}^{\hphantom{79}}_{\hphantom{}}\mkern-1.5mu{\vphantom{A}}^{\smash[t]{\vphantom{2}}\llap{79}}_{\vphantom{2}\llap{\smash[t]{}}}\mathrm{Br}};texclass:ORD" data-semantic-owns="10 12 11" data-semantic-level-number="1" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="{{\vphantom{A}}^{\hphantom{79}}_{\hphantom{}}\mkern-1.5mu{\vphantom{A}}^{\smash[t]{\vphantom{2}}\llap{79}}_{\vphantom{2}\llap{\smash[t]{}}}\mathrm{Br}}" data-semantic-type="superscript" data-semantic-role="unknown" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="4,9" data-semantic-parent="13" data-semantic-attributes="latex:{\vphantom{A}}^{\smash[t]{\vphantom{2}}\llap{79}}_{\vphantom{2}\llap{\smash[t]{}}}" data-semantic-owns="4 9" data-semantic-level-number="2" data-speech-node="true"><msubsup data-latex="{\vphantom{A}}^{\hphantom{79}}_{\hphantom{}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\hphantom{}}"><mrow data-mjx-texclass="ORD" data-latex="\hphantom{}"><mpadded height="0" depth="0"><mphantom></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\hphantom{79}}"><mrow data-mjx-texclass="ORD" data-latex="\hphantom{79}"><mpadded height="0" depth="0"><mphantom><mn data-latex="79">79</mn></mphantom></mpadded></mrow></mrow></msubsup><mspace width="-0.083em" linebreak="nobreak" data-latex="\mkern-1.5mu"></mspace><msubsup data-latex="{\vphantom{A}}^{\smash[t]{\vphantom{2}}\llap{79}}_{\vphantom{2}\llap{\smash[t]{}}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="empty:MSUBSUP;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="3" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{2}\llap{\smash[t]{}}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{2}"><mpadded width="0"><mphantom><mn data-latex="2">2</mn></mphantom></mpadded></mrow><mrow data-mjx-texclass="ORD" data-latex="\llap{\smash[t]{}}"><mpadded width="0" lspace="-1width"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{}"><mpadded height="0"></mpadded></mrow></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{\vphantom{2}}\llap{79}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{\vphantom{2}}"><mpadded height="0"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{2}"><mpadded width="0"><mphantom><mn data-latex="2">2</mn></mphantom></mpadded></mrow></mpadded></mrow><mrow data-mjx-texclass="ORD" data-latex="\llap{79}"><mpadded width="0" lspace="-1width"><mn data-latex="79" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:{\smash[t]{\vphantom{2}}\llap{79}};texclass:ORD" data-semantic-level-number="3" data-speech-node="true">79</mn></mpadded></mrow></mrow></msubsup><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-parent="13" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="2" data-speech-node="true">&#8290;</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Br}"><mi data-mjx-auto-op="false" data-latex="Br" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:\mathrm{Br};texclass:ORD" data-semantic-level-number="2" data-speech-node="true">Br</mi></mrow></mrow></mrow><mo data-latex=":" data-semantic-type="punctuation" data-semantic-role="colon" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="38" data-semantic-attributes="latex::" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">:</mo><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="32,36" data-semantic-content="22" data-semantic-parent="38" data-semantic-owns="32 22 36" data-semantic-level-number="1" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="31,21" data-semantic-content="20" data-semantic-parent="37" data-semantic-owns="31 20 21" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="15,17,18,19" data-semantic-content="28,29,30" data-semantic-parent="32" data-semantic-owns="15 28 17 29 18 30 19" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="79.9183" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:79.9183" data-semantic-level-number="4" data-speech-node="true">79.9183</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="31" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true"></mspace><mi data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:a" data-semantic-level-number="4" data-speech-node="true">a</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" 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data-semantic-parent="31" data-semantic-attributes="latex:u" data-semantic-level-number="4" data-speech-node="true">u</mi></mrow><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,&times;" data-semantic-level-number="3" data-speech-node="true">&times;</mo><mn data-latex="0.5069" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:0.5069" data-semantic-level-number="3" data-speech-node="true">0.5069</mn></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:=" 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data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="36" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="3" data-speech-node="true">&#8290;</mo><mi data-latex="u" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:u" data-semantic-level-number="3" data-speech-node="true">u</mi></mrow></mrow></math></mjx-assistive-mml></mjx-container></p>

<p class="mt-align-center lt-chem-21700" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="112" style="font-size: 85%; position: relative;"><svg width="4.276ex" height="2.573ex" role="img" focusable="false" viewbox="0 -840.1 1890.1 1137.4" aria-hidden="true" style="vertical-align: -0.673ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ce{^{81}Br}: 80.9163 \;amu \times 0.4931 = 39.90 \;amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{81}Br}: 80.9163 \\0003Bamu \times 0.4931 = 39.90 \\0003Bamu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 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data-mml-node="mpadded"><g data-mml-node="mphantom"></g></g></g></g></g><g data-mml-node="mspace" data-latex="\mkern-1.5mu" transform="translate(790.1,0)"></g><g data-mml-node="msubsup" data-latex="{\vphantom{A}}^{\smash[t]{\vphantom{2}}\llap{81}}_{\vphantom{2}\llap{\smash[t]{}}}" transform="translate(707.1,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="empty:MSUBSUP;nemeth:number;depth:4" data-semantic-id="4" data-semantic-parent="10" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mpadded"><g data-mml-node="mphantom"></g></g></g></g><g data-mml-node="TeXAtom" transform="translate(33,369.2) scale(0.707)" data-mjx-texclass="ORD" data-latex="{\smash[t]{\vphantom{2}}\llap{81}}"><g data-mml-node="TeXAtom" 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321L698 321C714 321 722 329 722 344C722 356 711 367 698 367M698 179L80 179C64 179 56 171 56 156C56 141 64 133 80 133L698 133C714 133 722 141 722 156C722 169 711 179 698 179Z"></path></defs></svg><mjx-break size="4"> </mjx-break><svg width="8.674ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 3833.8 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ce{^{81}Br}: 80.9163 \;amu \times 0.4931 = 39.90 \;amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{81}Br}: 80.9163 \\0003Bamu \times 0.4931 = 39.90 \\0003Bamu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 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data-semantic-parent="37" data-semantic-owns="31 20 21" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-id="31" data-semantic-children="15,17,18,19" data-semantic-content="28,29,30" data-semantic-parent="32" data-semantic-owns="15 28 17 29 18 30 19" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mn" data-latex="80.9163" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-id="15" data-semantic-parent="31" data-semantic-attributes="latex:80.9163" data-semantic-level-number="4" data-speech-node="true"><use data-c="38" href="#MJX-113-NCM-N-38"></use><use data-c="30" href="#MJX-113-NCM-N-30" transform="translate(500,0)"></use><use data-c="2E" href="#MJX-113-NCM-N-2E" transform="translate(1000,0)"></use><use data-c="39" href="#MJX-113-NCM-N-39" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-113-NCM-N-31" transform="translate(1778,0)"></use><use data-c="36" href="#MJX-113-NCM-N-36" transform="translate(2278,0)"></use><use data-c="33" href="#MJX-113-NCM-N-33" transform="translate(2778,0)"></use></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:5" data-semantic-id="28" data-semantic-parent="31" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true" transform="translate(3278,0)"></g></g></g></g></g></g></svg><mjx-break size="0"> </mjx-break><svg width="5.106ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 2257 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ce{^{81}Br}: 80.9163 \;amu \times 0.4931 = 39.90 \;amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{81}Br}: 80.9163 \\0003Bamu \times 0.4931 = 39.90 \\0003Bamu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:2" data-semantic-id="37" data-semantic-children="32,36" data-semantic-content="22" data-semantic-parent="38" data-semantic-owns="32 22 36" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-id="32" data-semantic-children="31,21" data-semantic-content="20" data-semantic-parent="37" data-semantic-owns="31 20 21" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-id="31" data-semantic-children="15,17,18,19" data-semantic-content="28,29,30" data-semantic-parent="32" data-semantic-owns="15 28 17 29 18 30 19" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:5" data-semantic-id="28" data-semantic-parent="31" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true"></g><g data-mml-node="mi" data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-id="17" data-semantic-parent="31" data-semantic-attributes="latex:a" data-semantic-level-number="4" data-speech-node="true" transform="translate(278,0)"><use data-c="1D44E" href="#MJX-113-NCM-I-1D44E"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="29" data-semantic-parent="31" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true" transform="translate(807,0)"><use data-c="2062" href="#MJX-113-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-id="18" data-semantic-parent="31" data-semantic-attributes="latex:m" data-semantic-level-number="4" data-speech-node="true" transform="translate(807,0)"><use data-c="1D45A" href="#MJX-113-NCM-I-1D45A"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="30" data-semantic-parent="31" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true" transform="translate(1685,0)"><use data-c="2062" href="#MJX-113-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="u" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-id="19" data-semantic-parent="31" data-semantic-attributes="latex:u" data-semantic-level-number="4" data-speech-node="true" transform="translate(1685,0)"><use data-c="1D462" href="#MJX-113-NCM-I-1D462"></use></g></g></g></g></g></g></svg><mjx-break size="3"> </mjx-break><svg width="8.548ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 3778.2 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ce{^{81}Br}: 80.9163 \;amu \times 0.4931 = 39.90 \;amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{81}Br}: 80.9163 \\0003Bamu \times 0.4931 = 39.90 \\0003Bamu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:2" data-semantic-id="37" data-semantic-children="32,36" data-semantic-content="22" data-semantic-parent="38" data-semantic-owns="32 22 36" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-id="32" data-semantic-children="31,21" data-semantic-content="20" data-semantic-parent="37" data-semantic-owns="31 20 21" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mo" data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="20" data-semantic-parent="32" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,&times;" data-semantic-level-number="3" data-speech-node="true"><use data-c="D7" href="#MJX-113-NCM-N-D7"></use></g><g data-mml-node="mn" data-latex="0.4931" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="21" data-semantic-parent="32" data-semantic-attributes="latex:0.4931" data-semantic-level-number="3" data-speech-node="true" transform="translate(1000.2,0)"><use data-c="30" href="#MJX-113-NCM-N-30"></use><use data-c="2E" href="#MJX-113-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-113-NCM-N-34" transform="translate(778,0)"></use><use data-c="39" href="#MJX-113-NCM-N-39" transform="translate(1278,0)"></use><use data-c="33" href="#MJX-113-NCM-N-33" transform="translate(1778,0)"></use><use data-c="31" href="#MJX-113-NCM-N-31" transform="translate(2278,0)"></use></g></g></g></g></g></svg><mjx-break size="4"> </mjx-break><svg width="7.542ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 3333.8 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ce{^{81}Br}: 80.9163 \;amu \times 0.4931 = 39.90 \;amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{81}Br}: 80.9163 \\0003Bamu \times 0.4931 = 39.90 \\0003Bamu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:2" data-semantic-id="37" data-semantic-children="32,36" data-semantic-content="22" data-semantic-parent="38" data-semantic-owns="32 22 36" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="22" data-semantic-parent="37" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="2" data-speech-node="true"><use data-c="3D" href="#MJX-113-NCM-N-3D"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-id="36" data-semantic-children="23,25,26,27" data-semantic-content="33,34,35" data-semantic-parent="37" data-semantic-owns="23 33 25 34 26 35 27" data-semantic-level-number="2" data-speech-node="true" transform="translate(1055.8,0)"><g data-mml-node="mn" data-latex="39.90" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:4" data-semantic-id="23" data-semantic-parent="36" data-semantic-attributes="latex:39.90" data-semantic-level-number="3" data-speech-node="true"><use data-c="33" href="#MJX-113-NCM-N-33"></use><use data-c="39" href="#MJX-113-NCM-N-39" transform="translate(500,0)"></use><use data-c="2E" href="#MJX-113-NCM-N-2E" transform="translate(1000,0)"></use><use data-c="39" href="#MJX-113-NCM-N-39" transform="translate(1278,0)"></use><use data-c="30" href="#MJX-113-NCM-N-30" transform="translate(1778,0)"></use></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:4" data-semantic-id="33" data-semantic-parent="36" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="3" data-speech-node="true" transform="translate(2278,0)"></g></g></g></g></g></svg><mjx-break size="0"> </mjx-break><svg width="5.106ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 2257 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ce{^{81}Br}: 80.9163 \;amu \times 0.4931 = 39.90 \;amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="38" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{81}Br}: 80.9163 \\0003Bamu \times 0.4931 = 39.90 \\0003Bamu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:2" data-semantic-id="37" data-semantic-children="32,36" data-semantic-content="22" data-semantic-parent="38" data-semantic-owns="32 22 36" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-id="36" data-semantic-children="23,25,26,27" data-semantic-content="33,34,35" data-semantic-parent="37" data-semantic-owns="23 33 25 34 26 35 27" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:4" data-semantic-id="33" data-semantic-parent="36" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="3" data-speech-node="true"></g><g data-mml-node="mi" data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="25" data-semantic-parent="36" data-semantic-attributes="latex:a" data-semantic-level-number="3" data-speech-node="true" transform="translate(278,0)"><use data-c="1D44E" href="#MJX-113-NCM-I-1D44E"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="34" data-semantic-parent="36" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="3" data-speech-node="true" transform="translate(807,0)"><use data-c="2062" href="#MJX-113-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="26" data-semantic-parent="36" data-semantic-attributes="latex:m" data-semantic-level-number="3" data-speech-node="true" transform="translate(807,0)"><use data-c="1D45A" href="#MJX-113-NCM-I-1D45A"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="35" data-semantic-parent="36" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="3" data-speech-node="true" transform="translate(1685,0)"><use data-c="2062" href="#MJX-113-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="u" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="27" data-semantic-parent="36" data-semantic-attributes="latex:u" data-semantic-level-number="3" data-speech-node="true" transform="translate(1685,0)"><use data-c="1D462" href="#MJX-113-NCM-I-1D462"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ce{^{81}Br}: 80.9163 \;amu \times 0.4931 = 39.90 \;amu" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="13,14,37" data-semantic-content="14" data-semantic-attributes="latex:\ce{^{81}Br}: 80.9163 \\0003Bamu \times 0.4931 = 39.90 \\0003Bamu" data-semantic-owns="13 14 37" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(38 (13 (10 4 9) 12 11) 14 (37 (32 (31 15 28 17 29 18 30 19) 20 21) 22 (36 23 33 25 34 26 35 27)))"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:2" data-semantic-="" data-semantic-children="10,11" data-semantic-content="12" data-semantic-parent="38" data-semantic-attributes="latex:{{\vphantom{A}}^{\hphantom{81}}_{\hphantom{}}\mkern-1.5mu{\vphantom{A}}^{\smash[t]{\vphantom{2}}\llap{81}}_{\vphantom{2}\llap{\smash[t]{}}}\mathrm{Br}};texclass:ORD" data-semantic-owns="10 12 11" data-semantic-level-number="1" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="{{\vphantom{A}}^{\hphantom{81}}_{\hphantom{}}\mkern-1.5mu{\vphantom{A}}^{\smash[t]{\vphantom{2}}\llap{81}}_{\vphantom{2}\llap{\smash[t]{}}}\mathrm{Br}}" data-semantic-type="superscript" data-semantic-role="unknown" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="4,9" data-semantic-parent="13" data-semantic-attributes="latex:{\vphantom{A}}^{\smash[t]{\vphantom{2}}\llap{81}}_{\vphantom{2}\llap{\smash[t]{}}}" data-semantic-owns="4 9" data-semantic-level-number="2" data-speech-node="true"><msubsup data-latex="{\vphantom{A}}^{\hphantom{81}}_{\hphantom{}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\hphantom{}}"><mrow data-mjx-texclass="ORD" data-latex="\hphantom{}"><mpadded height="0" depth="0"><mphantom></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\hphantom{81}}"><mrow data-mjx-texclass="ORD" data-latex="\hphantom{81}"><mpadded height="0" depth="0"><mphantom><mn data-latex="81">81</mn></mphantom></mpadded></mrow></mrow></msubsup><mspace width="-0.083em" linebreak="nobreak" data-latex="\mkern-1.5mu"></mspace><msubsup data-latex="{\vphantom{A}}^{\smash[t]{\vphantom{2}}\llap{81}}_{\vphantom{2}\llap{\smash[t]{}}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="empty:MSUBSUP;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="3" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{2}\llap{\smash[t]{}}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{2}"><mpadded width="0"><mphantom><mn data-latex="2">2</mn></mphantom></mpadded></mrow><mrow data-mjx-texclass="ORD" 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<p class="lt-chem-21700" style="background-color: unset;"><strong>C</strong> The sum of the weighted masses is the atomic mass of bromine is</p>

<p class="lt-chem-21700" style="background-color: unset;"><strong>D</strong> This value is about halfway between the masses of the two isotopes, which is expected because the percent abundance of each is approximately 50%.</p>
</div>

<div class="box-exercise">
<span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C)"></span><span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C)"></span><h5 class="box-legend"><span class="lt-icon-default">Exercise <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="113" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.532ex" role="img" focusable="false" viewbox="0 -677 2056 677" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-114-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-114-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-114-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path><path id="MJX-114-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" 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data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container></span></h5>

<p class="lt-chem-21700" style="background-color: unset;">Magnesium has the three isotopes listed in the following table:</p>

<table class="mt-responsive-table" align="center" cellpadding="1" cellspacing="1">
    <caption>Solutions to Example 2.4.1</caption>
    <thead>
        <tr>
            <th scope="col" style="text-align:center;"><strong>Isotope</strong></th>
            <th scope="col" style="text-align:center;"><strong>Exact Mass (amu)</strong></th>
            <th scope="col" style="text-align:center;"><strong>Percent Abundance (%)</strong></th>
        </tr>
    </thead>
    <tbody>
        <tr>
            <td class="lt-chem-21700" data-th="Isotope" style="text-align: center; background-color: unset;"><sup>24</sup>Mg</td>
            <td class="lt-chem-21700" data-th="Exact Mass (amu)" style="text-align: center; background-color: unset;">23.98504</td>
            <td class="lt-chem-21700" data-th="Percent Abundance (%)" style="text-align: center; background-color: unset;">78.70</td>
        </tr>
        <tr>
            <td class="lt-chem-21700" data-th="Isotope" style="text-align: center; background-color: unset;"><sup>25</sup>Mg</td>
            <td class="lt-chem-21700" data-th="Exact Mass (amu)" style="text-align: center; background-color: unset;">24.98584</td>
            <td class="lt-chem-21700" data-th="Percent Abundance (%)" style="text-align: center; background-color: unset;">10.13</td>
        </tr>
        <tr>
            <td class="lt-chem-21700" data-th="Isotope" style="text-align: center; background-color: unset;"><sup>26</sup>Mg</td>
            <td class="lt-chem-21700" data-th="Exact Mass (amu)" style="text-align: center; background-color: unset;">25.98259</td>
            <td class="lt-chem-21700" data-th="Percent Abundance (%)" style="text-align: center; background-color: unset;">11.17</td>
        </tr>
    </tbody>
</table>

<p class="lt-chem-21700" style="background-color: unset;">Use these data to calculate the atomic mass of magnesium.</p>

<dl>
    <dt><strong class="emphasis bold">Answer</strong></dt>
    <dd>
    <p class="lt-chem-21700" style="background-color: unset;">24.31 amu</p>
    </dd>
</dl>
</div>

<p class="lt-chem-21700 mt-align-center" style="background-color: unset;">Finding the Averaged Atomic Weight of an Element: <a target="_blank" href="https://youtu.be/bmP6Gr9zJiQ" rel="external noopener nofollow" class="link-https">Finding the Averaged Atomic Weight of an Element(opens in new window)</a><span> [youtu.be]</span></p>

<span id="Summary"></span><span id="Summary"></span><h2 style="background-color: unset;" class="lt-chem-21700">Summary</h2>

<p class="lt-chem-21700" style="background-color: unset;">The mass of an atom is a weighted average that is largely determined by the number of its protons and neutrons, whereas the number of protons and electrons determines its charge. Each atom of an element contains the same number of protons, known as the atomic number (Z). Neutral atoms have the same number of electrons and protons. Atoms of an element that contain different numbers of neutrons are called isotopes. Each isotope of a given element has the same atomic number but a different mass number (A), which is the sum of the numbers of protons and neutrons. The relative masses of atoms are reported using the atomic mass unit (amu), which is defined as one-twelfth of the mass of one atom of carbon-12, with 6 protons, 6 neutrons, and 6 electrons. The atomic mass of an element is the weighted average of the masses of the naturally occurring isotopes. When one or more electrons are added to or removed from an atom or molecule, a charged particle called an ion is produced, whose charge is indicated by a superscript after the symbol.</p>

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<hr class="autoattribution-divider" /><div class="autoattribution"><p><a target="_blank" class="internal mt-self-link" href="/Sandboxes/johnnyphung/chemistry_central/02:_Atoms_Molecules_and_Ions/2.04:_Atomic_Mass">2.4: Atomic Mass</a> is shared under a <a rel="nofollow" href="https://creativecommons.org/licenses/by-nc-sa/3.0" target="_blank">CC BY-NC-SA  3.0</a>  license and was authored, remixed, and/or curated by LibreTexts.</p></div>

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