13.2 The three stable isotopes of neon: ${}_{10}{}^{20}\mathit{N}\mathit{e},$ ${}_{10}{}^{21}\mathit{N}\mathit{e}$ and ${}_{10}{}^{22}\mathit{N}\mathit{e}$ have respective abundances of 90.51%, 0.27% and 9.22%. The atomic masses of the three isotopes are 19.99 u, 20.99 u and 21.99 u, respectively. Obtain the average atomic mass of neon.

<p><strong>13.2 </strong>Atomic mass of&nbsp;<span title="Click to copy mathml"><math><mmultiscripts><mrow><mrow><mi>N</mi><mi>e</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>20</mn></mrow></mrow></mmultiscripts></math></span>&nbsp;neon isotope,&nbsp;<span title="Click to copy mathml"><math><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math></span>&nbsp;= 19.99 u ad the abundance&nbsp;<span title="Click to copy mathml"><math><msub><mrow><mrow><mi>η</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math></span>&nbsp;= 90.51 %</p><p>Atomic mass of&nbsp;<span title="Click to copy mathml"><math><mmultiscripts><mrow><mrow><mi>N</mi><mi>e</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>21</mn></mrow></mrow></mmultiscripts></math></span>&nbsp;neon isotope,&nbsp;<span title="Click to copy mathml"><math><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></span>&nbsp;= 20.99 u ad the abundance&nbsp;<span title="Click to copy mathml"><math><msub><mrow><mrow><mi>η</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></span>&nbsp;= 0.27 %</p><p>Atomic mass of&nbsp;<span title="Click to copy mathml"><math><mmultiscripts><mrow><mrow><mi>N</mi><mi>e</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>22</mn></mrow></mrow></mmultiscripts></math></span>&nbsp;neon isotope,&nbsp;<span title="Click to copy mathml"><math><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msub></math></span>&nbsp;= 21.99 u ad the abundance&nbsp;<span title="Click to copy mathml"><math><msub><mrow><mrow><mi>η</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msub></math></span>&nbsp;= 9.22 %</p><p>The average atomic mass of neon is given as:</p><p>m =&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub><msub><mrow><mrow><mi>η</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub><mo>+</mo><mi></mi><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn><msub><mrow><mrow><mi>η</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></mrow></mrow></msub><mo>+</mo><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msub><msub><mrow><mrow><mi>η</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msub><mi></mi><mi></mi></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>η</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub><mo>+</mo><mi></mi><msub><mrow><mrow><mi>η</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>+</mo><mi></mi><msub><mrow><mrow><mi>η</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span>&nbsp;=&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>19.99</mn><mo>×</mo><mn>90.51</mn><mo>+</mo><mn>20.99</mn><mo>×</mo><mn>0.27</mn><mo>+</mo><mn>21.99</mn><mo>×</mo><mn>9.22</mn></mrow></mrow><mrow><mrow><mn>90.51</mn><mo>+</mo><mn>0.27</mn><mo>+</mo><mn>9.22</mn></mrow></mrow></mfrac></math></span>&nbsp;=&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>2017.71</mn></mrow></mrow><mrow><mrow><mn>100</mn></mrow></mrow></mfrac></math></span>&nbsp;= 20.1771 u</p>

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