13.23 In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are <math> <mmultiscripts> <mrow> <mrow> <mi mathvariant="bold-italic">M</mi> <mi mathvariant="bold-italic">g</mi> </mrow> </mrow> <mprescripts></mprescripts> <mrow> <mrow> <mn>12</mn> </mrow> </mrow> <mrow> <mrow> <mn>24</mn> </mrow> </mrow> </mmultiscripts> </math> (23.98504u), <math> <mmultiscripts> <mrow> <mrow> <mi mathvariant="bold-italic">M</mi> <mi mathvariant="bold-italic">g</mi> </mrow> </mrow> <mprescripts></mprescripts> <mrow> <mrow> <mn>12</mn> </mrow> </mrow> <mrow> <mrow> <mn>25</mn> </mrow> </mrow> </mmultiscripts> </math> (24.98584u) and <math><mmultiscripts><mrow><mrow><mi mathvariant="bold-italic">M</mi><mi mathvariant="bold-italic">g</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>12</mn></mrow></mrow><mrow><mrow><mn>26</mn></mrow></mrow></mmultiscripts></math> (25.98259u). The natural abundance of <math><mmultiscripts><mrow><mrow><mi mathvariant="bold-italic">M</mi><mi mathvariant="bold-italic">g</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>12</mn></mrow></mrow><mrow><mrow><mn>24</mn></mrow></mrow></mmultiscripts></math> is 78.99% by mass. Calculate the abundances of other two isotopes.

13.23 Average atomic mass of magnesium, m = 24.312 uMass of magnesium isotope Mg1224 ,m1= 23.98504uMass of magnesium isotope Mg1225 ,m2= 24.98584uMass of magnesium isotope Mg1226 ,m3= 25.98259uLet the abundance of magnesium isotope Mg1224 be η1 = 78.99 %Let the abundance of magnesium isotope Mg1225 be η2= x %Therefore, the abundance of magnesium isotope Mg1226 be η3= (100 - 78.99 - x) %= (21.01 – x)%The average atomic mass can be expressed as:m = m1η1+m2η2+m3η3η1+η2+η3 = 23.98504×78.99+24.98584x+25.98259(21.01-x)100 = 1894.578+24.98584x+545.894-25.98259x100=2440.472-0.99675x10024.312 = 2440.472-0.99675x100x = 9.3%Therefore the abundance of M g 12 25 is 9.3% and the abundance of Mg1226 is (21.01 – 9.3)11.71%

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Physics Ncert Solutions Class 12th Physics Class 12th Nuclei

13.23 In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are ${}_{12}^{24}{M g}$ (23.98504u), ${}_{12}^{25}{M g}$

(24.98584u) and ${}_{12}^{26}{M g}$ (25.98259u). The natural abundance of ${}_{12}^{24}{M g}$ is 78.99% by mass. Calculate the abundances of other two isotopes.

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Payal Gupta | Contributor-Level 10

4 months ago

13.23 Average atomic mass of magnesium, m = 24.312 u

Mass of magnesium isotope ${}_{12}^{24}{M g}$ , $m_{1}$ = 23.98504u

Mass of magnesium isotope ${}_{12}^{25}{M g}$ , $m_{2}$ = 24.98584u

Mass of magnesium isotope ${}_{12}^{26}{M g}$ , $m_{3}$ = 25.98259u

Let the abundance of magnesium isotope ${}_{12}^{24}{M g}$ be $η_{1}$ = 78.99 %

Let the abundance of magnesium isotope ${}_{12}^{25}{M g}$ be $η_{2}$ = x %

Therefore, the abundance of magnesium isotope ${}_{12}^{26}{M g}$ be $η_{3}$ = (100 - 78.99 - x) %

= (21.01 – x)%

The average atomic mass can be expressed as:

m = $\frac{m_{1} η_{1} + m_{2} η_{2} + m_{3} η_{3}}{η_{1} + η_{2} + η_{3}}$ = $\frac{23.98504 \times 78.99 + 24.98584 x + 25.98259 (21.01 - x)}{100}$ = $\frac{1894.578 + 24.98584 x + 545.894 - 25.98259 x}{100}$ = $\frac{2440.472 - 0.99675 x}{100}$

24.312 = $\frac{2440.472 - 0.99675 x}{100}$

x = 9.3%

Therefore the abundance of ${}_{12}^{25}{M g}$ is 9.3% and the abundance of ${}_{12}^{26}{M g}$ is (21.01 – 9.3)11.71%

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