13.1 (a) Two stable isotopes of lithium ${}_{3}^{6}{L i}$ and ${}_{3}^{7}{L i}$ have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium.

(b) Boron has two stable isotopes, ${}_{5}^{10}B$ and ${}_{5}^{11}B$ . Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of ${}_{5}^{10}B$ and ${}_{5}^{11}B$ 10.

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Answered by

Payal Gupta | Contributor-Level 10

3 months ago

13.1 Mass of ${}_{3}^{6}{L i}$ lithium isotope, $m_{1}$ = 6.01512 u

Mass of ${}_{3}^{7}{L i}$ lithium isotope, $m_{2}$ = 7.01600 u

Abundance of ${}_{3}^{6}{L i}$ , $η_{1}$ = 7.5%

Abundance of ${}_{3}^{7}{L i}$ , $η_{2}$ = 92.5%

The atomic mass of lithium atom is given as:

m = $\frac{m_{1} η_{1} + m_{2 η_{2}}}{η_{1} + η_{2}}$ = $\frac{6.01512 \times 7.5 + 7.01600 \times 92.5}{7.5 + 92.5}$ = 6.940934 u

Mass of ${}_{5}^{10}B$ Boron isotope, $m_{1}$ = 10.01294 u

Mass of ${}_{5}^{11}B$ Boron isotope, $m_{2}$ = 11.00931 u

Let the abundance of ${}_{5}^{10}B$ be x % and that of ${}_{5}^{11}B$ be (100-x) %

The atomic mass of Boron atom is given as :

10.8111 = $\frac{10.01294 x + 11.00931 (100 - x)}{x + (100 - x)}$

1081.11 = 1100.931 - 0.99637x

x = 19.89 %

Hence the abundance of ${}_{5}^{10}B$ is 19.89 % and that of ${}_{5}^{11}B$ &nb

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