Question

Carbon occurs in nature as a mixture of ${}^{12}C$ and ${}^{13}C$. The average atomic mass of carbon is 12.011. What is the % abundance of ${}^{12}C$ in nature?

• A. 88.9%
• B. 98.9%
• C. 89.9%
• D. 79.9%

Answer 1

Answer: (B)

98.9%

Average atomic mass of an element existing in different isotopes is given by:

$M_{avg}=\frac{{\sum }_{i=1}^n{M}_i{A}_i}{{\sum }_{i=1}^n{A}_i}$

where

$M_i=$atomic mass of an isotope with relative abundance of $A_i$

Given:

$M_{avg}=12.011u,M_1=12u,A_1=a,M_2=13u,A_2=1-a$

On subtitutiing we get:

$12.011=\frac{12\times a+13\times (1-a)}{a+(1-a)}$

$12.011=13-a$

$a=0.989$

Thus relative abundance of ${}^{12}C$ is 98.9% and of ${}^{13}C$ is 1.1%

option B is correct