Question

An element has average atomic mass $20.426u$ it has $2$ isotopes with masses $22.1824$ and $19.9574$. Calculate the abundance of its isotopes $X-22$ and $X-20$.

Answer 1

We know that,

$\begin{array}{c}20.426=\frac{\left(22.1824\times x\right)+\left(19.95\right)\left(100-x\right)}{100}\\ \Rightarrow x\left(22.1824-19.95\right)=2042.6-1995\\ \Rightarrow x\left(2.2324\right)=47.6\\ \Rightarrow x=\frac{47.6}{2.2324}=21.32\\ x-22\to 21.32\%\\ x-20\to (100-21.32)=78.68\%\end{array}$

Hence the abundance are $21.32\%$ and $78.68\%$ respectively