Question

The average atomic mass of a sample of an element $X$ is $16.4u$. What are the percentage of isotopes ${}_8^{16}X$ and ${}_8^{18}X$ respectively in the sample?

• A. $90\%,10\%$
• B. $20\%,80\%$
• C. $90\%,10\%$
• D. $80\%,20\%$

Answer 1

The correct option is D $80\%,20\%$

Let percentage of ${}_8^{16}X$ be $y$ and of ${}_8^{18}X$ be $100-y$.
$\therefore (16\times \frac{y}{100})+18\times \frac{(100-y)}{100}=16.4$
$\Rightarrow \frac{16y}{100}+\frac{1800-18y}{100}=16.4$
$\Rightarrow 2y=160$
$\Rightarrow y=80$
Hence, percentage of ${}_8^{16}X$ is $80\%$ and of ${}_8^{18}X$ is $20\%$.