Question

An element has two isotopes with mass mumbers $16$ and $18$ . The average atomic weight is $16.5$.The percentage abundance of these isotopes is _____ and ______ respectively.

• A. $75,25$
• B. $50,50$
• C. $25,75$
• D. $33.33,66.67$

Answer 1

The correct option is A

$75,25$

The explanation for the correct option: (a)

1. Isotopes are the elements with the same atomic number but different mass numbers.
2. Let the element be ‘X’ and the percentage abundance of ${\mathrm{X}}^{16}$$=\text{x \%}$.
3. The percentage abundance of ${\mathrm{X}}^{18}=(100-\mathrm{x})\%$.
4. The relative atomic mass $=16.5$. Then, the percentage abundance of ${\mathrm{X}}^{16}$ is:
5. $$\begin{gathered} \frac{16\times \text{x+18(100-x)}}{100}=16.5 \\ 16\text{x+1800-18x=1650} \\ 1800-2\text{x}=1650 \\ 150\text{=2x} \\ \text{x=}\frac{150}{2} \\ \text{x=75\%} \end{gathered}$$
6. Then the percentage abundance of ${\text{X}}^{18}$ is $100-\text{x=25}$.

The explanation for the incorrect options:

(b) The percentage abundance of these isotopes is $75$ and $25$ not $50,50$.

(c) $25$ and $75$ is not the percentage abundance. It is $75$ and $25$.

(d) The percentage abundance of these isotopes is $75$ and $25$ not $33.33$ and $66.67$.

Hence, option () is correct - The percentage abundance of these isotopes is $75$ and $25$.