Question

The average atomic mass of two isotopes with mass numbers $A$ and $A+2$ is $A+0.25$. Calculate the percentage abundance of the isotopes.

Answer 1

1. The average atomic mass is given as;

$Averageatomicmass=\frac{M_1{X}_1+M_2{X}_2}{X_1+X_2}$;

where M is the mass number and X is the percentage abundance of the isotope

2. The mass number of isotope 1 = $A$.

The mass number of isotope 2 = $A+2$

And, average atomic mass = $A+0.25$

3. Let the percentage abundance of isotope 1 be $x\%$.

Thus, the percentage abundance of isotope 2 = $(100-x)\%$

4. Putting these values in the above formula;

$$\begin{gathered} Avg.atomicmass=\frac{A\times \left(x\right)+(A+2)\times (100-x)}{x+100-x} \\ \Rightarrow A+0.25=\frac{100A+200-2x}{100} \\ \Rightarrow 2x=175 \\ \Rightarrow x=87.5\% \\ \Rightarrow 100-x=12.5\%. \end{gathered}$$

Hence, the percentage abundance of the isotope are $87.5\%$ and $12.5\%$.