Question

Boron has two stable isotopes ${ }_{5} B ^{10}$ and ${ }_{5} B ^{11}$. Their respective masses are $10.01294\, u$ and $11.00931 u$ and the atomic mass of boron is $10.811\, u$. The abundance of ${ }_{5} B ^{10}$ and ${ }_{5} B ^{11}$ are respectively nearing to

• A. $50 \%, 50 \%$
• B. $20 \%, 80 \%$
• C. $25 \%, 75 \%$
• D. $5 \%, 95 \%$

Answer 1

Answer: (B)

Let the percentage of ${ }_{5}^{10} B$ in sample be $x$.
Then, percentage of ${ }_{5}^{11} B$ is $(100-x)$. So, using formula of average atomic masses of isotopes,
$10.811=\frac{10.01294 \times x+11.00931(100-x)}{100}$
$\Rightarrow 1081.1=1100.931-0.99637 x$
$\Rightarrow 0.99637 x=19.831$
$\therefore x=\frac{19.831}{0.99637}=19.3 \approx 20 \%$