Rankers Physics

Nucleus: Practice Problem & Solution

Boron has two isotopes $^{10}_{5}B$ and $^{11}_{5}B$. If atomic weight of Boron is 10.81 then ratio of $^{10}_{5}B$ to $^{11}_{5}B$ in nature will be: (1998)
15 : 16
19 : 81
81 : 19
20 : 53

Solution Explained:

To solve this problem, we apply the core principles of Nucleus. Understanding the underlying formula is key to arriving at the correct answer below:

Let the fractional abundance of $^{10}B$ be $x$ and $^{11}B$ be $1-x$. The atomic weight is $10x + 11(1-x) = 10.81$. Solving this yields $11 - x = 10.81$, so $x = 0.19$. The ratio is $0.19 : 0.81 = 19 : 81$.

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