Nuclei - Result Question 11

11. Atomic weight of Boron is 10.81 and it has two isotopes $ _5 B^{10}$ and $ _5 B^{11}$. Then the ratio $ _5 B^{10}: _5 B^{11}$ in nature would be

[1998]

(a) $19: 81$

(b) $10: 11$

(c) $15: 16$

(d) $81: 19$

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Answer:

Correct Answer: 11. (a)

Solution:

  1. (a) Suppose that,

The number of ${ }^{10} B$ type atoms $=x$

and the number of ${ }^{11} B$ type atoms $=y$

Weight of ${ }^{10} B$ type atoms $=10 x$

Weight of ${ }^{11} B$ type atoms $=11 y$

Total number of atoms $=x+y$

$\therefore$ Atomic weight $=\frac{10 x+11 y}{x+y}=10.81$

$\Rightarrow 10 x+11 y=10.81 x+10.81 y$

$\Rightarrow 0.81 x=0.19 y \Rightarrow \frac{x}{y}=\frac{19}{81}$

If relative abundance of isotopes in an element has ratio $n_1: n_2$ whose atomic massers are $m_1$ and $m_2$ then atomic masses of elements is

$ M=\frac{n_1 m_1+n_2 m_2}{n_1+n_2} $