First slide

Radio activity

Question

A radio active nucleus emits both $α$ and $β^{+}$ particles. Initial mass number of the nucleus is 260. After emission of $α$ and $β^{+}$ particles, the final mass number of the nucleus is 236 and the nucleus becomes an isotone. Then number of emitted $β^{+}$ particles is

Moderate

A

8
B

12
C

7
D

5

Solution

Let number of emitted $α and β$ particles be x and y respectively.
$\begin{array}{l} ∴ (A - 4 x) - (Z - 2 x - y) = A - Z \\ \Rightarrow y = 2 x . ......... (1) \\ and A - 4 x = A^{1} \Rightarrow x = \frac{A - A^{1}}{4} \\ \Rightarrow x = \frac{260 - 236}{4} = 6 \\ ∴ y = 2 \times 6 = 12 \end{array}$

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