Question

A radioactive nucleus of mass number $A$ , initially at rest, emits on $\alpha $ -particle with a speed $v$ . What will be the recoil speed of the daughter nucleus?

• A. $\frac{2 v}{\left(\right. A - 4 \left.\right)}$
• B. $\frac{2 v}{\left(\right. A + 4 \left.\right)}$
• C. $\frac{4 v}{\left(\right. A - 4 \left.\right)}$
• D. $\frac{4 v}{\left(\right. A + 4 \left.\right)}$

Answer 1

Answer: (C)

Given that, the radioactive nucleus of mass number $A$ , initially at rest, emits an $\alpha $ - particle with a speed $v$ .
From conservation of linear momentum,
Initial moment before reaction $=$ final momentum after reaction
$0=4v \, -\left(A - 4\right)v_{1}$
$ \, \Rightarrow \, v_{1}=\left(\frac{4 v}{A - 4}\right)$
The recoil speed of the daughter nucleus will be $_{}=\left(\frac{4 v}{A - 4}\right)$