If mass of an atom is $M$ moving with speed $v$, what will be its speed after the emission of an $\alpha$-particle if speed of $\alpha$-particle is zero ?

• A

  $\frac{M v}{M+2}$
• Correct answer
  B

  $\frac{M v}{M-4}$
• C

  $\frac{M v}{M+4}$
• D

  $\frac{M-4}{M N}$.

Solution

$$ \text { Applying the principle of momentum conservation, } $$ $$ \begin{aligned} M v & =(M-4) v^{\prime} \quad\left[\begin{array}{r} \because \text { the speed of the } \\ \text { a-particle is zero }] \end{array}\right. \\ \Rightarrow \quad v^{\prime} & =\frac{M v}{M-4} \end{aligned} $$

Hence, the correct answer is option: 'B'.