If mass of an atom is $M$ moving with speed $v$, what will be its speed after the emission of an…

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 ?
  1. $\frac{M v}{M+2}$
  2. $\frac{M v}{M-4}$
  3. $\frac{M v}{M+4}$
  4. $\frac{M-4}{M N}$.

Solution

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

Asked in: NEET 2007

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