Question

In the nucleus of a mass number $A$, originally at rest, emits an $\alpha$ - particle with speed v. The daughter nucleus recoils with a speed :

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

Answer 1

The correct option is C $\frac{4v}{A-4}$

Applying law of conservation of momentum:

$MV=mv$

Let mass of each proton $=m$
Mass of daughter nucleus $=(Am-4m)$
Mass of $\alpha -particle=4m$

So, $(Am-4m)V=4m\times v$

$\therefore V=\frac{4mv}{m(A-4)}=\frac{4v}{A-4}$