Question

A $U-238$ nucleus originally at rest, decays by emitting an $\alpha -$particle, say with a velocity of $vm/s$. The recoil velocity in $\left(m{s}^{-1}\right)$ of the residual nucleus is

• A. $\frac{4v}{238}$
• B. $-\frac{4v}{238}$
• C. $\frac{v}{4}$
• D. $-\frac{4v}{234}$

Answer 1

The correct option is D $-\frac{4v}{234}$

Mass of alpha particle is $m_a=4m$ where $m$ is mass of a proton.

And mass of residual nucleus will be $m_r=(238-4)m=234m$

Momentum conservation $m_a{v}_a+m_r{v}_r=0$ putting values of masses and $v_a=v$

we get $v_r=-\frac{4v}{234}$

Option D is correct.