Question

A nucleus of mass number $A$ emits a particle; speed of a particle is $v$ then what is recoil speed of nucleus ?

• A. $\frac{Av}{A-1}$
• B. $v$
• C. $\frac{v}{A-1}$
• D. $\left(\frac{A-1}{A}\right)v$

Answer 1

Answer: (C)

$\frac{v}{A-1}$

C. $\frac{v}{A-1}$

The mass of nucleus is A. It is initially at rest,

$v_i=0$

the initial momentum, $P_i=0$

It emits an particle with velocity $v$ and recoil back. So the velocity of particle $v_r$.

the final momentum, $P_f=m_1{v}_1+m_2{v}_2$

$P_f=\left(1\right)v+(A-1)v_r$

By the conservation of linear momentum,

$P_i=P_f$

$0=v+(A-1)v_r$

$v_r=-\frac{v}{A-1}$

The negative sign shows that particle moves in opposite direction.