Question

A neutron is moving with velocity $u$. It collides head-on and elastically with an atom of mass number A. If the initial kinetic energy of the neutron is E, how much kinetic energy is retained by the neutron after the collision?

[Assume fission doesn't take place]

• A. ${\left[\frac{A}{(A+1)}\right]}^{2}E$
• B. $\left[\frac{A}{(A+1{)}^2}\right]E$
• C. ${\left[\frac{(A-1)}{(A+1)}\right]}^{2}E$
• D. $\left[\frac{(A-1)}{(A+1{)}^2}\right]E$

Answer 1

The correct option is C ${\left[\frac{(A-1)}{(A+1)}\right]}^{2}E$

Mass of neutron = 1 mp,

mass of A mass number = Amp

Velocity after collision $v_1=\left(\frac{Amp-1mp}{(A+I)mp}\right)v$

$=\frac{(A-1)}{(A+1)}v$

Kinetic energy $=\frac{1}{2}mp{\left(\left(\frac{A-1}{A+1}\right)v\right)}^2$

$={\left(\frac{A-1}{A+1}\right)}^2\left(\frac{1}{2}mp{v}^2\right)={\left(\frac{A-1}{A+1}\right)}^{2}E$