Question

A neutron collides head-on and elastically with an atom of mass number $A$, which is initially at rest. The fraction of kinetic energy retained by neutron is

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

Answer 1

The correct option is D ${\left(\frac{A-1}{A+1}\right)}^2$

Hint: “Head-on elastic collision”

Formula used:

$P_i=P_f$
$e=\frac{v_2-v_1}{u_1-u_2}$

Solution:

$mu=m{v}_1+mA{v}_2$

$v_1+u=v_2+0$

$v_1=\left(\frac{1-A}{1+A}\right)u$

Fraction of energy retained by neutron is

$\frac{\frac{1}{2}m{v}_1^2}{\frac{1}{2}m{u}^2}={\left(\frac{v_1}{u}\right)}^2={\left(\frac{1-A}{1+A}\right)}^2$

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

Final answer : $\left(b\right)$.