# A neutron travelling with a velocity v and K.E. ‘E’ collides perfectly elastically head on with nucleus…

Q: A neutron travelling with a velocity v and K.E. ‘E’ collides perfectly elastically head on with nucleus of an atom of mass number A at rest. The fraction of total energy retained by the neutron is :

(a) $\displaystyle (\frac{A-1}{A+1})^2$

(b) $\displaystyle (\frac{A-1}{A})^2$

(c) $\displaystyle (\frac{A+1}{A-1})^2$

(d) $\displaystyle (\frac{A-1}{A})^2$

Ans: (a)

velocity of body after collision is

$\displaystyle v_1 = \frac{(m_1-m_2)u_1}{m_1 +m_2}$

$\displaystyle v_1 = \frac{(1-A)u_1}{1 + A}$

Fraction of K.E retained is

$\displaystyle \frac{1/2 m v_1^2}{1/2 m u_1^2} = (\frac{v_1}{u_1})^2$

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