Question

A neutron makes a head on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is?

• A. $16/82$
• B. $8/9$
• C. $8/27$
• D. $2/3$

Answer 1

The correct option is B $8/9$

Velocity of neutron and deutron $v{1}_{v}2$

where $M_d$= mass of deutron

$M_n$ = mass of neutron

$v_2=\frac{2m_n}{m_n+m_d}$

$\because m_d=2n_e$

Hence $v_2=\frac{2}{3}v$

$v_1=\frac{1}{3}v$

V = velocity of neutron before collision.

Kinetic energy before collision of neutron )E) $v_2=\frac{2}{3}v$

$v_1=\frac{1}{3}v$

kinetic energy after collision ${(E}_1)=\frac{1}{2}{M}_n{v}_1^2=\frac{1}{2}\left(\frac{1}{9}{M}_n{v}^2\right)$

Fractional loss $=\frac{E-E_1}{E}=\frac{\frac{1}{2}{M}_n(v^2-\frac{1}{9}{v}^2)}{\frac{1}{2}{M}_n{v}^2}$

$=\frac{8}{9}$