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. $\frac{2}{3}$
• B. $\frac{8}{9}$
• C. $\frac{8}{27}$
• D. $\frac{16}{8}$

Answer 1

The correct option is B $\frac{8}{9}$

Step 1: Draw rough diagram for the given situation.



Step 2: Find speed of neutron after collision.

Applying conservation of momentum,

$mu=m{v}_1+2m{v}_2$

$\Rightarrow v_1+2v_2=u\dots \left(i\right)$

As collision is elastic coefficient of restitution,

$e=1$

$u=v_2-v_1\dots \left(ii\right)$

By adding equation $\left(i\right)$ and $\left(ii\right)$

$v_1=-\frac{u}{3}$

Step 3: Find fractional loss of neutron.

Fractional loss of K.E of neutron is

$=\frac{\frac{1}{2}m{u}^2-\frac{1}{2}m{v}_1^2}{\frac{1}{2}m{u}^2}$

$=1-{\left(\frac{v_1}{u}\right)}^2$

$1-\frac{1}{9}=\frac{8}{9}$

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