Question

A fast moving neutron collides with a Lithium atom at rest in ground state with kinetic energy K. List - 1 gives different values of K and List- 2 gives various possible phenomena

$\begin{array}{cccc}& \text{List-1}& & \text{List-2}\\ \text{I}& \text{K=81.6 eV}& \text{P}& \text{Elastic collision may take place}\\ \text{II}& \text{K=104.9 eV}& \text{Q}& \text{Elastic collision will take place}\\ \text{III}& \text{K=108.8 eV}& \text{R}& \text{Inelastic collision may take place}\\ \text{IV}& \text{K=200 eV}& \text{S}& \text{Perfectly inelastic collision may take place}\\ & & \text{T}& \text{Atom may get ionised}\\ & & \text{U}& \text{Photon may be emitted}\end{array}$

Match entries in List - 1 with those in List - 2.

• A. I $\to$ P,S,U; II $\to$ P,R,U; III $\to$ P,R,S,T; IV $\to$ P,R,U,T;
• B. I $\to$ Q II $\to$ P,S,U; III $\to$ P,R,S,U; IV $\to$ P,R,T,U;
• C. I $\to$ Q; II $\to$ P,R,S; III $\to$ P,R,T,U; IV $\to$ P,R,T,U
• D. I $\to$ P,R; II $\to$ P,R,U; III $\to$ R,S,T,U; IV $\to$ P,R,T,U;

Answer 1

The correct option is B I $\to$ Q II $\to$ P,S,U; III $\to$ P,R,S,U; IV $\to$ P,R,T,U;

K.E for perfectly inelastic (head on) collision $\Rightarrow$

$m_1{V}_0=(m_1+m_2)V$ [By COM] ...... (1)

$\frac{1}{2}{m}_1{V}_0^2=\frac{1}{2}(m_1+m_2)v^2+Q$ [By COE] ...... (2)

By (1) and (2) $K=Q(1+\frac{m_1}{m_2})$ here $K=\frac{1}{2}{m}_1{V}_0^2$
and Q is energy of photon emitted in various transition.

For Li,
$Q=13.6\times 3^2(1-\frac{1}{n^2})$ n = 1, 2, 3, ....
$Q=122.4(1-\frac{1}{n^2})\Rightarrow Q_1=91.8,Q_2=108.8,Q_3=114.75$
$Q_{max}=122.4$

Also, $K=Q(1+\frac{m_1}{m_2})=Q(1+\frac{1}{7})=Q\frac{8}{7}$

$K_{min}=Q_1\times \frac{8}{7}=104.9eV$
$K_{max}=Q_{max}\times \frac{8}{7}=122.4\times \frac{8}{7}=139.8eV$

Question I:
$K=81.6$
$K<K_{min}$. So only elastic collision is possible.

Question II:
$K=104.9$
$K=K_{min}$. So perfectly inelastic collision can happen, and electron can get excited. If electron is not excited then elastic collision will happen.

Question III:
$K=108.8$
So, perfectly inelastic collision can happen by exciting the electron to 2nd level. Or, inelastic collision can happen by exciting the electron to the 1st level.

Question IV:
$K=200>K_{max}$
Inelastic collision can happen exciting the electron. $K>K_{max}$ so, the atom can get ionised.