Question

A neutron having kinetic energy (K), collides head-on with a stationary H-atom. Find the nature of collision (elastic/inelastic/perfectly inelastic), when the neutron possesses a kinetic energy of: (i) 12 eV (ii) 20.4 eV (iii) 22 eV (iv) 24.18 eV

• A. 12 eV: Elastic; 20.4 eV: Inelastic; 22 eV: Inelastic; 24.18 eV: Inelastic
• B. 12 eV: Inelastic; 20.4 eV: Elastic; 22 eV: Elastic; 24.18 eV: Elastic
• C. 12 eV: Elastic; 20.4 eV: Elastic; 22 eV: Inelastic; 24.18 eV: Inelastic
• D. 12 eV: Inelastic; 20.4 eV: Inelastic; 22 eV: Elastic; 24.18 eV: Elastic

Answer 1

Answer: (A)

12 eV: Elastic; 20.4 eV: Inelastic; 22 eV: Inelastic; 24.18 eV: Inelastic

Answer 2

The minimum energy required to excite a hydrogen atom from its ground state (n=1) to the first excited state (n=2) is $\Delta E = E_2 - E_1 = -3.4 \text{ eV} - (-13.6 \text{ eV}) = 10.2 \text{ eV}$.

For a head-on collision between a neutron and a stationary hydrogen atom of approximately equal masses, the collision becomes inelastic if the neutron's initial kinetic energy ($K_i$) is sufficient to cause excitation. The threshold kinetic energy ($K_{th}$) for an inelastic collision is given by $K_{th} = 2 \times \Delta E_{min}$.

Using $\Delta E_{min} = 10.2$ eV: $K_{th} = 2 \times 10.2 \text{ eV} = 20.4 \text{ eV}$.

If $K < K_{th}$, the collision is elastic. If $K \ge K_{th}$, the collision is inelastic.

(i) Kinetic energy of 12 eV: $12 \text{ eV} < 20.4 \text{ eV} \implies$ Elastic collision. (ii) Kinetic energy of 20.4 eV: $20.4 \text{ eV} = 20.4 \text{ eV} \implies$ Inelastic collision. (iii) Kinetic energy of 22 eV: $22 \text{ eV} > 20.4 \text{ eV} \implies$ Inelastic collision. (iv) Kinetic energy of 24.18 eV: $24.18 \text{ eV} > 20.4 \text{ eV} \implies$ Inelastic collision.