An `alpha`-particle with a kinetic energy of `2.1eV` makes a head on collision with a hydrogen atom moving towards it with a kinetic energy of `8.4 eV`. The collision

Options

A. must be perfectly elastic
B. may be perfectly inelastic
C. may be inelastic
D. must be perfectly inelastic

Explanation

To solve the problem of the collision between an alpha particle and a hydrogen atom, we will analyze the kinetic energies involved and determine the nature of the collision.

### Step-by-Step Solution:

1. **Identify the Kinetic Energies**:
- The kinetic energy of the alpha particle (E1) is given as \(2.1 \, \text{eV}\).
- The kinetic energy of the hydrogen atom (E2) is given as \(8.4 \, \text{eV}\).

2. **Calculate the Total Kinetic Energy**:
- The total kinetic energy (E) before the collision is the sum of the kinetic energies of both particles:
\[ E = E1 + E2 = 2.1 \, \text{eV} + 8.4 \, \text{eV} = 10.5 \, \text{eV} \]

3. **Determine the Energy Requirement for Electron Transition**:
- The hydrogen atom's electron in the ground state requires \(10.2 \, \text{eV}\) to transition to the first excited state.
- Since the total kinetic energy available (10.5 eV) is greater than the energy required (10.2 eV), the electron can potentially absorb energy.

4. **Analyze the Nature of the Collision**:
- A perfectly inelastic collision would mean that all kinetic energy is lost, and the particles stick together. However, since the hydrogen atom's electron can absorb energy (10.2 eV), some energy may be lost in the form of an electron transition.
- A perfectly elastic collision would mean no kinetic energy is lost. However, since the total energy available is just slightly above the transition energy, it is likely that some energy will be absorbed by the electron, indicating that not all kinetic energy is conserved.

5. **Conclusion**:
- Since the collision cannot be perfectly elastic (as some energy will be lost due to the electron transition) and cannot be perfectly inelastic (as the total energy is sufficient for a transition), the collision is best described as an **inelastic collision**.

### Final Answer:
The correct option is **C: Inelastic collision**.