A neutron collies head-on with a stationary hydrogen atom in ground state. Which of the following statements is/are correct ?

Options

A. If kinetic enerfy of the neutron is less than `20.4 eV` collision must be elastic
B. If kinetic enerfy of the neutron is less than `20.4 eV` collision must be inelastic
C. Inelastic collision may be take place only when initial kinetic energy iof neutron is greater than `20.4 eV`
D. Perfectly inelcastic collision can not take place

Explanation

To solve the problem, we need to analyze the collision between a neutron and a stationary hydrogen atom in its ground state. We will evaluate each statement provided in the question based on the principles of quantum mechanics and the nature of collisions.

### Step-by-Step Solution:

1. **Understanding the Ground State of Hydrogen:**
- The ground state of a hydrogen atom corresponds to the principal quantum number \( n = 1 \).
- The ionization energy \( E \) for hydrogen in the ground state is given by the formula:
\[ E_n = -\frac{13.6}{n^2} \text{ eV} \]
- For \( n = 1 \):
\[ E_1 = -13.6 \text{ eV} \]
- The absolute value of this energy is \( 13.6 \text{ eV} \).

2. **Kinetic Energy of the Neutron:**
- The neutron can have varying kinetic energy, which will determine the nature of the collision.
- If the kinetic energy of the neutron is less than \( 13.6 \text{ eV} \), it cannot ionize the hydrogen atom, and the collision is elastic (no energy transfer).
- If the kinetic energy is equal to or greater than \( 13.6 \text{ eV} \), the neutron can excite the electron to a higher energy level, resulting in an inelastic collision.

3. **Analyzing Each Statement:**
- **Statement 1:** "If kinetic energy of the neutron is less than 20.4 electron volts, collision must be elastic."
- This statement is **incorrect** because if the kinetic energy is less than \( 13.6 \text{ eV} \, (not 20.4 \text{ eV}) \), the collision is elastic. The threshold for inelastic collision is \( 13.6 \text{ eV} \).

- **Statement 2:** "If kinetic energy of neutron is less than 20.4 electron volts, collision must be inelastic."
- This statement is **correct** because if the kinetic energy is between \( 13.6 \text{ eV} \) and \( 20.4 \text{ eV} \), the neutron can excite the electron, leading to an inelastic collision.

- **Statement 3:** "An elastic collision may take place only when the initial kinetic energy of neutron is greater than 20.4 electron volts."
- This statement is **incorrect** because elastic collisions can occur when the kinetic energy is less than \( 13.6 \text{ eV} \).

- **Statement 4:** "The initial kinetic energy of the neutron is equal to or greater than 13.6 electron volts."
- This statement is **incorrect** because it does not specify that the collision is inelastic; it only states the condition for excitation.

- **Statement 5:** "Perfectly elastic collision cannot take place."
- This statement is **incorrect** because perfectly elastic collisions can occur when the kinetic energy of the neutron is below \( 13.6 \text{ eV} \.

4. **Conclusion:**
- The only correct statement is **Statement 2**: "If kinetic energy of neutron is less than 20.4 electron volts, collision must be inelastic."