The minimum kinetic energy required for ionization of a hydrogen atom is `E_(1)` in case electron is collided with hydrogen atom , it is `E_(2)` if the the hydrogen ion is collided and `E_(1)` when helium ion collided . Then.

Options

A. `E_(1) = E_(2) = E_(3) `
B. `E_(1) gt E_(2) gt E_(3) `
C. `E_(1) lt E_(2) lt E_(3) `
D. `E_(1) gt E_(3) gt E_(2) `

Explanation

To solve the problem regarding the minimum kinetic energy required for the ionization of a hydrogen atom when different particles collide with it, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding Ionization Energy**:
The ionization energy of an atom is the minimum energy required to remove an electron from the atom. For hydrogen, the ionization energy (E1) is known to be approximately 13.6 eV.

2. **Collisions with Different Particles**:
- **E1**: This is the minimum kinetic energy required for ionization when an electron collides with a hydrogen atom.
- **E2**: This is the minimum kinetic energy required for ionization when a hydrogen ion (H⁺) collides with a hydrogen atom.
- **E3**: This is the minimum kinetic energy required for ionization when a helium ion (He²⁺) collides with a hydrogen atom.

3. **Comparing Energies**:
- When an electron collides with a hydrogen atom, it requires the least energy (E1 = 13.6 eV).
- When a hydrogen ion (H⁺) collides with a hydrogen atom, it has a positive charge and is more massive than an electron. Therefore, it requires more energy to ionize the hydrogen atom compared to an electron. Thus, we can say E2 > E1.
- When a helium ion (He²⁺) collides with a hydrogen atom, it has a charge of +2 and is even more massive than a hydrogen ion. Consequently, it will require the most energy for ionization. Therefore, E3 > E2.

4. **Establishing the Order of Energies**:
From the above comparisons, we can establish the following relationship:
\[ E1 < E2 < E3 \]
This means that the minimum kinetic energy required for ionization increases as the mass and charge of the colliding particle increases.

5. **Conclusion**:
The order of the minimum kinetic energies required for ionization is:
- E1 (electron) < E2 (hydrogen ion) < E3 (helium ion).

### Final Answer:
The relationship between the minimum kinetic energies required for ionization is:
\[ E1 < E2 < E3 \]