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_(3)` 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 will analyze the situation step by step.

### Step 1: Understanding Ionization Energy
The ionization energy is the minimum energy required to remove an electron from an atom. For a hydrogen atom, the ionization energy from its ground state is approximately 13.6 eV.

### Step 2: Identifying the Particles
We have three scenarios based on the colliding particles:
- **E1**: Minimum kinetic energy required when an electron collides with a hydrogen atom.
- **E2**: Minimum kinetic energy required when a hydrogen ion (H⁺) collides with a hydrogen atom.
- **E3**: Minimum kinetic energy required when a helium ion (He²⁺) collides with a hydrogen atom.

### Step 3: Analyzing E1 (Electron Collision)
When an electron collides with a hydrogen atom, it needs to overcome the ionization energy of 13.6 eV. Therefore, the minimum kinetic energy required, E1, is:
\[ E_1 = 13.6 \text{ eV} \]

### Step 4: Analyzing E2 (Hydrogen Ion Collision)
A hydrogen ion (H⁺) has a positive charge and can attract the electron more strongly than a neutral electron. Since it has a charge of +1 (Z = 1), the energy required to ionize the hydrogen atom will be less than that required for an electron. However, it still needs to overcome the ionization energy, so:
\[ E_2 > E_1 \]
But it will be less than the energy required for a helium ion.

### Step 5: Analyzing E3 (Helium Ion Collision)
A helium ion (He²⁺) has a charge of +2 (Z = 2) and will exert a stronger attractive force on the electron compared to both the electron and the hydrogen ion. Thus, it will require more energy to ionize the hydrogen atom:
\[ E_3 > E_2 \]

### Step 6: Conclusion
From the analysis above, we can summarize the relationships between the energies:
\[ E_1 < E_2 < E_3 \]

Thus, the correct order of minimum kinetic energies required for ionization is:
- E1 (electron collision) is the least.
- E2 (hydrogen ion collision) is intermediate.
- E3 (helium ion collision) is the greatest.

### Final Answer
The correct order is:
\[ E_1 < E_2 < E_3 \]