An electron with kinetic energy `5eV` is incident on a hydrogen atom in its ground state.The collision

Options

A. must be elastic
B. may be partially elastic
C. must be completely inelastic
D. may be completely inelastic

Answer

To solve the problem, we need to analyze the interaction between an electron with a kinetic energy of 5 eV and a hydrogen atom in its ground state. Here is a step-by-step solution:

### Step 1: Understand the Energy Levels of the Hydrogen Atom
The ground state of a hydrogen atom corresponds to the principal quantum number \( n = 1 \). The energy of the electron in the ground state of hydrogen is approximately \(-13.6 \, \text{eV}\). This means that to remove the electron from the atom (ionization), an energy of at least 13.6 eV is required.

### Step 2: Compare the Kinetic Energy of the Incident Electron
The kinetic energy of the incident electron is given as \( 5 \, \text{eV} \). We need to compare this energy with the ionization energy of the hydrogen atom.

### Step 3: Analyze the Collision
- If the energy of the incident electron is greater than 13.6 eV, the electron could ionize the hydrogen atom, leading to an inelastic collision.
- If the energy is exactly 13.6 eV, the collision would also be perfectly inelastic as the electron would be absorbed.
- If the energy is less than 13.6 eV (which is the case here, as \( 5 \, \text{eV} < 13.6 \, \text{eV} \)), the electron cannot ionize the hydrogen atom.

### Step 4: Conclusion on the Type of Collision
Since the kinetic energy of the incident electron (5 eV) is less than the ionization energy (13.6 eV), the collision must be elastic. In an elastic collision, the total kinetic energy is conserved, and no energy is absorbed by the hydrogen atom.

### Final Answer
The collision between the electron and the hydrogen atom is **elastic**.

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