An electron with kinetic energy `10 eV` 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 the incident electron and the hydrogen atom in its ground state. Here is the step-by-step solution:

### Step 1: Understand the Energy Levels of Hydrogen
The energy levels of a hydrogen atom are given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is the principal quantum number.

- For the ground state (\( n = 1 \)):
\[ E_1 = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]

- For the first excited state (\( n = 2 \)):
\[ E_2 = -\frac{13.6 \, \text{eV}}{2^2} = -3.4 \, \text{eV} \]

### Step 2: Calculate the Energy Required for Excitation
To find the energy required to excite the electron from the ground state to the first excited state, we calculate the difference in energy between these two states:
\[ \Delta E = E_2 - E_1 = (-3.4 \, \text{eV}) - (-13.6 \, \text{eV}) \]
\[ \Delta E = 10.2 \, \text{eV} \]

### Step 3: Compare the Kinetic Energy of the Incident Electron
The kinetic energy of the incident electron is given as \( 10 \, \text{eV} \). We need to compare this with the energy required for excitation:
- Required energy for excitation: \( 10.2 \, \text{eV} \)
- Available energy from the electron: \( 10 \, \text{eV} \)

### Step 4: Determine if Excitation Occurs
Since the energy required to excite the electron to the first excited state (10.2 eV) is greater than the kinetic energy of the incident electron (10 eV), the electron does not have enough energy to cause excitation.

### Step 5: Conclude the Type of Collision
Since the electron does not get absorbed and there is no energy loss in the process, the collision is elastic. In an elastic collision, the total kinetic energy before and after the collision remains the same.

### Final Answer
The collision must be elastic.