Potential at a point A is ` 3` volt and at a point `B` is ` 7 V`, an electron is moving towards `A` form `B`.

Options

A. (a)It must have some K.E. at B to reach A
B. (b)It need not have any K.E. at B to reach A
C. (c)to reach A, it must have more than or equal to 4eV K. E. at B
D. (d)when it will reach A, it will have K.E. more than or at least equal to 4eV if it was released from rest at B

Explanation

To solve the problem, we need to analyze the motion of an electron moving from point B to point A, considering the electric potential at both points.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Potential at point A, \( V_A = 3 \, \text{V} \)
- Potential at point B, \( V_B = 7 \, \text{V} \)
- The charge of an electron, \( q = -1.6 \times 10^{-19} \, \text{C} \)

2. **Understanding the Movement of the Electron**:
- The electron is moving from point B (higher potential) to point A (lower potential).
- Since the electron has a negative charge, it will naturally move towards lower potential.

3. **Calculate the Change in Electric Potential**:
- The change in potential when moving from B to A is given by:
\[ \Delta V = V_A - V_B = 3 \, \text{V} - 7 \, \text{V} = -4 \, \text{V} \]

4. **Calculate the Work Done on the Electron**:
- The work done on the electron due to the change in potential is given by:
\[ W = q \Delta V = (-1.6 \times 10^{-19} \, \text{C})(-4 \, \text{V}) = 6.4 \times 10^{-19} \, \text{J} \]
- This work done will convert into kinetic energy of the electron.

5. **Relate Work Done to Kinetic Energy**:
- The work-energy principle states that the work done on the electron will equal its change in kinetic energy:
\[ W = \Delta KE = KE_f - KE_i \]
- Assuming the electron starts from rest (initial kinetic energy \( KE_i = 0 \)), we have:
\[ KE_f = W = 6.4 \times 10^{-19} \, \text{J} \]

6. **Convert Kinetic Energy to Electron Volts**:
- To express the kinetic energy in electron volts:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
- Therefore, the kinetic energy in electron volts is:
\[ KE_f = \frac{6.4 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} = 4 \, \text{eV} \]

7. **Conclusion**:
- The electron must have at least 4 eV of kinetic energy to move from point B to point A. If it has less than this energy, it will not be able to reach point A.

### Final Answer:
The electron must have an initial kinetic energy of at least 4 eV to move from point B to point A.