When an electron of charge , e and mass , m moves with velocity v around the nuclear charge 'Ze' describing the circular orbit, the potential energy of the electron is

Options

A. `Ze^(2) //r`
B. `-Ze^(2) //r`
C. `Ze^(2) //r^2`
D. `mv^2//r`

Answer

To find the potential energy of an electron moving in a circular orbit around a nuclear charge \( Ze \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charges**:
- The charge of the nucleus is \( Ze \) (where \( Z \) is the atomic number).
- The charge of the electron is \( -e \).

2. **Use the Formula for Potential Energy**:
- The potential energy \( U \) between two point charges is given by the formula:
\[ U = -\frac{q_1 q_2}{r} \]
- Here, \( q_1 = Ze \) (nuclear charge) and \( q_2 = -e \) (charge of the electron).

3. **Substitute the Charges into the Formula**:
- Substitute \( q_1 \) and \( q_2 \) into the potential energy formula:
\[ U = -\frac{(Ze)(-e)}{r} \]
- This simplifies to:
\[ U = -\frac{Ze^2}{r} \]

4. **Final Expression for Potential Energy**:
- Therefore, the potential energy of the electron in the circular orbit around the nucleus is:
\[ U = -\frac{Ze^2}{r} \]

5. **Select the Correct Option**:
- From the given options, the correct expression for the potential energy of the electron is:
- **Option 2**: \( -\frac{Ze^2}{r} \)

### Final Answer:
The potential energy of the electron is \( -\frac{Ze^2}{r} \).

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