An electron of mass m and charge -e moves in circular orbit of radius r round the nucleus of charge +Ze in unielectron system. In CGS system the potential energy of electron is

Options

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

Explanation

To find the potential energy of an electron moving in a circular orbit around a nucleus in a unielectron system, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charges and Distance**:
- The charge of the electron is \(-e\).
- The charge of the nucleus is \(+Ze\).
- The distance between the electron and the nucleus is \(r\).

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

3. **Substitute the Values into the Formula**:
- Plugging in the values, we have:
\[ U = \frac{k \cdot (Ze) \cdot (-e)}{r} \]
- This simplifies to:
\[ U = -\frac{k \cdot Ze^2}{r} \]

4. **Convert to CGS Units**:
- In the CGS system, the value of \(k\) is \(1\). Therefore, we can simplify the potential energy further:
\[ U = -\frac{Ze^2}{r} \]

5. **Final Expression**:
- Thus, the potential energy of the electron in a circular orbit around the nucleus in CGS units is:
\[ U = -\frac{Ze^2}{r} \]