Potential energy of electron present in `He^(+)` is:

Options

A. `(e^(2))/(2pi epsilon_(0)r)`
B. `(3e^(2))/(4pi epsilon_(0)r)`
C. `(-2e^(2))/(4pi epsilon_(0)r)`
D. `(-e^(2))/(4piepsilon_(0)r^(2))`

Explanation

To find the potential energy of an electron in a helium ion \( \text{He}^+ \), we can use the formula for the potential energy \( U \) of an electron in a hydrogen-like atom. The potential energy \( U \) is given by the formula:

\[ U = -\frac{Z e^2}{4 \pi \epsilon_0 r} \]

where:
- \( Z \) is the atomic number (for helium, \( Z = 2 \)),
- \( e \) is the charge of the electron,
- \( \epsilon_0 \) is the permittivity of free space,
- \( r \) is the distance between the nucleus and the electron.

### Step-by-step Solution:

1. **Identify the Atomic Number (Z)**:
- For helium, the atomic number \( Z = 2 \).

2. **Use the Formula for Potential Energy**:
- Substitute \( Z \) into the potential energy formula:
\[ U = -\frac{2 e^2}{4 \pi \epsilon_0 r} \]

3. **Simplify the Expression**:
- The potential energy can be expressed as:
\[ U = -\frac{e^2}{2 \pi \epsilon_0 r} \]

4. **Conclusion**:
- The potential energy of the electron in the \( \text{He}^+ \) ion is:
\[ U = -\frac{2 e^2}{4 \pi \epsilon_0 r} \]

### Final Answer:
The potential energy of the electron present in \( \text{He}^+ \) is:
\[ U = -\frac{2 e^2}{4 \pi \epsilon_0 r} \]