The angular momentum of an electron in the hydrogen atom is `(2h)/(pi)`. What is the potential energy of this electron ?

Options

A. `-0.85 eV`
B. `-1.51 eV`
C. `-1.70 eV`
D. `-4.3 eV`

Explanation

To find the potential energy of an electron in a hydrogen atom given its angular momentum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Angular Momentum Formula**:
The angular momentum \( L \) of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ L = \frac{n h}{2 \pi} \]
where \( n \) is the principal quantum number and \( h \) is Planck's constant.

2. **Set Up the Equation**:
From the problem, we know that the angular momentum is given as:
\[ L = \frac{2h}{\pi} \]
We can set the two expressions for angular momentum equal to each other:
\[ \frac{n h}{2 \pi} = \frac{2h}{\pi} \]

3. **Solve for \( n \)**:
To find \( n \), we can simplify the equation:
\[ n h = 4h \quad \text{(by multiplying both sides by } 2\pi\text{)} \]
Dividing both sides by \( h \):
\[ n = 4 \]
Thus, the electron is in the 4th orbit.

4. **Calculate the Total Energy**:
The energy \( E \) of an electron in the nth orbit is given by:
\[ E = -\frac{13.6 \, \text{eV}}{n^2} \]
Substituting \( n = 4 \):
\[ E = -\frac{13.6 \, \text{eV}}{4^2} = -\frac{13.6 \, \text{eV}}{16} = -0.85 \, \text{eV} \]

5. **Relate Total Energy to Potential Energy**:
The potential energy \( U \) of the electron is related to the total energy \( E \) by the formula:
\[ U = 2E \]
Substituting the total energy we found:
\[ U = 2 \times (-0.85 \, \text{eV}) = -1.70 \, \text{eV} \]

### Final Answer:
The potential energy of the electron is:
\[ \boxed{-1.70 \, \text{eV}} \]