If `E_n` and `L_n` denote the total energy and the angular momentum of an electron in the nth orbit of Bohr atom, then

Options

A. `E_n prop L_n`
B. `E_n prop (1)/(L_n)`
C. `E_n prop L_n^2`
D. `E_n prop (1)/(L_n^2`

Explanation

To solve the problem, we need to establish the relationship between the total energy \( E_n \) and the angular momentum \( L_n \) of an electron in the nth orbit of a Bohr atom.

### Step-by-Step Solution:

1. **Understanding the Energy of the Electron**:
In the Bohr model of the atom, the total energy \( E_n \) of the electron in the nth orbit is given by:
\[ E_n \propto -\frac{1}{n^2} \]
This indicates that the energy is inversely proportional to the square of the principal quantum number \( n \).

2. **Understanding the Angular Momentum**:
The angular momentum \( L_n \) of the electron in the nth orbit is given by:
\[ L_n \propto n \]
This shows that the angular momentum is directly proportional to the principal quantum number \( n \).

3. **Relating Energy and Angular Momentum**:
To find a relationship between \( E_n \) and \( L_n \), we can express \( n \) in terms of \( L_n \):
\[ n \propto L_n \]
Therefore, we can write \( n \) as:
\[ n = k L_n \]
where \( k \) is a proportionality constant.

4. **Substituting \( n \) into the Energy Equation**:
Now, substituting \( n \) into the energy equation:
\[ E_n \propto -\frac{1}{(k L_n)^2} \]
This simplifies to:
\[ E_n \propto -\frac{1}{k^2 L_n^2} \]
Thus, we can conclude that:
\[ E_n \propto -\frac{1}{L_n^2} \]

5. **Final Relationship**:
Therefore, the relationship between the total energy \( E_n \) and the angular momentum \( L_n \) can be expressed as:
\[ E_n \propto -\frac{1}{L_n^2} \]

### Conclusion:
The correct answer is that \( E_n \) is proportional to \( -\frac{1}{L_n^2} \).