The energy of second Bohr orbit of the hydrogen atom is `- 328 k J mol^-1`, hence the energy of fourth Bohr orbit would be.

Options

A. `- 41 kJ mol^-1`
B. `-1312 kJ mol^-1`
C. `- 164 kJ mol^-1`
D. `-82 kJ mol^-1`

Explanation

To find the energy of the fourth Bohr orbit of the hydrogen atom, we can use the relationship between the energy levels of the Bohr model. The energy of an electron in a hydrogen atom is given by the formula:

\[ E_n = -\frac{R_H}{n^2} \]

where:
- \(E_n\) is the energy of the nth orbit,
- \(R_H\) is the Rydberg constant for hydrogen (approximately 1312 kJ/mol),
- \(n\) is the principal quantum number (the orbit number).

### Step-by-Step Solution:

1. **Identify the given information**:
- Energy of the second orbit (\(E_2\)) = -328 kJ/mol
- We need to find the energy of the fourth orbit (\(E_4\)).

2. **Use the energy relation**:
The energy of the orbits is inversely proportional to the square of the principal quantum number \(n\):
\[ \frac{E_2}{E_4} = \frac{n_4^2}{n_2^2} \]

3. **Substitute the values**:
- For the second orbit, \(n_2 = 2\).
- For the fourth orbit, \(n_4 = 4\).
- Substitute these values into the equation:
\[ \frac{-328}{E_4} = \frac{4^2}{2^2} \]

4. **Calculate the ratio**:
\[ \frac{-328}{E_4} = \frac{16}{4} = 4 \]

5. **Solve for \(E_4\)**:
Rearranging gives:
\[ E_4 = \frac{-328}{4} \]
\[ E_4 = -82 \text{ kJ/mol} \]

### Conclusion:
The energy of the fourth Bohr orbit of the hydrogen atom is \(-82 \text{ kJ/mol}\).