The energy of a hydrogen atom in its ground state is `-13.6 eV`. The energy of the level corresponding to the quantum number n=5 is

Options

A. `-0.54 eV`
B. `-5.40 eV`
C. `-0.85 eV`
D. `-2.72 eV`

Explanation

To find the energy of a hydrogen atom corresponding to the quantum number \( n = 5 \), we can use the formula for the energy levels of a hydrogen atom:

\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

where \( E_n \) is the energy of the level corresponding to the quantum number \( n \), and \( -13.6 \, \text{eV} \) is the energy of the ground state (when \( n = 1 \)).

### Step-by-Step Solution:

1. **Identify the given values:**
- Ground state energy \( E_1 = -13.6 \, \text{eV} \)
- Quantum number \( n = 5 \)

2. **Substitute \( n \) into the energy formula:**
\[ E_5 = -\frac{13.6 \, \text{eV}}{5^2} \]

3. **Calculate \( 5^2 \):**
\[ 5^2 = 25 \]

4. **Substitute \( 25 \) back into the energy formula:**
\[ E_5 = -\frac{13.6 \, \text{eV}}{25} \]

5. **Perform the division:**
\[ E_5 = -0.544 \, \text{eV} \]

6. **Final result:**
The energy of the hydrogen atom in the level corresponding to \( n = 5 \) is:
\[ E_5 = -0.544 \, \text{eV} \]