The energy of 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 the hydrogen atom at the quantum level corresponding to \( n = 5 \), we can use the formula for the energy of an electron in a hydrogen atom:

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

Where:
- \( E_n \) is the energy at the quantum level \( n \),
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)),
- \( n \) is the principal quantum number.

### Step-by-Step Solution:

1. **Identify the values**:
- For hydrogen, the atomic number \( Z = 1 \).
- The principal quantum number \( n = 5 \).

2. **Substitute the values into the formula**:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot (1)^2}{(5)^2} \]

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

4. **Substitute \( n^2 \) into the equation**:
\[ E_n = -\frac{13.6 \, \text{eV}}{25} \]

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

6. **Round to two decimal places**:
\[ E_n \approx -0.54 \, \text{eV} \]

### Final Answer:
The energy of the hydrogen atom at the quantum level corresponding to \( n = 5 \) is approximately \( -0.54 \, \text{eV} \).