The energy of hydrogen atom in its ground state is -13.6 eV , the energy of the level corresponding to n=7 is

Options

A. `-0.544 eV`
B. `-5.40 eV`
C. `-0.85 eV`
D. `-0.28 eV`

Answer

To find the energy of a hydrogen atom at the level corresponding to \( n = 7 \), we can use the formula derived from Bohr's theory of the hydrogen atom. The energy \( E_n \) of an electron in the nth energy level is given by:

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

### Step-by-Step Solution:

1. **Identify the given values**:
- The energy of the hydrogen atom in its ground state (n=1) is \( -13.6 \, \text{eV} \).
- We need to find the energy at \( n = 7 \).

2. **Substitute \( n = 7 \) into the formula**:
\[ E_7 = -\frac{13.6 \, \text{eV}}{7^2} \]

3. **Calculate \( 7^2 \)**:
\[ 7^2 = 49 \]

4. **Substitute \( 49 \) back into the equation**:
\[ E_7 = -\frac{13.6 \, \text{eV}}{49} \]

5. **Perform the division**:
\[ E_7 = -0.27755 \, \text{eV} \approx -0.28 \, \text{eV} \]

6. **Conclusion**:
The energy of the hydrogen atom at the level corresponding to \( n = 7 \) is approximately \( -0.28 \, \text{eV} \).

### Final Answer:
The energy of the level corresponding to \( n = 7 \) is \( -0.28 \, \text{eV} \).

---