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 the hydrogen atom at the level corresponding to \( n = 7 \), we can use the formula derived from Bohr's model of the atom. The energy of an electron in the nth orbit of a hydrogen atom 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 \( E_1 = -13.6 \, \text{eV} \).
- 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 energy formula**:
\[ E_7 = -\frac{13.6 \, \text{eV}}{49} \]

5. **Perform the division**:
\[ E_7 = -0.277 \, \text{eV} \]

6. **Round the answer to two decimal places**:
\[ E_7 \approx -0.28 \, \text{eV} \]

Thus, 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 \( -0.28 \, \text{eV} \).

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