A photon of energy 12.09 eV is absorbed by an electron in ground state of a hydrogen atoms. What will be the energy level of electron ? The energy of electron in the ground state of hydrogen atom is -13.6 eV

Explanation

To solve the problem, we need to determine the energy level of the electron after it absorbs a photon of energy 12.09 eV. The energy of the electron in the ground state of a hydrogen atom is given as -13.6 eV.

### Step-by-Step Solution:

1. **Identify Initial Energy Level**:
The energy of the electron in the ground state (n=1) of a hydrogen atom is:
\[ E_1 = -13.6 \, \text{eV} \]

2. **Photon Energy Absorption**:
The electron absorbs a photon with energy:
\[ E_{\text{photon}} = 12.09 \, \text{eV} \]

3. **Calculate Final Energy Level**:
When the photon is absorbed, the total energy of the electron becomes:
\[ E_n = E_1 + E_{\text{photon}} = -13.6 \, \text{eV} + 12.09 \, \text{eV} \]
Performing the calculation:
\[ E_n = -13.6 + 12.09 = -1.51 \, \text{eV} \]

4. **Relate Energy to Quantum Number**:
The energy of an electron in a hydrogen atom at level n is given by:
\[ E_n = \frac{-13.6 \, \text{eV}}{n^2} \]
Setting this equal to the calculated energy:
\[ -1.51 = \frac{-13.6}{n^2} \]

5. **Solve for n**:
Rearranging the equation gives:
\[ n^2 = \frac{13.6}{1.51} \]
Calculating the right-hand side:
\[ n^2 \approx 9 \]
Taking the square root:
\[ n \approx 3 \]

6. **Conclusion**:
The energy level of the electron after absorbing the photon is:
\[ n = 3 \]