the energy required to excite an electron in hydrogen atom to its first excited state is

Options

A. `8.5eV`
B. `10.2eV`
C. `12.7eV`
D. `13.6eV`

Explanation

To find the energy required to excite an electron in a hydrogen atom to its first excited state, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Energy Levels**:
- The energy of the electron in the ground state (n=1) of a hydrogen atom is given as \( E_1 = -13.6 \, \text{eV} \).
- The energy of the electron in the first excited state (n=2) is given as \( E_2 = -3.4 \, \text{eV} \).

2. **Calculate the Energy Difference**:
- To find the energy required to excite the electron from the ground state to the first excited state, we need to calculate the difference in energy between these two states.
- The energy required \( E \) can be calculated using the formula:
\[ E = E_2 - E_1 \]

3. **Substitute the Values**:
- Substitute the known values into the equation:
\[ E = (-3.4 \, \text{eV}) - (-13.6 \, \text{eV}) \]

4. **Perform the Calculation**:
- Simplifying the equation:
\[ E = -3.4 \, \text{eV} + 13.6 \, \text{eV} = 10.2 \, \text{eV} \]

5. **Conclusion**:
- The energy required to excite the electron in a hydrogen atom to its first excited state is \( 10.2 \, \text{eV} \).

### Final Answer:
The energy required to excite an electron in a hydrogen atom to its first excited state is **10.2 eV**.

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