The value of the energy for the first excited state of hydrogen will be

Options

A. `-13.6 eV`
B. `-3.40 eV`
C. `-1.51 eV`
D. `-0.85 eV`

Explanation

To find the value of the energy for the first excited state of hydrogen, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantum Number for the First Excited State:**
- The ground state of hydrogen corresponds to the principal quantum number \( n = 1 \).
- The first excited state corresponds to \( n = 2 \).

2. **Use the Energy Formula for Hydrogen:**
- The energy of an electron in a hydrogen atom is given by the formula:
\[ E = -\frac{13.6 \, Z^2}{n^2} \text{ eV} \]
- For hydrogen, the atomic number \( Z = 1 \).

3. **Substitute the Values into the Formula:**
- Substitute \( Z = 1 \) and \( n = 2 \) into the formula:
\[ E = -\frac{13.6 \times 1^2}{2^2} \]
- This simplifies to:
\[ E = -\frac{13.6}{4} \]

4. **Calculate the Energy:**
- Performing the division:
\[ E = -3.4 \text{ eV} \]

5. **Conclusion:**
- The value of the energy for the first excited state of hydrogen is \( -3.4 \text{ eV} \).

### Final Answer:
The energy for the first excited state of hydrogen is \( -3.4 \text{ eV} \).

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