The total energy of an electron revolving in the second orbit of a hydrogen atom is

Options

A. `-13.6 eV`
B. `-1.51 eV`
C. `-3.4 eV`
D. Zero

Answer

To find the total energy of an electron revolving in the second orbit of a hydrogen atom, we can use the formula derived from Bohr's theory of the hydrogen atom. The total energy \( E \) of an electron in the nth orbit is given by:

\[ E = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]

where:
- \( E \) is the total energy,
- \( Z \) is the atomic number of the atom,
- \( n \) is the principal quantum number (the orbit number).

### Step-by-Step Solution:

1. **Identify the Atomic Number (Z)**:
For hydrogen, the atomic number \( Z = 1 \).

2. **Identify the Principal Quantum Number (n)**:
The electron is in the second orbit, so \( n = 2 \).

3. **Substitute the Values into the Formula**:
Now, we substitute \( Z \) and \( n \) into the energy formula:
\[ E = -\frac{13.6 \, \text{eV} \cdot (1)^2}{(2)^2} \]

4. **Calculate the Denominator**:
Calculate \( (2)^2 \):
\[ (2)^2 = 4 \]

5. **Substitute and Simplify**:
Now substitute back into the equation:
\[ E = -\frac{13.6 \, \text{eV}}{4} \]

6. **Perform the Division**:
Calculate \( \frac{13.6}{4} \):
\[ \frac{13.6}{4} = 3.4 \]

7. **Final Result**:
Therefore, the total energy \( E \) is:
\[ E = -3.4 \, \text{eV} \]

### Conclusion:
The total energy of an electron revolving in the second orbit of a hydrogen atom is \( -3.4 \, \text{eV} \).