The energy of an electron in second Bohr orbit of hydrogen atom is :

Options

A. `- 5. 44 xx 10^(-19) eV`
B. `- 5.44 xx 10 ^(-19) cal `
C. `-5.44 xx 1 ^(-19) KJ`
D. ` - 5.44 xx 10 ^(-19) J`

Answer

To find the energy of an electron in the second Bohr orbit of a hydrogen atom, we can use the formula for the energy levels in a hydrogen atom, which is given by:

\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

where \( E_n \) is the energy of the electron in the nth orbit, and \( n \) is the principal quantum number.

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number:**
For the second Bohr orbit, the principal quantum number \( n = 2 \).

2. **Substitute \( n \) into the Energy Formula:**
Substitute \( n = 2 \) into the energy formula:
\[ E_2 = -\frac{13.6 \, \text{eV}}{2^2} = -\frac{13.6 \, \text{eV}}{4} \]

3. **Calculate the Energy:**
Now, perform the calculation:
\[ E_2 = -\frac{13.6}{4} = -3.4 \, \text{eV} \]

4. **Convert Electron Volts to Joules:**
To convert the energy from electron volts to joules, use the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):
\[ E_2 = -3.4 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} \]

5. **Perform the Multiplication:**
Calculate the energy in joules:
\[ E_2 = -3.4 \times 1.6 \times 10^{-19} = -5.44 \times 10^{-19} \, \text{J} \]

### Final Answer:
The energy of an electron in the second Bohr orbit of a hydrogen atom is:
\[ E_2 = -5.44 \times 10^{-19} \, \text{J} \]