In hydrogen atom, the energy of second shell `e^(Θ`

Options

A. `-5.44xx10^(-19)J`
B. `-5.44xx10^(-19)KJ`
C. `-5.44xx10^(19)Cal`
D. `-5.44xx10^(-19)erg`

Explanation

To solve the question regarding the energy of the second shell electron in a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Formula for Energy Levels in Hydrogen Atom**:
The energy of an electron in a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( E_n \) is the energy at the nth shell and \( n \) is the principal quantum number.

2. **Determine the Principal Quantum Number for the Second Shell**:
For the second shell, the principal quantum number \( n \) is 2.

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

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

5. **Calculate the Energy**:
Now substitute back into the equation:
\[ E_2 = -\frac{13.6 \, \text{eV}}{4} = -3.4 \, \text{eV} \]

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

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

8. **Final Result**:
The energy of the second shell electron in a hydrogen atom is:
\[ E_2 = -5.44 \times 10^{-19} \, \text{J} \]