The energy of an electron present in Bohr's second orbit of hydrogen atom is

Options

A. `-1312 J " atom"^(-1)`
B. `328 J " mol"^(-1)`
C. `-328 kJ mol^(-1)`
D. `-164 kJ mol^(-1)`

Answer

To find the energy of an electron present in Bohr's second orbit of a hydrogen atom, we can follow these steps:

### Step 1: Understand the formula for energy in Bohr's model
The energy of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E_n = -\frac{1312 \, z^2}{n^2} \, \text{kJ/mol} \]
where:
- \(E_n\) is the energy of the electron in the nth orbit,
- \(z\) is the atomic number (for hydrogen, \(z = 1\)),
- \(n\) is the principal quantum number (for the second orbit, \(n = 2\)).

### Step 2: Substitute the values into the formula
For hydrogen, we have:
- \(z = 1\)
- \(n = 2\)

Substituting these values into the formula:
\[ E_2 = -\frac{1312 \times 1^2}{2^2} \, \text{kJ/mol} \]

### Step 3: Calculate the denominator
Calculating \(2^2\):
\[ 2^2 = 4 \]

### Step 4: Calculate the energy
Now substituting back into the equation:
\[ E_2 = -\frac{1312}{4} \, \text{kJ/mol} \]
Calculating this gives:
\[ E_2 = -328 \, \text{kJ/mol} \]

### Step 5: Identify the correct answer
Based on the calculation, the energy of the electron in the second orbit of the hydrogen atom is:
\[ E_2 = -328 \, \text{kJ/mol} \]
Thus, the correct option from the given choices is the third option: **-328 kJ/mol**.

### Summary of the Solution:
The energy of an electron in the second orbit of a hydrogen atom is calculated to be -328 kJ/mol.

---