Energy required for the electron excitation in `Li^(++)` from the first to the third Bohr orbit is:

Options

A. `12.1 eV`
B. `36.3 eV`
C. `108. 8 eV`
D. `122.4 eV`

Explanation

To find the energy required for the electron excitation in \( \text{Li}^{++} \) from the first to the third Bohr orbit, we can follow these steps:

### Step 1: Identify the formula for energy in the nth orbit
The energy of an electron in the nth orbit of a hydrogen-like atom is given by the formula:
\[ E_n = -\frac{13.6 Z^2}{n^2} \text{ eV} \]
where \( Z \) is the atomic number and \( n \) is the principal quantum number.

### Step 2: Determine the atomic number for \( \text{Li}^{++} \)
For lithium (\( \text{Li} \)), the atomic number \( Z \) is 3. Therefore, for \( \text{Li}^{++} \), we will use \( Z = 3 \).

### Step 3: Calculate the energy for the first orbit (\( n = 1 \))
Using the formula for \( n = 1 \):
\[ E_1 = -\frac{13.6 \times 3^2}{1^2} = -\frac{13.6 \times 9}{1} = -122.4 \text{ eV} \]

### Step 4: Calculate the energy for the third orbit (\( n = 3 \))
Using the formula for \( n = 3 \):
\[ E_3 = -\frac{13.6 \times 3^2}{3^2} = -\frac{13.6 \times 9}{9} = -13.6 \text{ eV} \]

### Step 5: Calculate the energy difference (\( \Delta E \))
The energy required for excitation from the first to the third orbit is given by:
\[ \Delta E = E_3 - E_1 \]
Substituting the values we calculated:
\[ \Delta E = -13.6 - (-122.4) = -13.6 + 122.4 = 108.8 \text{ eV} \]

### Conclusion
The energy required for the electron excitation in \( \text{Li}^{++} \) from the first to the third Bohr orbit is \( 108.8 \text{ eV} \).