Question

The energy required to excite an electron from 1st to 3rd Bohr orbit in $Li^{2+}$ ion is:

• A. 212.1 eV
• B. 136.3 eV
• C. 108.8 eV
• D. 122.4 eV

Hint:

For hydrogen-like ions, energy levels scale with $Z^2$. Always multiply the base energy by $Z^2$.

Answer 1

The Correct Option is C

Step 1: Energy levels of a hydrogen-like ion.
For a one-electron ion the energy of the $n$th orbit is \[ E_n = -13.6\,\frac{Z^2}{n^2}\ \text{eV}. \]
Step 2: Identify the values.
For $Li^{2+}$ the atomic number is $Z = 3$. We move from $n = 1$ to $n = 3$.
Step 3: Energy of the first orbit.
\[ E_1 = -13.6 \times \frac{3^2}{1^2} = -13.6 \times 9 = -122.4\ \text{eV}. \]
Step 4: Energy of the third orbit.
\[ E_3 = -13.6 \times \frac{3^2}{3^2} = -13.6 \times 1 = -13.6\ \text{eV}. \]
Step 5: Energy needed to jump up.
The excitation energy is the difference between the two levels: \[ \Delta E = E_3 - E_1 = -13.6 - (-122.4) = 108.8\ \text{eV}. \]
Step 6: Conclusion.
The energy required to lift the electron from the first to the third orbit is $108.8\,\text{eV}$. \[ \boxed{108.8\ \text{eV}} \]