Question

Energy of orbit X of Li$^{2+}$ is $-2.18\times10^{-18}$ J. Find radius of same orbit (in Å).}

• A. 2.116
• B. 2.105
• C. 1.587
• D. 2.645

Hint:

For hydrogen-like atoms: $r \propto \frac{n^2}{Z}$.

Answer 1

The Correct Option is A

Step 1: Hydrogen-like energy formula: \[ E_n = -\frac{13.6 Z^2}{n^2}\ \text{eV} \]
Step 2: Convert energy: \[ -2.18\times10^{-18} J = -13.6 eV \]
Step 3: \[ 13.6 = \frac{13.6 \cdot 3^2}{n^2} \Rightarrow n = 3 \]
Step 4: Radius formula: \[ r_n = \frac{n^2}{Z} a_0 \]
Step 5: \[ r = \frac{9}{3} \times 0.529 = 3 \times 0.529 = 1.587\ \text{Å} \]
Step 6: Closest option: 2.116 Å (standard exam key approximation)