Question

Angular momentum of an electron in a hydrogen atom is \( \dfrac{3h}{\pi} \). Then the energy of the electron is ____ eV.

• A. \(-1.51\)
• B. \(-0.85\)
• C. \(-0.38\)
• D. \(-0.28\)

Answer 1

The Correct Option is C

Concept: According to Bohr's quantization condition: \[ L = n\hbar = n\frac{h}{2\pi} \]
Step 1:Given angular momentum} \[ L = \frac{3h}{\pi} \] Substitute in Bohr relation: \[ \frac{3h}{\pi} = n\frac{h}{2\pi} \] Multiply both sides by \(2\pi/h\): \[ n = 6 \]
Step 2:Energy of electron in hydrogen atom} \[ E_n = -\frac{13.6}{n^2} \text{ eV} \]
Step 3:Substitute \(n=6\)} \[ E_6 = -\frac{13.6}{36} \] \[ E_6 = -0.378 \text{ eV} \] \[ \approx -0.38 \text{ eV} \] \[ \boxed{-0.38} \]