Question

Angular momentum of the electron in a hydrogen atom is $\frac{3h}{2\pi}$ then find total energy of electron (in eV/atom)

• A. –1.51
• B. –122.4
• C. –40.8
• D. –4.53

Answer 1

The Correct Option is A

Quantization of angular momentum and the Bohr energy equation for Hydrogen atom.

STEPS:
1. From the given angular momentum $\frac{3h}{2\pi}$, we identify that the electron is in the $3^{rd}$ shell ($n=3$) because $L = n\hbar$.
2. The energy of an electron in the $n^{th}$ shell of Hydrogen is given by $E = \frac{-13.6}{n^2} \text{ eV}$.
3. Plugging in $n=3$:
$E = \frac{-13.6}{3^2} = \frac{-13.6}{9} = -1.51 \text{ eV}$
4. Therefore, the total energy is -1.51 eV. Option (1) is the correct choice.