Question

What is the angular momentum of an electron in an atom if the principal quantum number $ n = 2 $?

• A. \( \frac{h}{2\pi} \)
• B. \( \frac{2h}{\pi} \)
• C. \( \frac{2h}{2\pi} \)
• D. \( \frac{nh}{2\pi} \)

Hint:

In Bohr's atomic model, angular momentum is quantized and depends directly on the principal quantum number \( n \).

Answer 1

The Correct Option is D

According to the Bohr model of the atom, the angular momentum \( L \) of an electron in a quantized orbit is given by: \[ L = \frac{nh}{2\pi} \] where:

• \( n \) is the principal quantum number (given as 2),
• \( h \) is Planck’s constant (\( 6.62 \times 10^{-34} \,\text{Js} \)).

Substituting the value of \( n \): \[ L = \frac{2h}{2\pi} = \frac{h}{\pi} \] This matches option (D) in general form, since the angular momentum for any level \( n \) is \( \frac{nh}{2\pi} \).