Question

The orbital angular momentum of hydrogen atom in the ground state is ............

• A. 0
• B. \(\frac{h}{2\pi}\)
• C. \(\frac{h}{2}\)
• D. \(h\)

Hint:

In quantum mechanics, the angular momentum of an electron in the ground state is zero, as it is in the lowest energy orbital.

Answer 1

The Correct Option is A

Step 1: Understanding the hydrogen atom's angular momentum.
In the ground state of the hydrogen atom, the electron is in the lowest energy level (n=1), where its orbital angular momentum is zero. This is a direct consequence of the quantization of angular momentum in quantum mechanics.
Step 2: Analyzing the options.
(A) 0: Correct — In the ground state, the electron's angular momentum is zero because it occupies the lowest possible orbital.
(B) \(\frac{h}{2\pi}\): Incorrect — This is the value of angular momentum for the first excited state (n=2), not the ground state.
(C) \(\frac{h}{2}\): Incorrect — This corresponds to higher energy levels, not the ground state.
(D) \(h\): Incorrect — This is the angular momentum for a system in a higher quantum state.
Step 3: Conclusion.
The correct answer is (A) 0, as the orbital angular momentum in the ground state of a hydrogen atom is zero.