Question

Write the minimum orbital angular momentum of the electron in a hydrogen atom.

Hint:

In the ground state of the hydrogen atom, the minimum orbital angular momentum is equal to the reduced Planck's constant, \( \hbar \).

Answer 1

Step 1: Understanding orbital angular momentum.
The minimum orbital angular momentum of an electron in the hydrogen atom is given by the formula: \[ L = n \hbar \] where \( n \) is the principal quantum number, and \( \hbar \) is the reduced Planck's constant, given by: \[ \hbar = \frac{h}{2\pi} \] For the minimum orbital angular momentum, the electron is in the ground state where \( n = 1 \). Thus, the minimum angular momentum is: \[ L = 1 \times \hbar = \hbar \]
Step 2: Conclusion.
Therefore, the minimum orbital angular momentum is \( \hbar \).