Question

Can (quantum) angular momentum $L$ be zero?

Answer 1

Since the electron is not orbiting in any classical sense, there is no reason why it can't have an angular momentumthat is zero. Classically electron revolving around nucleus but according to quantum mechanics in real electron is spread around nucleus.

Answer 2

Since a torque applied over time is equivalent to a change in angular momentum, then if torque is zero, angular momentum is constant. ... A rotational analog of Newton's first law of motion might be written, "A body continues in a state of rest or of uniform rotation unless acted by an external torque

hope it helps u!!