Q:

Conservation of Angular Momentum of an Electron

In applying conservation of angular momentum for an electron we use the relation $mvr=\frac {nh}{2 \pi}$ however the angular momentum has terms of velocity and distance from the line of action. According to Heisenberg's principle of Uncertainty we can only measure one of them with absolute precision and increasing precision in either increases our error in the other. Also as we know we can only get a probability region (orbitals) where the electrons are more likely to be find. So how do we compute the angular momentum precisely with these constraints?
An example would be an electron in the 1s orbital of the hydrogen atom. The orbital itself is spherically symmetrical however the electron can be anywhere in the region and neither it's velocity or position can be computed with absolute certainty without compromising on the other

A:

Conservation laws , either of quantum numbers or of energy, momentum,angular momentum need a "before and after",usually an interaction is allowed or not according to the conservation laws.
The example:

an electron in the 1s orbital of the hydrogen atom.

There is no before and after in this case. The atom is eternal, unless it interacts.

The orbital itself is spherically symmetrical however the electron can be anywhere in the region and neither it's velocity or position can be computed with absolute certainty without compromising on the other.

The electrons velocity and position cannot be computed at all( let alone with certainty). It is a probabilistic case. If the atom interacts, and the electron is detected , one can start on conservation laws.

