Question

show that the angular momentum of an electron is an integral multiple of h/2π​

Answer 1

ANSWER: The angular momentum of orbits is NOT an integral multiple of h/2π (assuming we are talking about the total angular momentum). This is based on Bohr’s model, which preceded quantum mechanics — while it was able to explain the Hydrogen spectra, quantum mechanics has been far more applicable. It has been able to explain not only the Hydrogen spectra, but a number of other effects which could not be deduced through only the Bohr’s model (e.g. Stark effect, Zeeman effect). Moreover, quantum mechanics can also be used to work out the spectra of more complex atoms/molecules, although the computation might become increasingly tedious.

What quantum mechanics tells us about angular momentum is the following — you can simultaneously measure only the magnitude square and the component of the angular momentum along any one direction. Any other measurement (such as the angular momentum along another direction) would be constrained by the uncertainty principle. The magnitude squared can be of the form:

L2=h2l(l+1)/4π2

and the component of the form mh/2π where m∈{−l,−l+1...l−1,l} . You also need to factor in the spin angular momentum for a complete calculation. These can be mathematically derived using the definition of the angular momentum operators — you can check out chapters 12,13 and 14 of “Principles of Quantum Mechanics” by Shankar for a complete treatment.

Answer 2

Here is your answer＼(◎o◎)／