My textbook mentions that the orbital angular momentum is the second formula and the angular momentum of an electron is given by $nh/2π$ in Bohr model. Please help me realise the link between these formulas or what should I say if someone asks me about the angular momentum of an electron.


If you look at the component of angular momentum along just one axis, then the two formula actually agree nicely. Angular momentum along some axis is just some integer (call it $n$ or $l$), times $h/2\pi$. But this isn't actually equal to the total magnitude of angular momentum, which is given by $\sqrt{l(l+1)} h/2\pi$.

It's worth mentioning that the fact that the Bohr model agrees with the angular momentum along one axis is a bit of an accident.

  • $\begingroup$ Oh thanks. That clears some doubts. But then how does spin angular momentum fit into the picture? $\endgroup$ – NightKruger Sep 13 at 18:58
  • $\begingroup$ Spin behaves just the same way, but it can also come in half integer quantities. For a spin $s$ particle, the component of spin angular momentum on some axis can be any number $-s \frac{h}{2\pi}, (-s+1)\frac{h}{2\pi},...,s\frac{h}{2\pi}$. An electron has $s=\frac{1}{2}$, so its angular momentum along any axis can be $\pm\frac{1}{2} \frac{h}{2\pi}$. $\endgroup$ – Danny Sep 13 at 19:02
  • $\begingroup$ Well then what would I call the total angular momentum of the electron ? Is it the vector sum of the spin and orbital angular momentum? Or something else? $\endgroup$ – NightKruger Sep 13 at 19:10
  • $\begingroup$ @NightKruger Adding 2 angular momenta is not like classical addition of vectors, rather it involves expressing the tensor product of two representations of SU(2) [one for each angular momentum] and then expressing that as a sum of representations for the total angular momentum. That's not going to fit in a comment. $\endgroup$ – JEB Sep 13 at 19:35

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