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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.

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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.

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  • $\begingroup$ 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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