# Difference between $nh/2π$ and $\sqrt{\ell(\ell+1)}h/2π$

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 $$\sqrt{l(l+1)} h/2\pi$$.
• 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 $\pm\frac{1}{2} \frac{h}{2\pi}$. – Danny Sep 13 at 19:02