# Is the conservation of angular momentum violated in electron jumps from one orbital to another?

I don't really know any quantum mechanics. But in our class, we were introduced to Bohr's model of the atom with his postulate that the angular momentum of an electron in the $n$-th orbit is $\frac{nh}{2\pi}$

Recently I read that electrons could jump from one orbit to another, by absorbing energy (through light or heat). I'm wondering that, if the electron jump from orbit $n_1$ to orbit $n_2$, then it's angular momentum about the nucleus should change by $\frac{(n_2-n_1)h}{2\pi}$ which is against the law of conservation of angular momentum since the only force acting on the electron is the Coulombic attraction towards the nucleus which provides no torque. How then, does the angular momentum change without a torque? Does this have something to do with spin angular momentum that the electron also has? Or is it that these laws don't hold good at such scales? Or is it a flaw of Bohr's model altogether?

• "his postulate that the angular momentum of an electron in the n-th orbit is nh2π" - S orbitals have zero angular momentum for all $n$. – Alfred Centauri Apr 21 '16 at 19:07
• @AlfredCentauri they do indeed, but this was not the prediction of Bohr's model – anon01 Apr 22 '16 at 13:55
• @anon0909 Exactly. Orbitals arise in the purely quantum mechanical approach as far as I know. In Bohr's model, there were only orbits. – Aritra Das Apr 22 '16 at 18:51
• We should note that angular momentum conservation in atomic transitions is actually very important, and forms the basis for many of the "selection rules" which tell us which transitions are allowed. – zeldredge Apr 23 '16 at 23:39
• @zeldredge selection rules are not really exclusive. If you include spin orbit coupling and magnetic effects, you get (low probability) 'forbidden' transitions. – anon01 Apr 24 '16 at 4:11

## 3 Answers

In short, you must consider the total elements of the system for conservation of momentum. In this case, nearly all of the momentum is exchanged between the electron and a photon that is absorbed or radiated away (the light). Momentum is conserved, and is largely balanced by this electron-photon interaction, although smaller amounts may be exchanged with the nucleus.

As a side note: the Bohr model is a proto-quantum mechanical model - it had some quantized features but was not a fully developed theory, so treat it with a little skepticism (in particular, it does not describe the ground state that has zero angular momentum, among other shortcomings).

• why are you so irresolute "most of ... is exchanged", etc. No, it's not a matter of approximation: the electron carries the same angular momentum that is the difference between two electronic orbitals – Ilja Apr 23 '16 at 21:50
• the electron and photon are not the only bodies in this system - thats a simplified picture. what about, e.g. , the nucleus? – anon01 Apr 23 '16 at 21:55
• do you think the nucleus changes its spin projection? Well, it would at least surprise me; and besides, in such a qualitative model as Bohr's it is I think sufficiently precise to just say, that its inconsistency can be amended by considering the spin of the electron. Anyway, why I commented is, that your reasoning sounds so classical :) like talking about corrections from air resistance etc^^ – Ilja Apr 23 '16 at 22:01

When an electron moves from a higher orbital to a lower orbital, the atom emits a photon. This photon carries away the energy difference. However a photon always has an angular momentum of $\hbar$, which is exactly the size of the angular momentum difference for which you are looking for.

Angular momentum is conserved only if there's no external forces, in this case the electron gains energy by light or by heat wich is kinetic energy. They are both external forces so the conservation of angular moment does not apply.

• I up-vote this because it makes the simple point that there is an external force involved. However I'll point out that "collision with a photon" is a dubious concept. Don't take that phrase too seriously. – garyp Apr 23 '16 at 23:25