Principle Quantum Number - Transition

[cpmiller]

Homework Statement

Is the following transition allowed?

[4,3,0,1/2] -> [4,2,1, -1/2]

If so, find the energy involved and whether the photon is absorbed or emitted for the hydrogen atom.

Homework Equations

Selection rules for allowed transitions:
$$\Delta$$n = anything
$$\Delta$$l =$$\pm$$1
$$\Delta$$m_l = 0 or $$\pm$$1

The Attempt at a Solution

$$\Delta$$ n = 4-4 = 0
$$\Delta$$ l = 3-2 = 1
$$\Delta$$m_l = 0-1= -1

So all of the transitions are allowed, but it doesn't quite make sense to me.

There is no energy involved, because $$\Delta$$ n = 0, which means that this electron just suddenly spontaneously decided to be in a different configuration, can it do that?

(I also checked and it looks like both of the states are allowed...)

Can it do that, am I missing something?

Thanks for your help!

 

[Redbelly98]

Your reasoning makes sense, the transition does appear to be allowed.

While the Bohr theory predicts the same energies, in reality the energies will be slightly different. Does your textbook or lecture notes say anything about energies of different l-states within the same n?