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A nuetral helium atom in is in the excited electronic state, with one electron in the (2p) level and the other in the (3d) level. The atom is initally in a region with zero applied magnetic field.

(a) Can the electron in the (3d) level emit a photon and change to the (2p) level? If so, how many different photon energies would you expect to measure? Explain your answer.

(b) A magnetic field of 1.0 Tesla is applied to the atom. Can the electron in the (2p) level emit a photon and change to the (1s) level, with the electron in the (3d) level remaining in the (3d) level? If so, how many different photon energies would you expect to measure? Explain your answer.

I already know the answers. However, there is something I need help understanding. Since the principle quantum number n can only change by +/-1, and the photon energy is determined by the change in n, how can there be multiple photon energies for a single transition?

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The n is called principle quantum number because it gives the basic energy level. l and m

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give corrections on this basic energy level, and this allows for the possibility of many more transitions, as long as quantum numbers are conserved.

If you look at the hydrogen energy levels at extremely high resolution, you do find evidence of some other small effects on the energy. The 2p level is split into a pair of lines by the spin-orbit effect. The 2s and 2p states are found to differ a small amount in what is called the Lamb shift. And even the 1s ground state is split by the interaction of electron spin and nuclear spin in what is called hyperfine structure.

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