A hydrogen atom undergoes a transition from a 2 p state to the 1 s ground state.

Question

A hydrogen atom undergoes a transition from a 2p state to the 1s ground state. In the absence of a magnetic field, the energy of the photon emitted is 122 nm. The atom is then placed in a strong magnetic field in the z-direction. Ignore spin effects; consider only the interaction of the magnetic field with the atom's orbital magnetic moment.

A) How many different photon wavelengths are observed for the 2p -->> 1s transition?

Answer: 3

B) What are the three ml values for the initial state for the transition that leads to each photon wavelength?

Answer: -1, 0, 1

C) What is the ml value for the final state for the transition that leads to each photon wavelength?

D) One observed wavelength is exactly the same with the magnetic field as without. What is the initial ml value for the transition that produces a photon of this wavelength?

E) What is the final ml value for this transition?

F) One observed wavelength with the field is longer than the wavelength without the field. What is the initial ml value for the transition that produces a photon of this wavelength?

G) What is the final ml value for this transition?

H) One observed wavelength with the field is shorter than the wavelength without the field. What is the initial ml value for the transition that produces a photon of this wavelength?

I) What is the final ml value for this transition?

Explanation / Answer

There are three different transitions that are consistent with the selection rules. The initial ml values are 0,

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