The percentage of fine structure splitting of the 2 p state compared to photon energy emitted in the 2 p → 1 s transition.

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Chapter 36, Problem 52P

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The percentage of fine structure splitting of the 2p state compared to photon energy emitted in the 2p→1s transition.

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A hydrogen atom undergoes a transition from a 2p state to the 1s ground state. In the absence of a magnetic field, the wavelength 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 S 1s transition? What are the ml values for the initial and final states for the transition that leads to each photon wavelength? (b) One observed wavelength is exactly the same with the magnetic field as without. What are the initial and final ml values for the transition that produces a photon of this wavelength? (c) One observed wavelength with the field is longer than the wavelength without the field. What are the initial and final ml values for the transition that produces a photon of this wavelength? (d) Repeat part (c) for the wavelength that is shorter than the wavelength…

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b) One of the n = 5 terms of hydrogen is split by spin-orbit coupling into two levels with an energy difference of 0.0039 cm ¹. Determine the orbital angular momentum quantum number, I, for this state and predict the analogous splitting in Li2+. The fine structure constant, a = 0.0072973.