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What are the quantum numbers (n, 1, m) of the 1s, 2s, and 2p, orbitals for the (A) Hydrogen atom? (B, Write down a normalized linear combination (superposition) of the 1s, 2s, and 2pz wavefunctions containing equal weights from each orbital. First write in terms of kets, and then as a function of r, 0, and o. What would the wavelength of light be corresponding to an electron transitioning from the 2p, orbital to the 1s orbital in the presence of a magnetic field of 1 Tesla? (C)

What are the quantum numbers (n, 1, m) of the 1s, 2s, and 2p, orbitals for the (A) Hydrogen atom? (B, Write down a normalized linear combination (superposition) of the 1s, 2s, and 2pz wavefunctions containing equal weights from each orbital. First write in terms of kets, and then as a function of r, 0, and o. What would the wavelength of light be corresponding to an electron transitioning from the 2p, orbital to the 1s orbital in the presence of a magnetic field of 1 Tesla? (C)

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4 Spectrum of the Hydrogen Atom. (A) Hydrogen atom? (B, What are the quantum numbers (n, 1, m₁) of the 1s, 2s, and 2p, orbitals for the Write down a normalized linear combination (superposition) of the 1s, 2s, and 2pz wavefunctions containing equal weights from each orbital. First write in terms of kets, and then as a function of r, 0, and o. (C) What would the wavelength of light be corresponding to an electron transitioning from the 2p, orbital to the 1s orbital in the presence of a magnetic field of 1 Tesla? (D) Let's imagine that an electron in a Hydrogen atom is sitting in the 2p orbital. Along comes a spectroscopist who is interested in shining light on this system to promote transition to the 3d22 and 3d2-2 orbitals. How many peaks in the absorption spectrum do you expect to see corresponding to these two possible transitions? Justify your answer. (E) You now decide to apply a magnetic field of strength 1 Tesla to your system. Describe how you would expect the experimental spectrum to change. Assume that you can ignore any effects of electron spin in your system. (F) Describe how you would expect the experimental spectrum to change from (E) if you did include the effect of the single electron spin interacting with the magnetic field. Assume that the spin does not flip when transitioning between the orbitals.
Transcribed Image Text:4 Spectrum of the Hydrogen Atom. (A) Hydrogen atom? (B, What are the quantum numbers (n, 1, m₁) of the 1s, 2s, and 2p, orbitals for the Write down a normalized linear combination (superposition) of the 1s, 2s, and 2pz wavefunctions containing equal weights from each orbital. First write in terms of kets, and then as a function of r, 0, and o. (C) What would the wavelength of light be corresponding to an electron transitioning from the 2p, orbital to the 1s orbital in the presence of a magnetic field of 1 Tesla? (D) Let's imagine that an electron in a Hydrogen atom is sitting in the 2p orbital. Along comes a spectroscopist who is interested in shining light on this system to promote transition to the 3d22 and 3d2-2 orbitals. How many peaks in the absorption spectrum do you expect to see corresponding to these two possible transitions? Justify your answer. (E) You now decide to apply a magnetic field of strength 1 Tesla to your system. Describe how you would expect the experimental spectrum to change. Assume that you can ignore any effects of electron spin in your system. (F) Describe how you would expect the experimental spectrum to change from (E) if you did include the effect of the single electron spin interacting with the magnetic field. Assume that the spin does not flip when transitioning between the orbitals.
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