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Consider the ground state and $n = 2$ states of hydrogen atom. Indicate in the diagram (Fig. 1.14) the complete spectroscopic notation for all four states. There are four corrections to the indicated level structure that must be considered to explain the various observed splitting of the levels. These corrections are: (a) Lamb shift, (b) fine structure, (c) hyperfine structure, (d) relativistic effects. (1) Which of the above apply to the $n=1$ state? (2) Which of the above apply to the $n=2, l=0$ state? The $n=2, l=1$ state? (3) List in order of decreasing importance these four corrections. (i.e. biggest one first, smallest last). Indicate if some of the corrections are of the same order of magnitude. (4) Discuss briefly the physical origins of the hyperfine structure. Your discussion should include an appropriate mention of the Fermi contact potential.
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\text{Hyperfine structure}; \text{Lamb shift, Hyperfine structure}; \text{Fine structure, Lamb shift, Hyperfine structure}; E_m, E_D, E_{so} > \text{Lamb shift} \gtrsim \text{Hyperfine structure}; \text{Hyperfine structure arises from:}; \text{(a) Interaction between the nuclear magnetic moment and the magnetic field at the proton due to the electron's orbital motion,}; \text{(b) Dipole-dipole interaction between the electron and the nuclear magnetic moment,}; \text{(c) The Fermi contact potential due to the interaction between the spin magnetic moment of the electron and the internal magnetic field of the proton.}
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2
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(a) The ground state of the hydrogen atom is split by the hyperfine interaction. Indicate the level diagram and show from first principles which state lies higher in energy. (b) The ground state of the hydrogen molecule is split into total nuclear spin triplet and singlet states. Show from first principles which state lies higher in energy.
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\text{triplet } F = 1 \text{ is an excited state and singlet } F = 0 \text{ is the ground state}; \text{The spin triplet state lies higher in energy than the singlet state}
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3
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Lyman alpha, the $n = 1$ to $n = 2$ transition in atomic hydrogen, is at 1215 脜. (a) Define the wavelength region capable of photoionizing a H atom in the ground level ($n = 1$). (b) Define the wavelength region capable of photoionizing a H atom in the first excited level ($n = 2$). (c) Define the wavelength region capable of photoionizing a He$^+$ ion in the ground level ($n = 1$). (d) Define the wavelength region capable of photoionizing a He$^+$ ion in the first excited level ($n = 2$).
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911 \, \text{脜}; 3645 \, \text{脜}; 228 \, \text{脜}; 1215 \, \text{脜}
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