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Assuming LS coupling, determine the possible states (term symbols) of an atom with two optical

\n

electrons in the configuration 2p13p1

\n

Wrong answers will earn negative marks.

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For each of the Grotrian diagrams below, determine whether the labelled transitions are allowed, and if not, choose which of the transition rules have been violated.  Spin-orbit coupling is not considered in this question.

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ΔL = ±1 and 0 if Δl = ±1 

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ΔmJ =0, ±1 (not 0 to 0 if ΔJ= 0)

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ΔJ= 0,±1 (not 0 to 0) 

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ΔS= 0 

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ΔL = ±1 and 0 if Δl = ±1 

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ΔmJ =0, ±1 (not 0 to 0 if ΔJ= 0)

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ΔJ= 0,±1 (not 0 to 0) 

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ΔS= 0 

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ΔL = ±1 and 0 if Δl = ±1 

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ΔmJ =0, ±1 (not 0 to 0 if ΔJ= 0)

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ΔJ= 0,±1 (not 0 to 0) 

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ΔS= 0 

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ΔL = ±1 and 0 if Δl = ±1 

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ΔmJ =0, ±1 (not 0 to 0 if ΔJ= 0)

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ΔJ= 0,±1 (not 0 to 0) 

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ΔS= 0 

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ΔL = ±1 and 0 if Δl = ±1 

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ΔmJ =0, ±1 (not 0 to 0 if ΔJ= 0)

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ΔJ= 0,±1 (not 0 to 0) 

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ΔS= 0 

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Starting with the basic grotrian diagram in Figure 1.1, add arrows to show the allowed transitions up to n=3 (ignore lines starting at the n=4 level), and add in the spin-orbit splitting of the energy levels.

\n

Next, apply the transition rules to determine the number of allowed transitions between the following states (Hint: not the number of emission lines, the number of allowed transitions).

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2 1P --> 1 1S

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3 1S --> 2 1P

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3 1D --> 2 1P

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3 3S --> 2 3P

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3 3P --> 2 3S

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3 3D --> 2 3P

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One of the n=5 states of hydrogen is split by spin-orbit coupling into two levels with an energy difference of 0.0039 cm-1. (An energy can be obtained by multiplying cm-1 by hc)

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The l quantum number for this state is [[0]]

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Predict the analogous splitting for Li2+ (the fine-structure constant $\\alpha$ = 0.0072973)

\n

Energy difference = [[0]] cm-1

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A spectral line at 330.23 nm in the spectrum of a particular atom corresponds to a 4p (2P3/2) to 3s (2S1/2) transition. Determine the wavelengths of the various components which appear when the lines split by a magnetic field of 1 Tesla.  Warning: wrong answers will give you negative marks!

\n

Bohr magneton $\\mu_s$=9.273 X 10-24 J T-1

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