p41_025 - 25. (a) Promoting one of the electrons (described...

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25. (a) Promoting one of the electrons (described in problem 23) to a not-fully occupied higher level, we Fnd that the conFguration with the least total energy greater than that of the ground state has the n = 1 and 2 levels still Flled, but now has only one electron in the n = 3 level; the remaining two electrons are in the n = 4 level. Thus, E frst excited =2 E 1 +2 E 2 + E 3 E 4 µ h 2 8 mL 2 (1) 2 µ h 2 8 mL 2 (2) 2 + µ h 2 8 mL 2 (3) 2 µ h 2 8 mL 2 (4) 2 = (2+8+9+32) µ h 2 8 mL 2 = 51 µ h 2 8 mL 2 . (b) Now, the conFguration which provides the next higher total energy, above that found in part (a), has the bottom three levels Flled (just as in the ground state conFguration) and has the seventh electron occupying the n = 5 level: E second excited E 1 E 2 E 3 + E 5 µ h 2 8 mL 2 (1) 2 µ h 2 8 mL 2 (2) 2 µ h 2 8 mL 2 (3) 2
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