p40_010 - 2 E 1 3 2 E 1 ) = 14 E 1 , we get 2 n + 1 = 14,...

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10. (a) Let the quantum numbers of the pair in question be n and n + 1, respectively. Then E n +1 E n = E 1 ( n +1) 2 E 1 n 2 =(2 n +1) E 1 . Letting E n +1 E n =(2 n +1) E 1 =3( E 4 E 3 )=3(4 2 E 1 3 2 E 1 )=21 E 1 , we get 2 n + 1 = 21, or n = 10. (b) Now letting E n +1 E n =(2 n +1) E 1 =2( E 4 E 3 )=2(4
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Unformatted text preview: 2 E 1 3 2 E 1 ) = 14 E 1 , we get 2 n + 1 = 14, which does not have an integer-valued solution. So it is impossible to Fnd the pair of energy levels that Fts the requirement....
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