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Quantum. Please answer in full. Thanks.

The transition energies of the planar conformation of the cyclodecapentaene molecule, C10H10, can be approximated by those of a particle on a ring, given by:

Where

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Answer #1

a) f and i are quantum numbers so they are integers

so let's first write pairs of f,i such that f>i:

(1,0),(2,0),(2,1),(3,0),(3,1),(3,2),(4,0),(4,1),(4,2),(4,3),5,0),(5,1),(5,2),(5,3),(5,4)...............................

let's write the difference between the pairs:

(f212)

1,4,3,9,8,5,16,15,12,7,25,24,21,16,.....................

so the 1st fiive least energy odered pairs of (i,j) are:

(1,0),(2,1),(2,0),(3,2),(4,3)

b) The transitions in cyclooctatetraene dianion decrease because the moment of inertia of cyclooctatetraene dianion increases ar it is more heavier and has a bigger radius than cyclodecapentaene.

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Answer 1

a) f and i are quantum numbers so they are integers

so let's first write pairs of f,i such that f>i:

(1,0),(2,0),(2,1),(3,0),(3,1),(3,2),(4,0),(4,1),(4,2),(4,3),5,0),(5,1),(5,2),(5,3),(5,4)...............................

let's write the difference between the pairs:

(f212)

1,4,3,9,8,5,16,15,12,7,25,24,21,16,.....................

so the 1st fiive least energy odered pairs of (i,j) are:

(1,0),(2,1),(2,0),(3,2),(4,3)

b) The transitions in cyclooctatetraene dianion decrease because the moment of inertia of cyclooctatetraene dianion increases ar it is more heavier and has a bigger radius than cyclodecapentaene.