We dont know what atoms are involved so assuming that the bond length is 0.15 nm is an unwarranted assumption, and is in fact unnecessary. The problem states that the molecules are similar i.e., they have the same bond length.

Bond length = b
Length of 10 atom chain = 9b
Length of 6 atom chain = 5b

The ground state configuration of the 10 electrons is:
Therefore the lowest energy transition is from n = 5 to n = 6.


The ground state configuration of the 6 electrons is:
Therefore the lowest energy transition is from n = 3 to n = 4.


Divide DE6 by D E10

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