J.R. S. answered 11/05/17
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Ph.D. in Biochemistry--University Professor--Chemistry Tutor
If I understand the problem, they are asking for the energy of an electron falling from n=6 to n=5 and from n=6 to n=1.
For n=6 to n=5 you can do the following:
1/λ = 1.097x107m-1(1/nf2 - 1/ni2) = 1.097x107m-1 (1/52 - 1/62) = 1.097x107m-1 (1/25 - 1/36)
1/λ = 1.097x107m-1 (0.04 - 0.0278)
1/λ = 1.338x105m-1
λ = 7.47x10-6 m = 7470 nm
Do the same calculations for n=1. You should end up with a shorter wavelength that above.

J.R. S.
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