Can you help me with this atomic structure and periocity problem?

Question

Calculate the longest and shortest wavelengths of light emitted by electrons in the hydrogen atom that begin in the n=6 state and then fall to states with smaller values of n.

Answer 1

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/n_f² - 1/n_i²) = 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.