Please show all work for question below: A hydrogen atom in its ground state is

Question

Please show all work for question below:

A hydrogen atom in its ground state is excited to the n = 5 level. It then makes a transition directly to the n = 2 level before returning to the ground state. Note: There are TWO transitions here. First from n = 5 to n = 2, and then from n = 2 to n = 1. (You will discover that only ONE of those transitions result in a visible wavelength, the other is from the Lyman series or far UV part of the spectrum.)

a) What are the wavelengths of the emitted photons?
b) Would any of the emitted wavelengths be in the visible region?

Explanation / Answer

a)

For n=5 to n=1

E = -13.6 (1/5^2 - 1/2^2)

= -13.6 * (4 - 25)/ 100

= 2.85 eV

wavelength = 1240 / 2.85

= 435.08 nm which is in the visible region

For n = 2 to n = 1

E = -13.6 (1/52^2 - 1/1^2)

= -13.6 * (1 - 4)/ 4

= 10.2 eV

wavelength = 1240 / 10.2

= 121.56 nm which is not in the visible region

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