Question

Which electron transition in a hydrogen atom will emit a photon with the longest wavelength?

n = 2 to n = 1
n = 3 to n = 1
n = 1 to n = 2
n = 1 to n = 3

I would assume it would be a short electron transition since energy and wavelength are inversely related. But I am a little confused as if it would be going from to n = 2 to n = 1 or vice versa.

Answer 1

First, your rationale is OK about energy and wavelength. You KNOW the answer can't be c or d because the atom ABSORBS energy to do that. Atoms EMIT energy only when they go from a higher level to a lower level. So that leaves a or b as the only possibilities so you can guess and be right half the time. You can be right all the time by using
delta E = k[1/(n1)^2 - 1/(n2)^2]

n1 is always < n2 in this formula for emission.
For a we have
dE = k(1/1 - 1/4) = 0.75k and we don't worry about the value of k.
For b we have
dE = k(1/1 - 1/9) = approx 0.9k which makes b the more energetic one and that means the wavelength is shorter and your rationale is right on to pick a as the longer wavelength.