For which of the following transitions would a hydrogen atom absorb the lowest energy photon?

This question is kind of a freebie. Of the choices only one shows a lower to higher level transition which is what happens when a photon is absorbed.

If you want a more detailed understanding, look at this diagram.

https://en.wikipedia.org/wiki/Hydrogen_spectral_se...

Keep in mind that the longer the wavelength, the lower the energy.

So the lowest energy (longest wavelength) transition on the graph is the 3<--->4.

It's lower energy than 1<--->2 and 2<--->3

By implication the higher the single level transition, the lower the energy difference.

So even though a 4<--->5 transition is not shown on the diagram it would be lower energy than a 3<--->4.

When a hydrogen atom absorbs energy, as it does when an electric discharge passes through it,

the electron is raised from the orbit having n = 1 to a higher orbit, to n = 2 or n = 3 or even higher. The hydrogen atom is now in an excited state. These higher orbits are less stable than the lower ones, so the electron quickly drops to a lower orbit.

Answer is A.) n = 4 to n = 5

Look at the following websites:

http://web.mst.edu/~tbone/Subjects/TBone/atomicrev...

https://chemistry.tutorvista.com/inorganic-chemist...