Ok; you know that when an electron jumps from an allowed orbit to another it absorbs/emits energy in form of a photon of energy
Your "red" photon represents a transition between two orbits (of
but red means a wavelength:
so the "red" frequency will be:
And energy:
(where
Now we need to find the two orbits (their quantum numbers) from where and toward where the electron jumped:
We use Rydberg's Formula where we know that:
and also:
(I used Rydberg Constant in
I found:
Hope it helps!