Frequency of Photons in Hydrogen Gas: 100 Electrons in n=3 Orbit

[abohn1]

1. In a collection of hydrogen gas, 100 electrons are located in the n=3 orbit.

A. What is the frequency of a photon that could have been absorbed to cause an
electron to transition from its ground state to the n=3 orbit?

Now, as these electrons return to their ground states, assume that every available transition
is equally likely to happen (i.e. if there are two options, will take each option).

B. How many different frequencies will be seen in the photons emitted as the
electrons return to their ground state?

C. What are the frequencies?

D. How many photons of each frequency will be seen?

I think I'm okay on part A, I got 2.9 x 10^15 Hz...but the rest I have no idea where to begin. A little help just on what approach to take?

 

[Zakalwe]

First of all, I hate to be pedantic, but a "collection of hydrogen gas" implies H₂ molecules, not Hydrogen atoms. The energy levels in the molecule are completely different. Unless you were given the energy of the levels in an H<sub>2[\SUB] molecules, it seems unlikely that you're asked to derive them, so I will assume that they are talking about a collection of Hydrogen atoms.

A. I get the same answer as you.

B. You have electrons in level 3. They will decay to level 1. There are two possible decay "routes": either 3 -> 1 or 3 -> 2 -> 1. Each jump results in the emission of a photon (at least that's what I assume from the question). You should be ok with the rest.</sub>