Rydberg formula for hydrogen

Question

I've been told that if a hydrogen atom is exposed to electromagnetic radiation of wavelength $\lambda$ such that Rydberg's formula

$$\frac{1}{\lambda}=R\left(\frac{1}{n_{1}^2}-\frac{1}{n_{2}^2}\right)$$

is valid for two integers $n_1$ and $n_2$, then the electron in the hydrogen atom would go from level $n_1$ to level $n_2$.

1. If this is true, what would happen if, given a fixed $\lambda$ and an initial energy level $n_1$, $n_2$ turns out not to be an integer?

2. I've been reading that, actually, that equation doesn't describe what I've written above but the contrary process. Namely, that if the electron of the hydrogen atom is already excited and at an energy level $n_2$, then when it goes back to a lower level $n_1$ a photon of wavelength $\lambda$ is emitted. Are both processes (electron going from $n_1$ to $n_2$ and viceversa) described by that equation or just one of them?

3. I'm having trouble getting this whole level thing. I mean, a hydrogen atom has only one orbit, so how could its only electron go from one orbit to another if theres is just one of them?

Answer 1

1. Such a transition can't occur because $n_1$ and $n_2$ must be integers since there's no state with non-integer primary quantum number. So hydrogen atom doesn't emit a photon which has wavelength that doesn't satisfy Rydberg's formula.
2. This formula explains both emission and absorption. Emission spectrum and Absorption spectrum of the same atom has same line because emission process is just the reverse process of absorption process.
3. The election in the hydrogen can be in 1s orbital or 2s orbital, etc. Electron exists in an orbital at some time but there can be transitions. It doesn't mean that hydrogen has only one orbital.