A line in the Paschen series of hydrogen has a wavelength of 1010nm. From what state did the electron originate?

Question

anonymous · Answer

We can use teh Rydberg formula for this $$\frac{1}{\lambda}=R\left[\frac{1}{(n_2)^2}-\frac{1}{(n_1)^2}\right]$$where $\lambda$ is the wavelength of emitted (or absorbed) light, $R$ is teh Rydberg constant ($R=1.097373\times10^{7}\rm{ m}^{-1}$), and $n_1$ and $n_2$ are the initial and final energy respectively levels of the transition.  For the Paschen series of emission, we know that all transitions are to the n=3 state.  we now have enough information to solve for $n_1$, given that we are told that the emission line is 1010 nm.  Plugging in the numbers and solving for $n_1$ gives a value of $n_1=6.919$ which we can round up to 7.  Therefore the transition originates in the n = 7 level of the atom.

anonymous · Answer

Thanks @JonnyMcA I had the same ? :)