# Harvard Astronomy 201b

## CHAPTER: Hydrogen Slang

In Book Chapter on February 12, 2013 at 10:02 pm

Lyman limit: the minimum energy needed to remove an electron from a Hydrogen atom. A “Lyman limit photon” is a photon with at least this energy.

$E = 13.6 {\rm eV} = 1~ {\rm Rydberg} = hcR_{\rm H}$,

where $R_{\rm H}=1.097 \times 10^{7} {\rm m}^{-1}$ is the Rydberg constant, which has units of $1/\lambda$. This energy corresponds to the Lyman limit wavelength as follows:

$E = h\nu = hc/\lambda \Rightarrow \lambda=912 \AA$.

Lyman series: transitions to and from the n=1 energy level of the Bohr atom. The first line in this series was discovered in 1906 using UV studies of electrically excited hydrogen gas.

Balmer series: transitions to and from the n=2 energy level. Discovered in 1885; since these are optical transitions, they were more easily observed than the UV Lyman series transitions.

There are also other named series corresponding to higher n. Examples include Paschen (n=3), Brackett (n=4), and Pfund (n=5). The wavelength of a given transition can be computed via the Rydberg equation

$\frac{1}{\lambda}=R_{\rm H} \big(\frac{1}{n_f^2}-\frac{1}{n_i^2}\big)$.

Note that the Lyman (or Balmer, Paschen, etc.) limit can be computed by inserting $n_i=\infty$.

Lyman continuum corresponds to the region of the spectrum near the Lyman limit, where the spacing between energy levels becomes comparable to spectral line widths and so individual lines are no longer distinguishable.