The Hydrogen Spectrum

The figure shows the transitions between Hydrogen atom states.

The ground state of Hydrogen has \bgroup\color{black}$n=1$\egroup and \bgroup\color{black}$\ell=0$\egroup. This is conventionally called the 1s state. The convention is to name \bgroup\color{black}$\ell=0$\egroup states ``s'', \bgroup\color{black}$\ell=1$\egroup states ``p'', \bgroup\color{black}$\ell=2$\egroup states ``d'', and \bgroup\color{black}$\ell=3$\egroup states ``f''. From there on follow the alphabet with g, h, i, ...

The first excited state of Hydrogen has \bgroup\color{black}$n=2$\egroup. There are actually four degenerate states (not counting different spin states) for \bgroup\color{black}$n=2$\egroup. In terms of \bgroup\color{black}$\psi_{n\ell m}$\egroup, these are \bgroup\color{black}$\psi_{200}$\egroup, \bgroup\color{black}$\psi_{211}$\egroup, \bgroup\color{black}$\psi_{210}$\egroup, and \bgroup\color{black}$\psi_{21-1}$\egroup. These would be called the 2s and 2p states. Remember, all values of \bgroup\color{black}$\ell<n$\egroup are allowed.

The second excited state has \bgroup\color{black}$n=3$\egroup with the 3s, 3p and 3d states being degenerate. This totals 9 states with the different allowed \bgroup\color{black}$m$\egroup values.

In general there are \bgroup\color{black}$n^2$\egroup degenerate states, again not counting different spin states.

The Hydrogen spectrum was primarily investigated by measuring the energy of photons emitted in transitions between the states, as depicted in the figures above and below.

Transitions which change \bgroup\color{black}$\ell$\egroup by one unit are strongly preferred, as we will later learn.

Jim Branson 2013-04-22