ψ 100 ?*
16.2 The Hydrogen Spectrum
The figure shows the transitions between Hydrogen atom states.
The ground state of Hydrogen hasn= 1 andℓ= 0. This is conventionally called the 1s state. The
convention is to nameℓ= 0 states “s”,ℓ= 1 states “p”,ℓ= 2 states “d”, andℓ= 3 states “f”.
From there on follow the alphabet with g, h, i, ...
The first excited state of Hydrogen hasn= 2. There are actually four degenerate states (not
counting different spin states) forn= 2. In terms ofψnℓm, these areψ 200 ,ψ 211 ,ψ 210 , andψ 21 − 1.
These would be called the 2s and 2p states. Remember, all values ofℓ < nare allowed.
The second excited state hasn= 3 with the 3s, 3p and 3d states being degenerate. This totals 9
states with the different allowedmvalues.
In general there aren^2 degenerate states, again not counting different spin states.
The Hydrogen spectrum was primarily investigated by measuring theenergy of photons emitted in
transitions between the states, as depicted in the figures above and below.