Gross hydrogen emission spectrum

One reasonable and memorable approximation excluding any fine structure is:

E_{n} = - \frac{1 3 . 6 e V}{n ^{2}}

Hydrogen spectral series mnemonic

Hydrogen 1-2 spectral line (121.6 nm, 10.2e V)

E_{n} = - 13.6 e V [\frac{1}{2 ^{2}} - \frac{1}{1 ^{2}}] = 10.2 e V

which with Planck-Einstein relation gives about 121.6 nm (

2.47 \times 1 0^{1} 5

Hz), which is a reasonable match with the value of 121.567... from the NIST Atomic Spectra Database.

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