Question

The wavelength of the yellow doublet components of the resonance `Na` line caused by the transition `3p rarr 3S` are equal to `589.00` and `589.56nm`. Find the splitting of the `3P` term in `eV` units.

Answer 1

The splitting of the `Na` lines is due to the fine structure splitting of `3p` lines (The `3S` state in nearly single except for possible hyperfine effects). The splitting of the `3p` level then equals the energy difference
`DeltaE=(2piħc)/(lambda_(1))-(2piħc)/(lambda_(2))=(2piħc(lambda_(2)-lambda_(1)))/(lambda_(1)lambda_(2))~~(3piħcDelta lambda)/(lambda^(2))`
Here `Delta lambda`= wavelength difference & `lambda=` average wavelength. Substitution gives
`DeltaE=2.0meV`