Someone notices that no spectral line joins sodium's and terms

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · Radiative transitions, external fields and collisions

Reading the Spectrum, Ch Radial functions, orbital size and Rydberg states

Problem

Someone notices that no spectral line joins sodium's

3s

and

4s

terms, and argues: "since the line is missing, sodium must not actually have a

4s

level." The measured term values are

T(3s) = 41449.45\,\mathrm{cm^{-1}}

T(4s) = 15710\,\mathrm{cm^{-1}}

and

T(3p) = 24493\,\mathrm{cm^{-1}}

. ((a)) Compute the wavenumber and vacuum wavelength that the

4s

3s

line would have if it occurred. ((b)) Apply the dipole selection rule to

4s \to 3s

and state whether it is allowed. ((c)) Compute the wavelength of the

4s \to 3p

line and explain what its presence tells you about the claim that sodium has no

4s

level.

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