A sodium atom in a static electric field of emits its yellow D line

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Radiative transitions, external fields and collisions · Radiative transitions, external fields and collisions

Reading the Spectrum, Ch Atoms in an electric field: the Stark effect and polarizability

Problem

A sodium atom in a static electric field of E=1.0×107 V m−1E = 1.0\times10^7\,\mathrm{V\,m^{-1}} emits its yellow D line, a transition from an excited 3p3p level down to the 3s3s ground level. The polarizabilities are α/4πϵ0=24.1×10−30 m3\alpha/4\pi\epsilon_0 = 24.1\times10^{-30}\,\mathrm{m^3} for the 3s3s ground level and α/4πϵ0=53.2×10−30 m3\alpha/4\pi\epsilon_0 = 53.2\times10^{-30}\,\mathrm{m^3} for this 3p3p level (an excited level, whose polarizability need not equal the ground level's). ((a)) Calculate the quadratic Stark shift of each level, in cm−1\mathrm{cm^{-1}}. ((b)) Hence find the shift of the D-line photon energy, in cm−1\mathrm{cm^{-1}} and in MHz, and state whether the line moves to higher or lower frequency. ((c)) The line's Doppler width in the vapour is 0.057 cm−10.057\,\mathrm{cm^{-1}}, and a grating spectrograph resolves 1.0×10−3 nm1.0\times10^{-3}\,\mathrm{nm} at 589 nm589\,\mathrm{nm}. Find the size of the wavelength shift, and judge whether the shift is measurable as a change of wavelength or as a change of frequency.

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