The prominent yellow doublet lines in the spectrum of sodium result from transis

Question

The prominent yellow doublet lines in the spectrum of sodium result from transistions from the 3P_3/2 and 3P_1/2 states to the ground state.  The wavelengths of these two lines are 589.0 nm and 589.6 nm.  (a) Calculate the energies in eV of the photons corresponding to these wavelengths.  (b) The difference in energy on these two photons equals the difference in energy E of the 3P_3/2 and 3P_1/2 states.  This energy difference is due to the spin-orbit effect.  Calculate E.  (c) If the 3p electron in sodium sees an internal magnetic field B, the spin-orbit energy splitting will be of the order of E = 2_B*B, where _B is the Bohr Magneton.  Estimate B from the energy difference E found in part (b).

Explanation / Answer

(a) E of a photon = h(c/) E_1 = h(c/589.0nm) = 3.375 x 10^-19 J E_2 = h(c/589.6nm) = 3.371 x 10^19 J (b) E = E_1 - E_2 E = 3.43443807 x 10^-22 J (c) E = 2_B * B _B = 5.79 x 10^-5 eV/T B = E/2*_B 3.43443807 x 10^-22 J / (2* 5.79 x 10^-5 eV/T) = B =2.9658 x 10^-18

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