The prominent yellow doublet lines in the spectrum of sodium resultfrom the tran

Question

The prominent yellow doublet lines in the spectrum of sodium resultfrom the transitions from the 3P3/2 to the3P1/2 states to the ground state. The wavelengths ofthese two lines are 589.0 nm and 589.6 nm. (a) Calculate theenergies (in eV) of the photon corresponding to these wavelengths.(b) The difference in energy of these photons equals the differencein energy E of the 3P3/2 and 3P1/2states. This energy difference is due to the spin-orbit effect.Calculate E. (c) If the 3P electron in sodium sees aninternal magnetic field B, the spin-orbit energy splitting will beof the order of E = 2BB, whereB is the Bohr magneton. Estimate B from the energydifference E found in part (b).

Explanation / Answer

(a)   energy of each photon is just   E =h c /     so: . for   589.0nm        E = 4.14 x10-15 * 3.00 x 108 / 589 x10-9 = .                  = 2.108659 eV . for   589.6nm        E = 4.14 x10-15 * 3.00 x 108 / 589.6 x10-9 = .                  = 2.106513 eV . (b)    E = 2.108659 -2.106513 = 0.002146 eV . (c)   first convert the energy toJoules:        0.002146 eV = 3.434 x 10-22 Joules . Then...         B = E / 2B = 3.434 x10-22 / 2 * 9.274015 x 10-24 = .                           =    18.5 Tesla for   589.6nm        E = 4.14 x10-15 * 3.00 x 108 / 589.6 x10-9 = .                  = 2.106513 eV . (b)    E = 2.108659 -2.106513 = 0.002146 eV . (c)   first convert the energy toJoules:        0.002146 eV = 3.434 x 10-22 Joules . Then...         B = E / 2B = 3.434 x10-22 / 2 * 9.274015 x 10-24 = .                           =    18.5 Tesla

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