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Chapter 6: Q60P (page 1405)

A lithium atom has three electrons, and the 2S1/2 ground-state electron configuration is 1s22s. The 1s22pexcitedstate is split into two closely spaced levels, 2P3/2 and 2P1/2 , by thespin-orbit interaction (see Example 41.7 in Section 41.5). A photonwith wavelength 67.09608 mm is emitted in thep3/22鈫�s1/22transition, and a photon with wavelength 67.09761 mm is emittedin the p1/22鈫�s1/22transition. Calculate the effective magneticfield seen by the electron in the 1s22pstate of the lithium atom.

Short Answer

Expert verified

The effective magnetic field is 7.28脳10-3T.

Step by step solution

01

Identification of the concept

The potential energy is given as,

U=鈥�渭zB鈥︹赌︹赌︹赌︹赌︹赌︹赌︹赌�(1)

Where B is the effective magnetic field magnitude and in turn, is given as,

B=鈭�E渭B鈥︹赌︹赌︹赌︹赌�..鈥︹赌︹赌�..(2)

Here, 渭B is the Bohr Magneton which is expressed as,

渭B=eh2m=eh4蟺尘

02

Determination of the effective magnetic field.

From equation (2), where the energy difference can be calculated as,

鈭�E=hc位B=hc渭B位1-位2位1位2=2蟺尘ce位1-位2位1位2

Substituting all the values, the effective magnetic field is found to be 7.28脳10-3T.

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