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Draw a diagram of permitted transitions between the terms .^(2)P_(3//2) and .^(2)S_(1//2) in a weak magnetic field. Find the displacements (in rad//units) of Zeeman components of that line in a magnetic field B= 4.5kG. |
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Answer» Solution :For the `.^(2)P_(3//2)` LEVEL `g=4//3` (SEE above) and the energies of sublevels are `E'=E'_(0)-(4)/(3)mu_(B)M'Ƶ` where `M'Ƶ= +-(1)/(2)` for the four sublevels For the `.^(2)S_(1/2)`level, `g=2` (since `L=0`) and `E=E_(0)-2mu_(B)BM_(Ƶ)` where `M_(Ƶ) = +-(1)/(2)` PERMITTED transitions must have `DeltaM_(Ƶ)=0, +-1` Thus only the following transitions occur `{:((3)/(2),rarr,(1)/(2),,),(-3//2,,rarr,,-1//2):}}Delta omega=+-mu_(B) B// ħ = 3.96xx10^(10)rad//s` `{:((1)/(2),rarr,(1)/(2),,),(-(1)/(2),,rarr,,-(1)/(2)):}} Delta omega= +-(1)/(3)mu_(B) B// ħ= 1.32xx10^(10) rad//s` `{:((1)/(2),rarr,-(1)/(2),,),(-(1)/(2),,rarr,,(1)/(2)):}} Delta omega= +-(5)/(3) (mu_(B)B)/( ħ)= 6.6xx10^(10) rad//s` These six lines are shown below 
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