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The wavelength of the Na yellow doublet (.^(2)P rarr .^(2)S) are equal to 589.59 and 589.00nm. Find: (a) the ratio of the intervals between neighbouring sublevels of the Zeeman splitting of the term .^(2)P_(3//2) and .^(2)P_(1//2) in a weak magnetic field, (b) the magnetic field induction B at which the interval between neighbouring sublevels of the Zeemansplitting of the term .^(2)P_(3//2) is eta=50 times smaller than the natural splitting of the .^(2)P. |
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Answer» SOLUTION :(a) For the `.^(2)P_(3//2)` term `g=1+((3)/(2)xx(5)/(2)+(1)/(2)xx(3)/(2)-1xx2)/(2xx(3)/(2)xx(5)/(2))= 1+(10)/(30)=(4)/(3)` and the enrgy of the `.^(2)P_(3//2)` sublevels will be `E(M_(Ƶ))=E_(0)-(4)/(3)mu_(B)BM_(Ƶ)` where `M_(Ƶ)= +- (3)/(2),+-(1)/(2)`. Thus, between NEIGHBOURING sublevels. `deltaE(.^(2)P_(3//2))=(4)/(3)mu_(B)B` For the `.^(2)_(1//2)` term `g=1+((1)/(2)xx(3)/(2)+(1)/(2)xx(3)/(2)-1xx2)/(2xx(1)/(2)xx(3)/(2))` `=1+(6-8)/(6)=1-(1)/(3)=(2)/(3)` and the SEPERATION between the two sublevels into which the `.^(2)P_(1//2)` term will split is `deltaE(.^(2)P_(1//2))=(2)/(3)mu_(B)B` The ratio of hte two splitting is `2:1` (b) The interval betweenneighbouring ZEEMAN sublevels of the `.^(2)P_(3//2)` term is `(4)/(3)mu_(B)B`. The energy seperation between `D_(1)` and `D_(2)` lines is `(2piħc)/(lambda^(2)) Delta lambda` (this is the natural seperation of the `.^(2)P` them) Thus `(4)/(3)mu_(B)=(2 piħcDelta lambda)/(lambda^(2)eta)` or `B=(3 piħcDelta lambda)/(2mu_(B)lambda^(2) eta)` Substitution gives `B= 5.46kG` |
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