Saved Bookmarks
| 1. |
What kind of Zeeman effect, normal or anomalous, is observed in a weak magnetic field in the case of spectral lines caused by the follwing transitions: (a).^(1)P rarr .^(1)S,(b).^(2)D_(5//2) rarr .^(2)P_(3//2), (c ) .^(3)D_(1) rarr .^(3)P_(0) , (d) .^(5)I_(5) rarr .^(5)H_(4) ? |
|
Answer» Solution :(a) The term `.^(1)P_(1)` splits into `3` lines with `M_(Ƶ)` where `g=1+(1xx2+0-1xx2)/(2xx1xx2)=1` The term `.^(1)S_(0)` does not split in weak magnetic field. THUS the transition between `.^(1)P_(1)&.^(1)S_(0)` will result in `3` lines i.e., normal Ƶeeman triplet. (b) The term `.^(2)D_(5//2)` will split ot in`6` terms in accordance with the formula `DeltaE=-gmu_(B)M_(Ƶ)` `M_(Ƶ)= +-(5)/(2), +-(3)/(2),+-(1)/(2)`, and `g=1+(5xx7+1xx3-4xx2xx3)/(2xx5xx7)=(6)/(5)` THER term `.^(2)P_(3//2)` will also split into 4 lines in accordance with the above formula with `M_(Ƶ)= +-(3)/(2)+-(1)/(2)` and `g=1+(3xx5+1xx3-4xx1xx2)/(2xx3xx5)=(4)/(3)=(4)/(3)` It is seen that the `Z` eeman splitting is auomalous as `g` factors are DIFFERENT. (c )`.^(3)D_(1) rarr ^(3)P_(0)` The term `.^(3)D_(1)` splits into `3` levels`(g=5//2)` The term `.^(3)P_(0)` does not split. Thusthe `Z` eeman spectrum is normal. (d) For the `5l_(5)` term `g=1+(5xx6+2xx3-6xx7)/(2xx5xx6)` `=1+(36-42)/(60)=1-(1)/(10)=(9)/(10)` For the `.^(5)H_(4)` term `g=1+(4xx5+2xx3-5xx6)/(2xx4xx5)=1+(26-30)/(40)=(9)/(10)` We see that the splitting in the two levels given by `DeltaE= 0g mu_(B)BM_(Ƶ)` is the same though the number of levels is different (11 and 9). It is then easy to see that only the lines with following energies occur `ħ omega_(0),ħ omega_(0)+- gmu_(B)B`. The `Z` eeman pattern is normal. 
|
|