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A certain atom has three electrons (s,p and d) in addition to filled shells, and is in a state with the greatest possible total mechanical moment for a given configuraion. In the corresponding vector model of the atom find the angle between the spin momentum and the total anular momentum of the given atom |
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Answer» <P> Solution :The total angular momentum is greatest when `L,S` are both greatest and add to form `J`. Now for triplet of `s,p,d` electronsMaximum SPIN `RARR S=(3)/(2)` corresponding to `M_(s)ħsqrt((3)/(2).(5)/(2))=(ħsqrt(15))/(2)` Maximum ORBITAL angular momentum `rarr` `L=3` corresponding to `M_(L)=ħsqrt((3)/(2).(5)/(2))=(ħsqrt(15))/(2)` Maximum total angular momentum `J=(9)/(2)` corresponding to `M=(ħ)/(2)sqrt(99)` In vector model `vec(L)=vec(J)-vec(S)` or in magnitude squared `L(L+1)ħ^(2)=J(J+1)ħ^(2)+S(S+1)ħ^(2)-2vec(J).vec(S)` Thus `cos( lt vec(J),vec(S))=(J(J+1)+S(S+1)-L(L+1))/(2sqrt(J(J+1)sqrt(S(S+1))))` Substitution GIVES `lt (vec(J),vec(S))=31.1^(@)`. |
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