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Determine the spin angular momentum of an atom in the state D_(2) if the maximum value of the magnetic moment projection in thatl state is equal to four Bohr magnetons. |
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Answer» Solution :The expression for the PROJECTION of the MAGNETIC moment is `mu_(Z)= gm_(J)mu_(B)` where `m_(J)` is the projection of `vec(J)` on the `Ƶ`-axis. Maximum value of the `m_(J)` is `J`. THUS `gJ=4` Since `J=2`, we get `g=2`. Now `2=1+(J(J+1)+S(S+1)-L(L+1))/(2J(J+1))` `=1+(6+S(S+1)-6)/(2xx6), as L=2` `=1+(S(S+1))/(12)` ltnrgt Hence `S(S+1)=12 or S=3` Thus `M_(s)= ħsqrt(3xx4)=2sqrt(3) ħ`. |
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