Calculate the crystal field stabilization energy and spin only magnetic moment for the following configuration of octahedral complexes. (i) d^(3) (in week as well as strong ligand field) (ii) d^(5) (in week as well as strong ligand field) (iii) d^(7) (in week ligand field) (iv) d^(9) (in week as well as strong ligand field).

Calculate the crystal field stabilization energy and spin only magneti

1.	Calculate the crystal field stabilization energy and spin only magnetic moment for the following configuration of octahedral complexes. (i) d^(3) (in week as well as strong ligand field) (ii) d^(5) (in week as well as strong ligand field) (iii) d^(7) (in week ligand field) (iv) d^(9) (in week as well as strong ligand field).
Answer» Solution :CFSE `=(-0.4x + 0.6y) Delta_(0)` where x = no. of electrons in `t_(2g)` and y is no. of electrons in `e_(g)` Magnetic moment `(mu)=sqrt(n(n+2))` where n = no. of unpaired electrons. (i) `d^(3)` in weak as well as strong ligand field has configuration `=t_(2g)^(3)` CFSE `=-0.4xx3=-1.2 Delta_(0)` `mu=sqrt(3(3+2))=sqrt(15)=3.83` BM (ii) `d^(5)` in strong ligand field has the configuration =`t_(2g)^(5)` (1 unpaired electron) CFSE `=-0.4xx5=-2.0 Delta_(0)` `mu=sqrt(1(1+2))=sqrt(3)=1.73` BM `d^(5)` in WEEK ligand field has the configuration `=t_(2g)^(3)e_(g)^(2)` (5 unpaired electrons) CFSE =`3XX(-0.4)+2xx(+0.6)=0` `mu=sqrt(5(5+2))=sqrt(35)=5.92` BM (iii) `d^(7)` in weak field ligand has the configuration = `t_(2)^(5)e_(g)^(2)` (3 unpaired electrons) `CFSE = 5xx(-0.4)+2(+0.6)=-0.8 Delta_(0)` (iv) `d^(9)` has only ONE possible arrangement = `t_(2g)^(6)e_(g)^(3)` (3 unpaired electrons) `CFSE = 6(-0.4)+3(+0.6)=-0.6` `mu=sqrt(3(3+2))=sqrt(15)=3.87` BM