Question
Which of the following statements is correct about $${\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{2 + }}$$ complex?
A.
Electronic configuration $$ = 3{d^7} \to t_{2g}^5\,e_g^2,$$ no. of unpaired electrons $$ = 3,\mu = 3.87\,B.M.$$
B.
Electronic configuration $$ = 3{d^6} \to t_{2g}^4\,e_g^2,$$ no. of unpaired electrons $$ = 2,\mu = 2.87\,B.M.$$
C.
Electronic configuration $$ = 3{d^7} \to t_{2g}^6\,e_g^1,$$ no. of unpaired electrons $$ = 1,\mu = 2.87\,B.M.$$
D.
Electronic configuration $$ = 3{d^7} \to t_{2g}^3\,e_g^4,$$ no. of unpaired electrons $$ = 3,\mu = 3.87\,B.M.$$
Answer :
Electronic configuration $$ = 3{d^7} \to t_{2g}^5\,e_g^2,$$ no. of unpaired electrons $$ = 3,\mu = 3.87\,B.M.$$
Solution :
In $${\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{2 + }},$$ oxidation state of $$Co = + 2,C{o^{2 + }} = 3{d^7}$$
$$\eqalign{ & \mu = \sqrt {n\left( {n + 2} \right)} \cr & \,\,\,\, = \sqrt {3\left( {3 + 2} \right)} \cr & \,\,\,\, = \sqrt {15} \cr & \,\,\,\, = 3.87\,B.M. \cr} $$
In $${\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{2 + }},$$ oxidation state of $$Co = + 2,C{o^{2 + }} = 3{d^7}$$
$$\eqalign{ & \mu = \sqrt {n\left( {n + 2} \right)} \cr & \,\,\,\, = \sqrt {3\left( {3 + 2} \right)} \cr & \,\,\,\, = \sqrt {15} \cr & \,\,\,\, = 3.87\,B.M. \cr} $$