For the complex `[Cr(H_(2)O)_(6)]^(2+)` calculate the total pairing energy in high spin and low spin state. Given the mean pairing energey `=23500cm^(-1)` .

Explanation

In `[Cr(H_(2)O)_(6)]^(2+)` ion `Cr` is present as `Cr^(2)+` ion Electronic configuration of `Cr^(2+)` ion is `3d^(4),Cr^(2+)` ion in high spin states
``t_(2g)overset(3)`e_(g)overset(1)`
`CFSE = - 3 xx 0.4 Delta_(0) + 1 xx 0.6 Delta_(0)`
`= - 1.2 +0.6 Delta_(0) = - 0.6 Delta_(0) = - 0.6 xx 13900 cm^(-1)`
`=-8340cm^(-1)`
`Cr^(2+)` ion in low spin state ``t_(2g)overset(3)`e_(g)overset(1)`
`CFSE =-4 xx 0.4Delta_(0) + P`
`= - (1.6 xx 13900 + 23500)cm^(-1)`
`=(-22240 + 23500)cm^(-1) = + 1260 cm^(1)`
`CFSE` for high spin state is greater than `CFSE` for low spin state hence high spin state is more stable .