question_answer

If energy of one exchange is \[{{E}_{1}}\], then exchange energy of following arrangement is             

A)  \[-6{{E}_{1}}\]                                 

B)  \[-8{{E}_{1}}\]

C)  \[-9{{E}_{1}}\]                                 

D)  Zero

Correct Answer: C

Solution :

Total exchange energy             \[=-\,\left\{ \frac{r!}{2(r-2)!}\,+\frac{s!}{2(s-2)!} \right\}\times {{E}_{1}}\]             r= number of \[{{e}^{-}}\] having clockwise spin s = number of \[{{e}^{-}}\] having anticlockwise spin \[r=3,\,s=4\] \[=\left[ \frac{3!}{2\times 1}+\frac{4!}{2\times 2!} \right]\,\,{{E}_{1}}\,=-\left[ 3+\frac{4\times 3}{2} \right]{{E}_{1}}=-9{{E}_{1}}\]