Two ionic solids `AB` and `CB` crystallize in the same lattice. If `r_(A^(o+))//r_(B^(ɵ))` and `r_(C^(o+))//r_(B^(ɵ))` are `0.50` and `0.70`, respectively, then the ratio of edge length of `AB` and `CD` is

Options

A. `0.68`
B. `0.78`
C. `0.88`
D. `0.98`

Answer

C

Explanation

`r_(A^(o+))/(r_(B^(ɵ)))=0.50` and `r_(C^(o+))/(r_(B^(ɵ)))=0.70`
`rArr (r_(A^(o+)) xx r_(B^(o+)))/(r_(B^(ɵ))) = 1+0.5 = 1.5`
Similarly, `rArr (r_(AC^(o+)) xx r_(B^(o+)))/(r_(B^(ɵ)) = 1 + 0.5 = 1.70`
`:. (r_(A^(o+)) + r_(B^(o+)))/(r_(C^(o+)) + r_(B^(ɵ)))=(1.5)/(1.7) = 0.88`
Also, `a_(AB) = 2(r_(A^(o+)) + r_(B^(o+)))` and `a_(CB) = 2(r_(C^(o+)) + r_(B^(ɵ)))` and `a_(CB) = 2(r_(C^(o+)) + r_(B^(ɵ)))`
`:. (a_(AB))/(a_(CB)) = (1.5)/(1.7) = 0.88`