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AX,AY,BX, and BY have rock salt type str...

`AX,AY,BX`, and `BY` have rock salt type structure with following internuclear distances:
`|{:("Salt","Anion-anion","Cation-anion"),(,"distance in"Å,"distance in"Å),(AX,2.40,1.70),(AY,1.63,1.15),(BX,2.66,1.88),(By,2.09,1.48):}|`
A salt `MY` crystallizes in the `CsCl` structure. The anions at the corners touch each other and cation is in the centre. The radius ratio `(r_(o+)//r_(Θ))` for this structure is

A

`0.225`

B

`0.414`

C

`0.732`

D

`1.0`

Text Solution

Verified by Experts

The correct Answer is:
C

The distance between opposite corners fo the face of a cube with sides `2r_(ɵ)(CB) = 2sqrt(2)r_(ɵ)`
The distance between the centers of touching atoms
`(AC)= 2r_(ɵ)`
`:.` The distance between two oppsite anions `= sqrt(12)r_(ɵ)`
`= (2r_(o+) + 2r_(ɵ))`
`:. sqrt(12)r_(ɵ) = (2r_(o+) +2r_(ɵ))`
`3.46r_(ɵ) = (2r_(o+) + 2r(ɵ))`
`1.46r_(ɵ) = 2r_(o+) rArr (r_(o+))/(r_(ɵ)) = 0.732`
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