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KCl crystallises in the same type of l...

KCl crystallises in the same type of lattice as does NaCl Given that `r_(Na^(+))//r_(Cl^(-))=0.55andr_(K^(+))//r_(Cl^(-))=0.74`.Calculate the ratio of the side of the unit cell for KCl to that of NaCl.

A

a) 1.122

B

b) 0.0891

C

c) 1.414

D

d) 0.414

Text Solution

Verified by Experts

The correct Answer is:
A
Given `r_(Na^(+))//r_(cl^(-))=0.55`
`r_(K^(+))//r_(Cl^(-))=0.74`
`(r_(KCl))/(r_(NaCl))=`?
`(r_(Na^(+)))/(r_(Cl^(+)))=0.55`
`(r_(Na^(+)))/(r_(Cl^(-)))+1=0.55+1`
`(r_(Na)^(+)+r_(Cl^(-)))/(r_(Cl^(-)))=1.55`
`(r_(K^(+)))/(r_(Cl^(-)))=0.74`
`(r_(K^(+)))/(r_(Cl^(-)))+1=0.74+1`
`(r_(K^(+))+r_(Cl^(-)))/(r_(Cl^(-)))=1.74` .... (ii)
Eqs (ii)//(i)
`(r_(K^(+))+r_(Cl^(-)))/(r_(Na^(+))+r_(Cl^(-)))=(1.74)/(1.55)=1.1226`
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