`CsCl`crystallizes in body centred cubic lattice. If `'a'` is its edge length then which of the following expressions is correct ?

Options

A. ` r_(Cs+) + r_(Cl^(-)) = sqrt3 a `
B. `r_(Cs^(+)) + r_(Cl^(-)) = 3a `
C. ` r_(Cs^(+) + r_(Cl^(-)) = (3a)/2`
D. `r_(Cs^(+)) + r_(Cl^(-)) = sqrt3/2 a `

Answer

d

Explanation

In body-centred cubic (bcc) , oppositely charged ions touch each other along the body diagonal .

Body diagonal , ` AE = 2r_(Cs^(+)) + 2r_(Cl^(-))`
But body diagonal = ` sqrt 3a `
( From right angled ` DeltaCDE, CE =sqrt(a^(2) +a^(2)) = sqrt2a `
From right angled ` Delta ACE`
` AE = sqrt( AC^(2)+ CE^(2)) = sqrt(a^(2) + 2a^(2)) = sqrt(3a^(2)) = sqrt3 a `)
`2(r_(Cs^(+)) +r_(Cl^(-)) = sqrt3 a or r_(Cs) + r_(Cl^(-)) = sqrt3/2 a `