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In NaCl type structure, if all ions alon...

In NaCl type structure, if all ions along an axis joining centres of the opposite face centers are missing, the expression for packing fraction in limiting case is:

A

`(pi)/(3sqrt2)(1+(r_(c)^(3))/(r_(a)^(3)))`

B

`(pi)/(4sqrt2)(1+(r_(c)^(3))/(r_(a)^(3)))`

C

`(pi)/(sqrt2)(1+(r_(c)^(3))/(r_(a)^(3)))`

D

`(pi)/(2sqrt(2))(1+(r_(c)^(3))/(r_(a)^(3)))`.

Text Solution

Verified by Experts

The correct Answer is:
B
When all the ions along the axis joining face centres is removed. i.e., two anions at face centres and cation at body centre are removed.
`P.F.=(3xx(4)/(3)pi(r_(c)^(3)+r_(a)^(3)))/((2sqrt(2)r_(a))^(3))=(4pi(r_(c)^(3)+r_(a)^(3)))/(16sqrt(2)r_(a)^(3))=(pi)/(4sqrt(2))(1+(r_(c)^(3))/(r_(a)^(3)))`.
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Knowledge Check

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