Question

For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity), the packing fraction is approximately:

Options

• 0.74

• 0.63

• 0.52

• 0.48

Answer 1

0.63

Explanation:

Assume the

X = r₊

Y = r₋

a = edge length of unit cell

2r₋ = a

`a/(r_−)` = 2

Also `r_+/r_-` = 0.414

Packing fraction = `(3 ("Volume of"  r_+) + 1 ("Volume of"   r_-))/"Volume of unit cell"`

= `(3 xx 4/3 xx pi r_+^3 + 1 xx 4/3 xx pi r_-^3)/(a/r)^3`

= `(4/3 pi [3((r_+)/(r_-))^3 + 1])/2^3`

= `(4/3 xx 3.14  [3 xx (0.414)^3 + 1])/8`

= `(4.176 xx [3 xx (0.070) + 1])/8`

= `(4.176 xx (0.21 + 1))/8`

= `(4.176 xx 1.21)/8`

= `5.05296/8`

= 0.63