The pyknometric density of `NaCl` crystal is `2.165 xx 10^(3 kg m^(-3)` while its `X`-ray density is `2.178 xx 10^(-3) kg m^(-3)`. The fraction of unoccupied sites in `NaCl` crystal is
a. `5.96` b. `5.96 xx 10^(-2)`
c. `5.96 xx 10^(-1)` d. `5.96 xx 10^(-3)`

Options

A. 5.96
B. `5.96xx10^(-2)`
C. `5.96xx10^(-1)`
D. `5.96xx10^(-3)`

Explanation

Molar volume from pykonometic density = `("weight of mass")/("density")=("Weight" (W))/(2.165xx10^(3))m^(3)`
Molar volume from X-ray density= `(W)/(2.178xx10^(3))m^(3)`
Volume unoccupied `=(W)/(10^(3))((1)/(2.165)-(1)/(2.178))m^(3)=(0.013Wxx10^(-3))/(2.165xx2.178)`
`therefore` Fraction unoccupied `=((0.013Wxx10^(-3))/(2.165xx2.178))//((Wxx10^(-3))/(2.165))=5.96xx10^(-3)`