In an ionic compound `A^(+)X^(-)`, the radii of `A^(+) and X^(-)` ions ar 1.0pm and 2.0om, respectively. The volume of the unit cell of the crystal AX will be:

Options

A. `27 "pm"^(3)`
B. `64"pm"^(3)`
C. `125 "pm"^(3)`
D. `216 "pm"^(3)`

Answer

D

Explanation

`(r_(A^(+)))/(r_(X^(-)))=(1)/(2) =0.5`
As it is in the range of `0.441 "to" 0.732`, Ax has octahedral structure like NaCl. Hence the edge length is
`2(r_(A)+r_(X^(-)))=2 (1+2)=6` pm
Volume `=a^(3)=(6)^(3)=216 "pm"^(3)`