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 lies in the range 0.414-0.732, AX has octahedral structure like that of NaCl.
Hence, edge length (a)=`2(r_+ +r_(-))`
=2(1+2)pm =6 pm
Volume of the unit cell=`a^3`=`"(6 pm)"^3="216 pm"^3`