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In an ionic compound A^(+)X^(-), the rad...

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:

A

`27 "pm"^(3)`

B

` 64 "pm"^(3)`

C

` 125 "pm"^(3)`

D

` 216 "pm"^(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
` (r_(A^+))/(r_(X^(-))) = 1/2 = 0.5 `,As it lies in the range that of NaCl.
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)`
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