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Question

A solid AB has rock salt structure. If the edge lenght is 520 pm and radius of A+ is 80 pm, the radius of anion B− would be -

A
440 pm
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B
220 pm
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C
360 pm
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D
180 pm
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Solution

The correct option is D 180 pm
Solid AB forms rock salt structure. Here, B ions occupies the fcc/ccp lattice points ( 8 corners and 6 face centres) and A+ occupies the octahedral voids of the ccp arrangement ( 12 edge centre and 1 body centre)
Here,
the B ion in corner of cubic unit cell does not touches the B ion in face centre of the unit cell.
Thus,
4rBa2

Ions A+ and B touch each other along the edge.
Thus,
Unit cell length 2=rA++rB
rA+rB=5202
80+rB=260

Radius of B=rB=26080
rB=180 pm

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