1

### AIPMT 2012 Prelims

A metal crystallises with a face-centred cubic lattice. The edge of the unit cell is 408 pm. The diameter of the metal atom is
A
288 pm
B
408 pm
C
144 pm
D
204 pm

## Explanation

Given $a$ = 408 pm

For the face centred cubic structure

r = ${a \over {2\sqrt 2 }}$ = ${{408} \over {2\sqrt 2 }}$ = 144 pm

$\therefore$ Diameter = 2r = 2$\times$144 = 288 pm
2

### AIPMT 2011 Mains

A solid compound XY has NaCl structure. If the radius of the cation is 100 pm, the radius of the anion (Y$-$) will be
A
275.1 pm
B
322.5 pm
C
241.5 pm
D
165.7 pm

## Explanation

For NaCl crystal, ${{{r_ + }} \over {{r_ - }}} = 0.414$

Given, r+ = 100 pm

$\therefore$ ${{100} \over {{r_ - }}} = 0.414$

$\Rightarrow$ ${r_ - } = {{100} \over {0.414}}$ = 241.5 pm
3

### AIPMT 2010 Prelims

AB crystallizes in a body centered cubic lattice with edge length '$a$' equal to 387 pm. The distance between two oppositely charged ions in the lattice is
A
335 pm
B
250 pm
C
200 pm
D
300 pm

## Explanation

For a bcc lattice, 2(r+ + r) = $\sqrt 3 a$

$\therefore$ r+ + r = ${{\sqrt 3 \times 387} \over 2}$ = 335 pm
4

### AIPMT 2009

Copper crystallises in a face-centred cubic lattice with a unit cell length of 361 pm. What is the radius of copper atom in pm?
A
157
B
181
C
108
D
128

## Explanation

Since Cu crystallises in a face-centred cubic lattice,

Atomic radius, r = ${a \over {2\sqrt 2 }}$

$\therefore$ r = ${{361} \over {2\sqrt 2 }}$ = 128 pm