1

### 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
2

### 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
3

### AIPMT 2009

Lithium metal crystallises in a body-centred cubic crystal. If the length of the side of the unit cell of lithium is 351 pm, the atomic radius of lithium will be
A
151.8 pm
B
75.5 pm
C
300.5 pm
D
240.8 pm

## Explanation

Since Li crystallises in body-centred cubic

crystal, atomic radius, r = ${{\sqrt 3 a} \over 4}$.

$\therefore$ r = ${{\sqrt 3 } \over 4} \times 351$ = 151.8 pm
4

### AIPMT 2008

Percentage of free space in a body centred cubic unit cell is
A
34%
B
28%
C
30%
D
32%

## Explanation

The ratio of volumes occupied by atoms in unit cell to the total volume of the unit cell is called as packing fraction or density of packing. For body centred cubic structure, packing fraction = 0.68 i.e., 68% of the unit cell is occupied by atoms and 32% is empty.