1

### AIPMT 2008

Which of the following statements is not correct?
A
The number of carbon atoms in a unit cell of diamond is 4
B
The number of Bravais lattices in which a crystal can be categorized is 14
C
The fraction of the total volume occupied by the atoms in a primitive cell is 0.48.
D
Molecular solids are generally volatile.

## Explanation

Packing fraction for a cubic unit cell is given by

f = ${{Z \times {4 \over 3}\pi {r^3}} \over {{a^3}}}$

where a = edge length, r = radius of cation and anion.

Efficiency of packing in simple cubic or primitive cell = π/6 = 0.52 or 52 %

It means 52 % of unit cell is occupied by atoms and 48 % is empty.
2

### AIPMT 2008

With which one of the following elements silicon should be doped so as to give p-type of semiconductor?
A
Selenium
B
Boron
C
Germanium
D
Arsenic

## Explanation

The semiconductors formed by the introduction of impurity atoms containing one elecron less than the parent atoms of insulators are termed as p-type semiconductors. Therefore silicon containing 14 electrons has to be doped with boron containing 13 electrons to give a p-type semi-conductor.
3

### AIPMT 2007

If NaCl is doped with 10$-$4 mol% of SrCl2, the concentration of cation vacancies will be (NA = 6.02 $\times$ 1023 mol$-$1)
A
6.02 $\times$ 1016 mol$-$1
B
6.02 $\times$ 1017 mol$-$1
C
6.02 $\times$ 1014 mol$-$1
D
6.02 $\times$ 1015 mol$-$1

## Explanation

As each Sr2+ ion introduces one cation vacancy, therefore concentration of cation vacancies = mole % of SrCl2 added.

$\therefore$ Concentration of cation vacancies

= 10–4 mole %

= ${{{{10}^{ - 4}}} \over {100}} \times 6.023 \times {10^{23}}$

= $6.023 \times {10^{23}}$ $\times$ 10-6

= $6.023 \times {10^{17}}$
4

### AIPMT 2007

The fraction of total volume occupied by the atoms present in a simple cube is
A
${\pi \over {3\sqrt 2 }}$
B
${\pi \over {4\sqrt 2 }}$
C
${\pi \over 4}$
D
${\pi \over 6}$

## Explanation

The maximum properties of the available volume which may be filled by hard sphere in simple cubic arrangement is ${\pi \over 6}$ or 0.52.