If 'a' stands for the edge length of the cubic systems: simple cubic, body centered cubic and face centered cubic, then the ratio of radii of the spheres in these systems will be respectively,

$\left(\mathrm{a}\right)<mspace\; width="1em"></mspace>\frac{1}{2}\mathrm{a}:<mspace\; width="1em"></mspace>\frac{\sqrt{3}}{4}\mathrm{a}:\frac{1}{2\sqrt{2}}\mathrm{a}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\left(\mathrm{b}\right)<mspace\; width="1em"></mspace>\frac{1}{2}\mathrm{a}:\sqrt{3}\mathrm{a}:\frac{1}{\sqrt{2}}\mathrm{a}$
$\left(\mathrm{c}\right)<mspace\; width="1em"></mspace>\frac{1}{2}\mathrm{a}:\frac{\sqrt{3}}{2}\mathrm{a}:\frac{\sqrt{2}}{2}\mathrm{a}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\left(\mathrm{d}\right)<mspace\; width="1em"></mspace>1\mathrm{a}:\sqrt{3}\mathrm{a}:\sqrt{2}\mathrm{a}$

Percentage of free space in a body centered cubic unit cell is

(1) 30%                       

(2) 32%

(3) 34%                       

(4) 28%

With which one of the following elements silicon should be doped so as to give p-type of semiconductor?
(1) Germanium

(2) Arsenic

(3) Selenium

(4) Boron

The fraction of total volume occupied  by the atoms present in a simple cube is:

$$\begin{gathered} 1.<mspace\; width="1em"></mspace>\mathrm{\pi }/6<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace> \\ 2.<mspace\; width="1em"></mspace>\mathrm{\pi }/3\sqrt{2} \\ 3.<mspace\; width="1em"></mspace>\mathrm{\pi }/4\sqrt{2}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace> \\ 4.<mspace\; width="1em"></mspace>\mathrm{\pi }/4 \end{gathered}$$

The incorrect statement among the following is:

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 the lithium will be

1. 240.8 pm

2. 151.8 pm

3. 75.5 pm

4. 300.5 pm

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?

1. 128

2. 157

3. 181

4. 108

if a is the length of the side of a cube, the distance between the body centered atom and

one corner atom in the cube will be :-

1. $\frac{2}{\sqrt{3}}a$

2. $\frac{4}{\sqrt{3}}a$

3. $\frac{\sqrt{3}}{4}a$

4. $\frac{\sqrt{3}}{2}a$

The vacant space in bcc lattice cell is ;

1. 26%

2. 48%

3. 23%

4. 32%

The correct statement regarding defects in the crystalline solid is

1. Schottky defects have no effect on the density of crystalline solids

2. Frenkel defects decreases the density of crystalline solids

3. Frenkel defcct is a dislocation defect

4. Frenkel defect is found in halides of alkaline metals