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,

$$\begin{gathered} \left(\mathrm{a}\right) \frac{1}{2}\mathrm{a}: \frac{\sqrt{3}}{4}\mathrm{a}:\frac{1}{2\sqrt{2}}\mathrm{a} \left(\mathrm{b}\right) \frac{1}{2}\mathrm{a}:\sqrt{3}\mathrm{a}:\frac{1}{\sqrt{2}}\mathrm{a} \\ \left(\mathrm{c}\right) \frac{1}{2}\mathrm{a}:\frac{\sqrt{3}}{2}\mathrm{a}:\frac{\sqrt{2}}{2}\mathrm{a} \left(\mathrm{d}\right) 1\mathrm{a}:\sqrt{3}\mathrm{a}:\sqrt{2}\mathrm{a} \end{gathered}$$

Which of the following statements is not correct?

(a) The fraction of the total volume occupied by the atoms in a primitive cell is 0.48

(b) Molecular solids are generally volatile

(c) The number of carbon atoms in an unit cell of diamond is 8

(d) The number of Bravais lattices in which a crystal can be categorized is 14

Sodium metal crystallizes in bcc lattice with cell edge $=4.29 \stackrel{0}{A}$. The radius of sodium atom will be-

(1) 1.50 $\stackrel{0}{A}$                                                 

(2) 1.86  $\stackrel{0}{A}$

(3) 2.80 $\stackrel{0}{A}$                                               

(4) None of these 

A metallic element exists as cubic lattice. Each edge of the unit cell is 2.88 $\stackrel{0}{A}$. The density of the metal is 7.20 g $c{m}^{-3}$. How many unit cell will be present in 100 g of the metal -

(A) $6.85\times {10}^2$                             

(B) $5.82\times {10}^{23}$

(C) $4.37\times {10}^5$                             

(D) $2.12\times {10}^6$

Fraction of total volume occupied by atoms in a simple cube is-

(1) $\frac{\mathrm{\pi }}{2}$                                   

(2) $\frac{\sqrt{3}\mathrm{\pi }}{8}$

(3) $\frac{\sqrt{2}\mathrm{\pi }}{6}$                             

(4) $\frac{\mathrm{\pi }}{6}$

Analysis shows that an oxide ore of  nickel has formula  Ni_0.98O_1.00. The percentage of nickel as Ni³⁺ ions is nearly

1. 2

2. 96

3. 4.08

4. 98

Frenkel defect is not found in the halides of alkali metals because alkali metals have

1. High electropositivity.

2. High ionic radii.

3. High reactivity.

4. Ability to occupy interstitial sites.

A solid PQ have rock salt type structure in which Q atoms are at the corners of the unit cell and P at edge. If the body centred atoms in all the unit cells are missing, the resulting stoichiometry will be-

(A) PQ                                               

 (B) $P{Q}_2$

(C) $P_3{Q}_4$                                             

(D) $P_4{Q}_3$

8 : 8 co-ordination of CsCl is found to change into 6 : 6
co-ordination on:

(a) applying pressure
(b) increasing temperature
(c) both (a) and (b)
(d) none of these

At room temperature, sodium crystallises in a body centred cubic cell with a 4.24 $\stackrel{0}{A}$. The theoretical density of sodium is- (Atomic mass of sodium=23.0 g $mo{l}^{-1}$)

(A) $2.05 g c{m}^{-3}$                                         

(B) $3.45 g c{m}^{-3}$

(C) $1.00 g c{m}^{-3}$                                         

(D) $3.55 g c{m}^{-3}$