Iron exhibits bcc structure at room temperature. Above 900 °C, it transforms to fcc structure. The ratio of density of iron at room temperature to that at 900 °C is:

(Molar mass and atomic radii of iron remain constant with temperature) 

1. $\frac{\sqrt{3}}{\sqrt{2}}$

2. $\frac{4\sqrt{3}}{3\sqrt{2}}$

3. $\frac{3\sqrt{3}}{4\sqrt{2}}$

4. $\frac{1}{2}$

The density of solid argon (Ar = 40g/mol) is 1.68 g/mL at 40 K. If the argon atom is assumed to be a sphere of radius $1.50\times {10}^{-8} \mathrm{cm}$, what % of solid Ar is apparently empty space? (Use $\mathrm{N}=6\times {10}^{23}$)

1. 35.64

2. 64.36

3. 74%

4. None of these

In an atomic bcc, what fraction of edge is not covered by atoms ?

1. 0.32

2. 0.16

3. 0.134

4. 0.268

Sodium (Na = 23) crystallizes in a bcc arrangement with the interfacial separation between the atoms at the edge 53.6 pm. The density of sodium crystal is :

1. 2.07 g/cc

2. 2.46 g/cc

3. 1.19 g/cc

4. none of these

The distance between an octahedral and tetrahedral void in fcc lattice would be :

1. $\sqrt{3}$a

2. $\frac{\sqrt{3}}{2}a$

3. $\frac{\sqrt{3}}{3}a$

4. $\frac{\sqrt{3}}{4}a$

In the spinel structrue, oxides ions are cubical-closest packed whereas 1/8th of tetrahedral voids are occupied by ${\mathrm{A}}^{2+}$ cation and 1/2 of octahedral voids are occupied by ${\mathrm{B}}^{3+}$ cations. The general formula of the compound having spinel structure is :

1. ${\mathrm{A}}_2{\mathrm{B}}_2{\mathrm{O}}_4$

2. ${\mathrm{AB}}_2{\mathrm{O}}_4$

3. ${\mathrm{A}}_2{\mathrm{B}}_4{\mathrm{O}}_2$

4. ${\mathrm{A}}_4{\mathrm{B}}_2{\mathrm{O}}_2$

An ionic compound AB has fluorite type structures. If the radius  ${\mathrm{B}}^{-}$ is 200 pm, then the ideal radius of ${\mathrm{A}}^{+}$ would be :

1. 82.8 pm

2. 146.4 pm

3. 40 om

4. 45 pm

CsCl has bcc structure with edge length 4.3 pm. The shortest inter ionic distance in between Cs⁺ and Br^- is :

1. 3.72 pm

2. 1.86 pm

3. 7.44 pm

4. 4.3 pm

Ionic radii of Mg²⁺ and O^2- ions are 66 pm and 140 pm respectively. The type of interstitial void and coordination number of Mg²⁺ ion respectively are

1. Tetrahedral, 12

2. Octahedral, 6

3. Tetrahedral, 6 

4. Octahedral, 8

An element crystallizes in a structure having FCC unit cell of an edge length 200 pm. If 200 g of this element contains 24 x 10²³ atoms, the density of the element is - 

1. 50.3 g/cc 

2. 63.4 g/cc

3. 41.6 g/cc 

4. 34.8 g/cc