An element has a body-centered cubic (BCC) structure with a cell edge of 288 pm. The atomic radius is:

1. $\frac{\sqrt{2}}{4}\times 288$ pm

2. $\frac{4}{\sqrt{3}}\times 288$ pm

3. $\frac{4}{\sqrt{2}}\times 288$ pm

4. $\frac{\sqrt{3}}{4}\times 288$ pm

The formula of nickel oxide with metal deficiency defect in its crystal is $N{i}_{0.98}O$. The crystal contains ${\mathrm{Ni}}^{2+}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{Ni}}^{3+}$ ions. The fraction of nickel existing as $N{i}^{2+}$ ions in the crystal is-

1. 0.96

2. 0.04

3. 0.50

4. 0.31

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. $\frac{1}{2}$

A given metal crystallizes out with a cubic structure having an edge length of 361 pm. If there are four metal atoms in one unit cell, the radius of one atom is:

1. 40 pm
2. 127 pm
3. 80 pm
4. 108 pm

A metal crystallizes with a fcc lattice. The edge of the unit cell is 408 pm. The diameter of the metal atom is: 

1. 288 pm

2. 408 pm

3. 144 pm

4. 204 pm