A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm^–3. The molar mass of the metal is:

(N_A Avogadro's constant = 6.02 × 10²³ mol^–1)

1. 30 g mol^–1
2. 27 g mol^–1
3. 20 g mol^–1
4. 40 g mol^–1

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

Lithium metal crystallizes in a body-centered 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

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: 

1. $\frac{1}{2}\mathrm{a\; :}$ $\frac{\sqrt{3}}{4}\mathrm{a}$ $:$ $\frac{1}{{\displaystyle 2}\sqrt{2}}\mathrm{a}$

2. $\frac{1}{2}\mathrm{a\; :}$ $\sqrt{3}\mathrm{a}$ $:$ $\frac{1}{\sqrt{2}}\mathrm{a}$

3. $\frac{1}{2}\mathrm{a\; :}$ $\frac{\sqrt{3}}{2}\mathrm{a}$ $:$ $\frac{\sqrt{2}}{{\displaystyle 2}}\mathrm{a}$

4. $1\mathrm{a\; :}$ $\sqrt{3}\mathrm{a}$ $:$ $\sqrt{2}\mathrm{a}$

The appearance of colour in solid alkali metal halides is generally due to:

1. F-centres.

2. Schottky defect.

3. Frenkel defect.

4. Interstitial positions.

The incorrect statement among the following is -

If NaCl is doped with ${10}^{-5}$ mol% of $SrC{l}_2$, the number of cation vacancies will be - 

1. $6.02\times {10}^{16}$                 

2. $6.02\times {10}^{18}$

3. $6.02\times {10}^{20}$                 

 4. 2$\times 6.02\times {10}^{23}$

The unit cell dimensions of a cubic lattice (edges a, b, c and the angles between them, α, β, γ) are : 

1. a = b = c, $\mathrm{\alpha }= \mathrm{\beta }= \mathrm{\gamma }= 90°$

2. a = b $\ne$c, $\mathrm{\alpha }= \mathrm{\beta }= \mathrm{\gamma }= 90°$

3. a = b = c, $\mathrm{\alpha }= \mathrm{\gamma }= 90°,$ $\mathrm{\beta }\ne 90°$

4. a $\ne$b $\ne$c, $\mathrm{\alpha }= \mathrm{\beta }= 90°,$ $\mathrm{\gamma }\ne 90°$

The formula of nickel oxide with metal deficiency defect in its crystal is $N{i}_{0.98}O$. The crystal contains ${\mathrm{Ni}}^{2+} \mathrm{and} {\mathrm{Ni}}^{3+}$ 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