Lithium borohydride $\left(LiB{H}_4\right),$crystallises in an orthorhombic system with 4 molecules per unit cell. The unit cell dimensions are : a = 6.81Å, b= 4.43Å, c=7.17Å. If the molar mass of $LiB{H}_4$ is 21.76 g mol^–1. The density of the crystal is –

(1) 0.668 g cm^–3

(2) 0.585 g cm²

(3) 1.23 g cm^–3

(4) None

CsBr has a (bcc) arrangement and its unit cell edge length is 400 pm. Calculate the interionic distance in CsCl [CBSE 1993]

(1) 346.4 pm

(2) 643 pm

(3) 66.31 pm

(4) 431.5 pm

The diffraction of barium with X-radiation of wavelength 2.29Å gives a first – order reflection at 30°. What is the distance between the diffracted planes.

(1) 3.29 Å

(2) 4.39 Å

(3) 2.29 Å

(4) 6.29 Å

The vacant space in bcc lattice cell is ;

(a) 26%

(b) 48%

(c) 23%

(d) 32%

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

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,

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

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) $2.12\times {10}^6$