Chapter Chosen

The Solid State

Book Chosen

Chemistry I

Subject Chosen


Book Store

Download books and chapters from book store.
Currently only available for.
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12
Calculate the efficiency of packing in case of a metal crystal for
(i) simple cubic
(ii) body- centred cubic
(iii) face - centred cubic . (With the assumptions that atoms are touching each other).


(i) Simple Cubic: A simple cubic unit cell has one sphere (or atom) per unit cell. If r is the radius of the sphere, then volume occupied by one sphere present in unit cell = 43πr3
Edge length of unit cell (a) = r + r = 2r
Volume of cubic (a3) = (2r)3 = 8r3
Volume of occupied by sphere  = 43πr3
Percentage volume occupied = percentage of efficiency of packing

= Volume of sphereVolume of cube ×100= 43πr38r3×100= 16×3.143×100 = 52.4%

For simple cubic metal crystal the efficiency of packing = 52.4%.

(b) Body centred cubic: From the figure it is clear that the atom at the centre will be in touch with other two atoms diagonally arranged and shown with solid boundaries.

In EFD         b2 = a2+a2                              = 2a2                        b = 2aNow in AFD                        c2 = a2+ b2                            = a2+2a2 = 3a2                        c = 3a

The length of the body diagonal c is equal to 4r where r is the radius of the sphere (atom). But c = 4r, as all the three spheres along the diagonal touch each other

∴              3a = 4r

or                   a=4r3

or                    r=34a.

Fig. BCC unit cell. In this sort of structure total number of atoms is two and their volume is 2×43πr3.

Volume of the cube, a
3 will be equal to
43r or a3 = 43r3.

Therefore, Percentage of efficiency Volume occupied by four - spheres

= in the unit cellTotal volume of the unit cell×100%= 2×43πr3×100(4/3r)3%= (8/3) πr3 × 100[64/(33)r3]% = 68%

(c) Face centred cubic: A face centred cubic cell (fcc) contains four spheres (or atoms) per unit volume occupied by one sphere of radius

r = 4/3 πr3

Volume occupied by four spheres present in the unit cell

r = 4/3 πr3 x 4 = 16/3 πr3

Fig.  Face centred cubic unit cell. Figure indicates that spheres placed at the corners touches a face centred sphere. Length of the face diagonal
= r + 2r + r = 4r

Hence, for face centred cubic, efficiency of packing = 74%.


Refractive index of a solid is observed to have the same value along all directions. Comment on the nature of this solid. Would it show clevage property?

Refractive index of a solid which have the same value along all directions are isotropic in nature. It would not show cleavage property.

Why is glass considred a super-cooled liquid?

Glass is amorphous solids and  have a tendency to flow, though very slowly. Therefore, these are called pseudo solids or super cooled liquids .

Why do solids have a definite volume?

A solid have a definite volume because the inter molecular distance  between its molecules are fixed.

Why are solids rigid?

Solids are rigid because the internuclear distance between the  molecules of a solid are very less and closely packed and their positions are fixed due to the strong forces of attraction between them.

Classify the following as amorphous or crystalline solids: Polyurethane, naphthalene, benzoic acid, teflon, potassium nitrate, cellophane, polyvinyl chloride, fibre glass, copper.

Amorphous solids: Polyurethane, teflon, cellophane, polyvinyal chloride, fibre glass.
Crystalline solids: naphthlene, benzoic acid, potassium nitrate, copper.