(i) The energy gap between valence band and condition band in an insulator is very large where as in a conductor, the energy gap is very small or there is overlapping between valence band and conduction band.
(ii) In a conductor, there is verysmall energy gap or there is verlapping between valence band and conduction band but in a semiconductor, there is always a small energy gap between them.

\(d=2.8 \ g \ cm^{ 3 };Z=4(for \ fcc),a=4\times 10^{ -8 }cm;N_{ A }=6.022\times 10^{ 23 }mol^{ -1 }\)
\(\Rightarrow M=\frac { d\times a^{ 3 }\times N_{ A } }{ Z } \)
\(=\frac { 28g\quad cm^{ 3 }(4\times 10^{ -8 }cm)^{ 3 }\times 6.022\times 10^{ 23 } }{ 4 } \)
\( \Rightarrow M=2.8\times 16\times 10^{ -1 }\times 6.022\\ =26.98 \ g \ mol^{ -1 }\)

Given : a = 4.077 x 10^-8cm, Z = 4,M = 108 g mol^-1 N_A = 6.023 x 10²³
\(d=\frac { Z\times M }{ a^{ 3 }\times N_{ A } } \)
\(=\frac { 4\times 108 }{ (4.077\times 10^{ -8 })^{ 3 }\times 6.023\times 10^{ 23 } } \)
\(r\quad =\frac { a }{ 2\sqrt { 2 } } =\frac { 4.077\times 10^{ -8 }cm }{ 2\sqrt { 2 } } \)
\(=1.44\times 10^{ -8 }cm\)

353.3 nm

Density,   \(d=\frac { Z\times M }{ { a }^{ 3 }\times { N }_{ 0 } } \)
 or  \({ a }^{ 3 }=\frac { Z\times M }{ d\times { N }_{ 0 } } \)
\(d={ 4.0g\ cm }^{ -3 }\)
 \(M={ 168.5gmol }^{ -1 }\)
For cubic lattice, \(Z=1\)
\(\therefore \)   \({ a }^{ 3 }=\frac { 1\times 168.5 }{ 4.0\times 6.022\times { 10 }^{ 23 } } \)
 \(=69.9\times { 10 }^{ -24 }{ cm }^{ 3 }\)
\(\therefore \)   \(a=4.12\times { 10 }^{ -8 }cm=412 \ pm\)

Length of the edge = \(289pm=289\times { 10 }^{ -12 }m=289\times { 10 }^{ -10 }cm\)
Atomic mass of Cr, \(A=52u\)
Density of metal, \(d=7.2g{ cm }^{ -3 }\)
Now, \(d=\frac { Z\times M }{ { a }^{ 3 }\times { N }_{ 0 } } \)
\({ 7.2 \ gcm }^{ -3 }=\frac { Z\times { 52g }\quad mol^{ -1 } }{ (289\times { 10 }^{ 10 }cm)^{ 3 }\times (6.022\times { 10 }^{ 23 }{ mol }^{ -1 }) } \)
or \(Z=\frac { { (7.2g\quad cm) }^{ -3 }\times (289\times { 10 }^{ 10 }cm)^{ 3 }\times (6.022\times { 10 }^{ 23 }{ mol }^{ -1 }) }{ { (52g\quad mol }^{ -1 }) } \)
\(=2.01\)
Since the unit cell contains 2 atoms, it is body centred cubic (bcc).

Electrical properties of solids. Depending upon the electrical conductivity, solids can be broadly classified into three main types. These are
(i) Conductors (ii) Insulators and (iii) Semiconductors.
The conductivity of solids varies between 107 ohms in metals to about 10-20 ohms' in insulators.Solids can be classified into three types on the basis of their conductivities:
(i) Conductors with conductivities ranging between 104 to 107 ohms. Metals having conductivities in the order of 107 ohnr+ m-I are good conductors.
(ii) Insulators with very low conductivities ranging between 10-20 to 10-10 ohms.
(iii) Semiconductors with conductivities in the intermediate range from 10-6 to 104 ohms.
The electrical conductivity of solids may be due to the electrons, holes or ions. Ionic substances such as alkali metal halides, in which the conduction is mainly due to ions are poor conductors, generally insulators. However, due to some defects, they become conductors.
Unlike metals, the conductivity of insulators and semiconductors is mainly dependent on the impurities and defects present. The conduction of electricity is carried by the excess electrons or holes present in these solids.

0.919

1.125

1.5427g cm^-3

When group 14 element is doped with group 15 elements, we get n-type semiconductor, e.g. silicon doped with arsenic.

In a ccp structure, there is 1 octahedral void in the centre of the body and 12 octahedral voids are on 12 edges of the cube.Each octahedral void on the edge is

common to four other unit cells (as shown in figure). Thus, in cubic close-packed structure, octahedral voids in the centre of the cube = 1.
Effective number of octahedral voids on edges = 12 x 1/4 = 3
Total number of octahedral voids = 1 + 3 = 4

(i) Density remains the same in Frenkel defect, where as Schottky defect leads to lowering of density.
(ii) Electrical conductivity increases in both Frenkel and Schottky defects.