Using the edge length of a unit cell, we can calculate the density \((\rho)\) of the crystal by considering a cubic unit cell as follows.
Mass of the unit cell \(=\left\{\begin{array}{l}\text { total number of } \\ \text { atoms belongs to } \\ \text { that unit cell }\end{array}\right\} \times\left\{\begin{array}{l}\text { mass of } \\ \text { one atom }\end{array}\right\}\)         (1)
Mass of one atom \(=\frac{\text { Molar mass }\left(\mathrm{gmol}^{-1}\right)}{\text { Avogadro number }\left(\mathrm{mol}^{-1}\right)}=\frac{\mathrm{M}}{\mathrm{N}_{\mathrm{A}}}\) (2)
Mass of the unit cell \(=n \times \frac{M}{N_{A}}\)    (3)
For a cubic unit cell, all the edge lengths are equal i.e, a = b = c
Volume of the unit cell \(=a \times a \times a=a^{3}\)  (4)
\(\therefore\) Density of the unit cell \(\rho=\frac{\mathrm{nM}}{\mathrm{a}^{3} \mathrm{~N}_{\mathrm{A}}}\)
[ \(\therefore\) Density = Mass/Volume]

Using the edge length of a unit cell, we can calculate the density \((\rho)\) of the crystal by considering a cubic unit cell as follows.
Mass of the unit cell \(=\left\{\begin{array}{l}\text { total number of } \\ \text { atoms belongs to } \\ \text { that unit cell }\end{array}\right\} \times\left\{\begin{array}{l}\text { mass of } \\ \text { one atom }\end{array}\right\}\)         (1)
Mass of one atom \(=\frac{\text { Molar mass }\left(\mathrm{gmol}^{-1}\right)}{\text { Avogadro number }\left(\mathrm{mol}^{-1}\right)}=\frac{\mathrm{M}}{\mathrm{N}_{\mathrm{A}}}\)    (2)
Mass of the unit cell \(=n \times \frac{M}{N_{A}}\)         (3)
For a cubic unit cell, all the edge lengths are equal i.e , a = b = c
Volume of the unit cell \(=a \times a \times a=a^{3}\)   (4)
\(\therefore\) Density of the unit cell \(\rho=\frac{\mathrm{nM}}{\mathrm{a}^{3} \mathrm{~N}_{\mathrm{A}}}\) 
[ \(\therefore\) Density = Mass/Volume]

Characteristics:
1) Ionic solids have high melting points.
2) These solids do not conduct electricity, because the ions are fixed in their lattice positions.
3) They do conduct electricity in molten state (or) when dissolved in water because, the ions are free to move in the molten state or solution.
4) They are hard as only strong external force can change the relative positions of ions.

(i) The defects in ionic solids is by adding impurity ions.
(ii) If the impurity ions are in different valance state from that of host, vacancies are created in the crystal lattice of the host.
(iii) For example, addition of CdCl₂ to silver chloride yields solid solutions where the divalent cation Cd²⁺ occupies the position of Ag⁺.
(iv) This will disturb the electrical neutrality of the crystal.
(v) In order to maintain the same, proportional number of Ag⁺ ions leaves the lattice.
(vi) This produces a cation vacancy in the lattice, such kind of crystal defects are called impurity defects.

Schottky defect:
(i) Schottky defect arises due to the missing of equal number of cations and anions from the crystal lattice.
(ii) This effect does not change the stoichiometry of the crystal.
(iii) Ionic solids in which the cation and anion are of almost of similar size show schottky defect. Ex: NaCl.
(iv) Presence of large number of schottky defects in a crystal, lowers its density.

Frenkel defect:
(i) Frenkel defect arises due to the dislocation of ions from its crystal lattice.
(ii) The ion which is missing from the lattice point occupies an interstitial position.
(iii) This defect is shown by ionic solids in which cation and anion differ in size.
(iv) Unlike Schottky defect, this defect does not affect the density of the crystal.
(v) For example AgBr, in this case, small Ag⁺ ion leaves its normal site and occupies an interstitial position.

Crystal defects are classified as follows
(i) Point defects
(ii) Line defects
(iii) Interstitial defects
(iv) Volume defects
Point defects are further classified as follows

(i) Similarities between ionic and metallic crystals:
(a) Ionic and metallic crystals have electrostatic forces of attraction.
(b) Both the crystals exhibit high melting point.
(c) The bonds in metallic and ionic crystals are non-directional.
(ii) Differences between ionic and metallic crystals:

(i) By knowing the density of an unknown metal and the dimension of its unit cell, the atomic mass of the metal can be: determined.
(ii) Let 'a' be the edge length of a unit cell of a crystal, 'd' be the density of the metal, 'm' be the atomic mass of the metal and 'z' be the number of atoms in the unit cell.
(iii) Now,
Density of the unit cell
\(=\frac{Mass\ of\ the\ unit\ cell}{Volume\ of\ the\ unit\ cell}\)
\(d=\frac{Z\times m}{a^3}\) ...(1)
[Since, mass of the unit cell = Number of atoms in the unit cell x Atomic mass]
[Volume of the unit cell = (edge length of the cubic unit cell)³]
(iv) From equation (1), We have
\(m=\frac{d\times a^3}{Z}\) ....(2)
(v) Now, 
Mass of the metal (M) \(=\frac{Atomic\ mass(M)}{Avogadro's\ number(N_A)}\)
M=\(\frac{d\times a^3 \times N_A}{Z}\)
(vi) From equation (3), we can determine the atomic mass of the unknown metal.

Density of the element, d = 2.7 x 10³ kg m^-3
Molar mass, M = 2.7 x 10^-2 kg mol^-1
Edge length, a = 405 pm
= 405 x 10^-12 m
= 4.05 x 10^-10 m
Avogadro's number, N_A= 6.022 x 10²³ mol^-1
\(\therefore d=\frac { Z\times M }{ { a }^{ 3 }\times { N }_{ A } } \)
\(\Rightarrow Z=\frac { d\times { a }^{ 3 }{ N }_{ A } }{ M } \)
\(=\frac { 2.7\times { 10 }^{ 3 }kg\quad { m }^{ -3 }{ (4.05\times { 10 }^{ -10 }m) }^{ 3 }\times 6.022\times { 10 }^{ 23 }{ mol }^{ -1 } }{ 2.7\times { 10 }^{ -2 }kg\quad { mol }^{ -1 } } \)
= 4.004 = 4.
This implies that four atoms of the element are present per unit cell. Hence the unit cell is face centred cubic.

Molecular solids: 
In molecular solids, the constituents are neutral molecules. They are held together by weak Vander Waals forces. Generally molecular solids are soft and they do not conduct electricity. These molecular solids are further classified into three types.
(i) Non-polar molecular solids:
(a) In non-polar molecular solids constituent molecules are held together by weak dispersion forces or London forces.
(b) They have low melting points and are usually in liquids or gaseous state at room temperature.
Ex: Naphthalene, anthracene etc.,
(ii) Polar molecular solids:
(a) The constituents are molecules formed by polar covalent bonds. 
(b) They are held together by relatively strong dipole-dipole interactions.
(c) They have higher melting points than the nonpolar molecular solids. 
Ex: Solid CO₂, solid NH₃ etc.

(iii) Hydrogen bonded molecular solids:
(a) The constituents are held together by hydrogen bonds.
(b) They are generally soft solids under room temperature.
(c) Examples: solid ice (H₂O), glucose, urea etc.

(i) Solids have definite volume and shape 
(ii) Solids are rigid and incompressible
(iii) Solids have strong cohesive forces.
(iv) Their constituents have fixed positions and can only oscillate about their mean positions.

(i) It is given that the atoms of A are present at the corners of the cube.
(ii) Therefore, number of atoms of Q in one unit cell = 8 x \(\frac{1}{8}\) = 1
(iii) It is also given that the atoms of P are present at the body - centre.
(iv) Therefore, number of atoms of P in one unit cell.
(v) This means that the ratio of the number of P atoms to the number of Q atoms, P: Q = 1:1.
(vi) Hence, the formula of the compound is PQ.
(vii) The coordination number of both P and Q is 8.

(i) The colour develops because of the presence of electrons in the 8 anionic sites.
(ii) These electron absorb energy from the visible region of radiation and get excited. 
(iii) For example when crystals of NaCl are heated in an atmosphere of sodium vapours, the sodium atoms get deposited on the surface of the crystal and the deposited Na atoms.
(iv) During this process, the Na atoms on the surface lose electrons to form Na⁺ ions 
(v) These electrons get excited by absorbing energy from the visible light and impart yellow colour to the crystals.