A. An element has atomic mass 93g mol^–1 and density 11.5 g cm^–3. If the edge length of its unit cell is 300 pm, identify the type of unit cell.

B. Write any two differences between amorphous solids and crystalline solids.

OR

A. calculate the number of unit cells in 8.1 g of aluminium if it crystallizes in a f.c.c. structure. (Atomic mass of Al = 27 g mol^–1)

B. Give reasons :

(i) In stoichiometric defects, NaCl exhibit Schottky defect and not Frenkel defect.

(ii) Silicon on doping with Phosphorus forms an n-type semiconductor.

(iii) Ferrimagnetic substances show better magnetism than antiferromagnetic substances.

(A) Given –

Atomic mass = 93 gmol^-1 = 93g per 6.023 10²³ atoms (avagadro number)

Density = 11.5 gcm^-3

Edge length = a = 300 pm = 300 10^-10cm

Volume = a³ = 27 10 ^-24 cm³

Type of unit cell = ?

Effective number of atoms = N = ?

We know that density = total mass / total volume

=

11.5 g / cm³ =

N = 11.5 6.023 10²³ 27 10 ^-24 cm³ / 93

= 2

We know that BCC ( body centred cube ) has effective number of atoms 2.

(B) Differences:

1. Crystalline solids have a long-range order (periodic repeating pattern observed over long distances) whereas amorphous solids have short range order (periodic repeating pattern observed over short distances).

2. Crystalline solids are anisotropic (some properties differ with the difference in directions within the same crystal ) whereas amorphous solids are isotropic (properties doesn’t differ with the difference in directions within the same crystal).

OR

(A) given weight = 8.1g

atomic mass = 27gmol^-1 = 6.023 10²³ atoms weigh 27g

(1 mole = Avogadro's number of atoms )

Now, we know that total number of atoms in FCC unit cell is 4.

So 1 unit cell weighs the same as 4 atoms of Al

6.023 10²³ atoms weigh 27g

4 atoms mass = ?

4 atoms mass = (27 4) / 6.023 10²³

18 10^-23 g

1 unit cell mass is 18 10^-23 g

Number of unit cells in 8.1 g = ?

Number of unit cells =

= 450 ×10²⁰ unit cells

(B) (i) The Frenkel defect is shown by ionic solids having a large difference in their atomic sizes and Schottky defect is shown by the solids having similar sized anion and cation. NaCl contains Na and Cl which have almost same size, therefore exhibiting Schottky defect.

(ii) Silicon belongs to group 14 and has 4 valence electrons. When it is doped with phosphorous which belongs to group 15 and has 5 valence electrons, 4 out of 5 electrons form covalent bonds with Silicon and the remaining 1 is left free and delocalized which increases the conductivity of the silicon crystal. As the increase in conductivity is due to the negative charged electron, hence silicon doped with an electron-rich impurity is called n-type semiconductor.

(iii) Ferrimagnetism is observed when the magnetic moments of the domains in the substance are aligned in parallel and anti-parallel directions in unequal numbers. So, there exists some resultant magnetic moment.

But in the case of antiferromagnetic substances, the domains are oppositely oriented and cancel out each other's magnetic moment and become 0.

So, ferrimagnetic substances show better magnetism than antiferromagnetic substances.