problem 1: Answer the following problem in brief:

a) Can a unit cell in the shape of a pentagon make a two dimension crystal lattice? Describe.

b) Find out the volume of the primitive cell of a bcc lattice.

c) Is it possible to carry out electron diffraction studies in air? Validate.

d) Describe why diamond crystals have a regular tetrahedron structure.

e) Find out the velocity of a longitudinal wave all along the x-direction for which the particle displacement is represented by u₁ = u₀ exp [i (k x − ω₀t)].

f) How does the linear monoatomic chain of atoms act like a low pass filter?

g) Sketch the first and second Brillouin zone for a 2-d square lattice.

h) What is the consequence of lowering the dopant concentration on the Fermi energy and carrier concentration of an n -type semiconductor?

i) Differentiate between substitutional and interstitial impurities with the help of a diagram.

j) Enlist the factors which find out the power available from a photovoltaic device.

problem 2:

a) Nb has a density of 8.57 g cm⁻³, a lattice constant of 4.05 Å and an atomic weight of 92.91 u. Find out the number of atoms per unit cell of Nb and predict its crystal structure.

b) Aluminium which crystallizes in c structure has an atomic radius of 1.43 Å. Find out the distance between its (100) and (111) planes.

c) Find out the boundaries of the first Brillouin zone for Chromium that has a bcc crystal structure and a lattice constant of 2.88 Å.

d) The values of 2d for three different diffracting crystals are 25.757Å, 8.742Å and 4.027Å.  By using Bragg’s Law, find out which of such crystals must be used to measure the intensities of X-rays for which λ = 1.937 Å, given that the optimal range of 2θ for each crystal lies between 30° - 130 °.

problem 3:

a) Compute the closest neighbor distance for CeCl given that its lattice energy is 652 kJ mol⁻¹, its Madelung constant is 1.763 and its repulsive exponent is 10.6.

(Take ε₀ = 8.86 × 10⁻¹² Farad m⁻¹).

b) The elastic stiffness constants for Ag are as shown below:

C₁₁ = 1.24 × 10¹¹ Nm⁻²; C₄₄ = 0.461 × 10¹¹ Nm⁻²; C₁₂ = 0.934 × 10¹¹ Nm⁻².

If the density of silver is 10.5 ×10³ kg m⁻³, find out the bulk modulus of silver and the velocity of propagation of the longitudinal and transverse elastic waves in the [110] direction.

c) The lattice constant for KI is 7.06 Å and the Young’s modulus in the [100] direction is 3.15 x 10¹⁰ Nm⁻². Compute the force constant and the frequency at which electromagnetic radiation is strongly reflected by the KI crystal. The atomic weights of K and I are 39 and 127 correspondingly.

d) find out the temperature at which the lattice heat capacity and the electronic heat capacity of Ag are equivalent. The Debye temperature and the Fermi energy for Ag are 216 K and 5.51 eV respectively.

problem 4:

a) What is the temperature at which the probability of the electrons in silver to have energy 1.01 EF is 10%. (EF for silver is 5.51 eV).

b) By tabulating the values of [(P/αa) sin αa + cos αa] for P = 5Π/2 and different values of αa find out the width of the first allowed energy band.

c) The resistivity of Ge at 40°C is 0.2 ohm m. find out its resistivity at 20°C.

d) Find out the wavelength of the photon whose energy is enough to break up the Cooper pairs in mercury, given that the critical temperature of mercury is 4.2 K.

problem 5:

a) Compute the susceptibility for a He atom in its ground (1s) state.

b) Differentiate between a substitutional solid solution and an interstitial solid solution with suitable illustrations.

c) What are modifiers? Describe with exs the changes in the properties of glasses due to some typical modifiers.

d) describe the process of photocopying based on the principle of xerography.