Engineering Physics-Nagpur-Winter-2015

B.E. Second Semester All Branches (C.B.S.)

Time: 2 hours
Maximum marks: 40

List of constants :
1. Planck’s constant ‘h’ = 6.63×10^-34J.S.
2. Velocity of light ‘C’ = 3×10⁸ m/s
3. Charge on electron ‘e’ = 1.602×10^-19C.
4. Mass of electron ‘m’ = 9.11×10^-31 kg
5. Avogadro’s constant ‘N_A‘= 6.023×10²⁶ $latex \frac{atoms}{kmole}$
6. Boltzman’s constant ‘K’ = 8.6×10^–5 eV/K.
1. (a) In Compton effect, considering elastic collision between a photon and a free electron write down equations of energy and momentum conservation. [3M]

(b) Prove that a free electron can not absorb a photon completely. [3M]

(c) X-ray of wavelength 1 Å are scattered from a carbon block in a direction 90°. Calculate the observed Compton shift. How much kinetic energy is imparted to the recoil electron? [4M]

OR

2. (a) What is de Broglie hypothesis ? Show how the quantization of angular momentum follows from the concept of matter waves. [3M]

(b) Describe an experiment, which supports the existence of matter waves. [4M]

(c) A bullet of mass 45 gm and an electron both travel with a velocity of 1200 m/s. What wavelengths can be associated with them ? Why is the wave nature of bullet not revealed through diffraction effect? [3M]

3. (a) What do you understand by a wave packet ? Obtain the relation between group velocity and phase velocity.
[4M]

(b) Arrive at Heisenberg uncertainty principle with the help of a thought experiment. [3M]

(c) Compute the minimum uncertainty in the location of a body having mass of 2 gm moving with a speed of 1.5 m/s and the minimum uncertainty in the location of electron moving with speed of 0.6×10⁸ m/s. Given DP = 10^–3 P. [3M]

OR

4. (a) Explain physical significance of wave function y. [2M]

(b) Using Schrodinger’s time independent equation, obtain an expression for eigen function of particle in one dimensional potential well of infinite height. [5M]

(c) An electron is confined to move in a one dimensional potential well of length 5 Å. Find the quantized energy values for the three lowest energy states in eV. [3M]

5. (a) Define : [4M]
(i) Space Lattice
(ii) Co-ordination number
(iii) Atomic packing fraction
(iv) Unit Cell.

(b) What are Miller Indices ? Draw the planes (210) and (010) for simple cubic structure. [3M]

(c) Aluminum has FCC structure. Its density is 2700kg/m3. Calculate unit cell dimension and atomic radius. Atomic weight of aluminum is 26.98. [3M]

OR

6. (a) Show that FCC structure possesses maximum packing density and minimum percentage of void space among BCC and FCC. [4M]

(b) Derive Bragg’s law of X-ray diffraction. [3M]

(c) The Bragg angle corresponding to the first order reflection from the plane (111) in a crystal is 30° when X-rays of wavelength 1.75 Å are used. Calculate inter planer spacing and lattice constant. [3M]

7. (a) Show that for an intrinsic semiconductor, the Fermi level lies at the middle of the band gap. [3M]

(b) Derive the expression for Hall voltage and Hall coefficient for extrinsic semiconductor. [4M]

(c) A strip of n-type germanium semiconductor of width 1 mm and thickness 1 mm has a Hall coefficient 10² m³/C. If the magnetic field used is 0.1 T and the current through the sample is 1 mA, determine the Hall voltage produced and also find carrier concentration of electron. [3M]

OR

8. (a) Draw the energy band diagram for a pn-junction diode in equilibrium and show that height of potential barrier is given by $latex V_0=\frac{K_T}el\;n\left[\frac{N_DN_A}{n_i^2}\right]$ where symbols have their usual meaning. [4M]

(b) Explain, why in a transistor (i) the base is thin and lightly doped (ii) the collector is large in size. [2M]

(c) Calculate the conductivity of Germanium plate having area 1 cm² and thickness 0.03 mm when a potential difference of 2 volts is applied across the faces. Given : concentration of free electron in Ge is 2×10¹⁹ /m³ and
μ_e = 0.39 m²/V.s and μ_h = 0.19 m²/V.s. Also calculate the current produced in it. [4M]