## Engineering Physics - December 2012

### RGPV First Year Engineering (Set B) (Semester 1)

Total marks: --

Total time: --
INSTRUCTIONS

(1) Assume appropriate data and state your reasons

(2) Marks are given to the right of every question

(3) Draw neat diagrams wherever necessary

### Answer the any one question from Q1 & Q2

**1 (a)**Explain the concept of wave packet and give Mathematical proof of Heisenberg's uncertainty relation between energy and time. 7 marks

**1 (b)** Write shrodinger time dependent and Time Independent wave equation. Explain it's physical significance and discuss the term in equation which is related with physical problem.
7 marks

**2 (a)** An electron is confined in one dimensional square well of length 0.4 × 10^{-9} m. Find the energy of particle when its Eigen function has four antinodes and show that the particle can never have energy equal to 800 eV. [ Given h=6.63 × 10^{-34} J sec, m=9.13×10^{-31} kg].
7 marks

**2 (b)** Derive an expression of kinetic energy of recoil electron in compton scattering. Why compton scattering is observed in x-rays, not in visible light waves.
7 marks

### Answer the any one question from Q3 & Q4

**3 (a)**Describe Fresnel Biprism. Discuss the effect of introducing thin mica sheet in the path of one of the interfering beams in a experiment. Deduce the expression for displacement of fringes. 7 marks

**3 (b)** In a Newton's ring experiment the diameter of 5^{th} dark ring is reduced to half of its value after placing a liquid between plane. Glass plate and convex surface. Calculate the refractive index of liquid.
7 marks

**4 (a)** Give construction and theory of plane transmission grating. Obtain an expression for resolving power of plane transmission grating.
7 marks

**4 (b)** For a calcite, ?_{??}=1.658 and ?_{?=1.486 for sodium light of ??=5893 A°. Calculate the minimum thickness of quarter wave plate for calcite.}
7 marks

### Answer the any one question from Q5 & Q6

**5 (a)**Mention sailent feature of liquid model and explain various terms given in Bethe-Weizsacker semi-empirical mass formula. 7 marks

**5 (b)** Give applications and limitations of GM counter.
7 marks

**6 (a)** Give construction and working of Bainbridge mass spectrograph. If two isotopes of an element with mass m_{1} and m_{2} enters the mass spectrograph, what will be the ratio of the radii of their paths.
7 marks

**6 (b)** A cyclotron has magnetic field of 2×10^{4} Gauss and radius of 85 cm. Calculate frequencies of the alternating electric field that must be applied and to what energy proton and electron can be accelerated.

[1 amv=1.67 × 10^{-27} kg, e=1.6×10^{-19} C]
7 marks

### Answer the any one question from Q7 & Q8

**7**Draw periodic potential observed by an electron. Moving in one dimensional crystal lattice. Discuss Kronig-Penney model proposed for periodic potential. Write shrodinger wave equation for such potential and discuss its solution. 7 marks

**8 (a)** What is Hall effect? Deduce an expression for Hall coefficient of a solid and describe method for its determination experimentally, what important informations are obtained from its measurements?
7 marks

**8 (b)** A current of 1 ? A flow in a copper strip of length 10 cm and width 5 cm along its length. The strip in placed in a magnetic field of strength 3×10^{-6} weber/m^{2} perpendicular to its length. If R_{4}=0.55×10^{10} volt-m^{3}/ ampere weber, find the Hall voltage developed in it.
7 marks

### Answer the any one question from Q9 & Q10

**9 (a)**Differentiate between spontaneous and stimulated emission. 7 marks

**9 (b)** How laser light is different from ordinary light? Discuss the construction and working of HeNe laser or CO_{2} laser. Write any two characteristics of these lasers.
7 marks

**10 (a)** Derive an expression for ray dispersion in multimode step index fibers.
7 marks

**10 (b)** Discuss the attenuation and dispersion in optical fibre.
7 marks

**10 (c)** Define and explain following terms for an optical fibre.

(i) Propagation modes.

(ii) Normalized frequency.
7 marks