BSc Physics SEM V 2017 18 2017-18 Physics I Mathematical And Statistical Physics Question Paper - Mumbai University | munotes

Questions asked in this paper

• 2. Figures to the right indicate full marks

1. Q4 Symbols have usual meaning unless otherwise stated
2. Q5 Use of non-programmable calculator is allowed Table of Laplace Transforms
3. Q1 (a) Attempt any one :—
   • (i) Explain the Poisson distribution and derive the required relations. 10
   • (ii) Write a detailed summary of Methods of counting. 10
   • (b) Attempt any one :—
   • (i) State and explain the laws of Large Numbers. 3
   • (ii) What do you understand by probability functions ? 5
4. Q2 (a) Attempt any one :—
   • (i) Explain the method of solving the differential equations by Laplace 10 Transform and solve the following equation: y" + 4y' + =
   • (ii) Describe the method of solving the second order non-homogenous linear 10 ordinary differential equations with constant coefficients. Solve the
   • (b) Attempt any one :—
   • (i) Solve the equation (D? + 5D + 4)y = cos 2x, where D =
   • (ii) Find the Fourier Transform of . 0,
5. Q3 (a) Attempt any one :—
   • (i) Consider two interactive systems A and They are neither adiabatically 10 isolated nor their external parameters are kept fixed. Show that in equilibrium the temperature and pressure on both sides of the partition S0125/S1014R PHYSICS : PAPER I MATHEMATICAL IN METHODS IN PHYSICS/ THERMAL AND STATISTICAL PHYSICS. ( )
   • (ii) Describe the concept of Gibb's free energy (G). Use this concept toexplain 10 co-existence of two phases and the phase equilibrium curve. Hence discuss the triple point
   • (b) Attempt any one :-—
   • (i) Show that the entropy of a system in a heat bath is given by : 5
   • (ii) Define microstates, macrostate and system state. Two states of a system 5 have an energy difference of 0-028 eV. The relative probability that the lower state be occupied with respect to the upper state is Caiculate temperature of the system
6. Q4 (a) Attempt any one :—
   • (i) Consider a large box having area A is divided into k cells of area ai, 10 N identical balls are thrown in the box in a completely random manner. Obtain the condition for the most probable distribution of N balls in k cells,
   • (ii) What are Bosons? Derive Bose-Einstein distribution law. 10
   • (b) Attempt any one :—
   • (i) Show that, at low frequency Planck's radiation formula reduces to 5
   • (ii) If the mean velocity of hydrogen molecules at a given temperature is 5 1-45 km/sec, calculate their root mean square velocity and most probable velocity at the same temperature 5S. (a) Attempt any one :—
   • (i) Two students are working separately on the same problem. If the first 4 student has probability 1/2 of solving it and the second student has probability 3/4 of solving it, what is the probability that at least one of them solves it ?
   • (ii) people each select at random between 1 and 4 is the probability that 2 people selected the number 29?
   • (b) Attempt any one :-—
   • (i) Show that the cosine transform of the first order derivative is given by 4
   • (ii) Calculate the Laplace Transform F (p) for At) = 1 and At) = cos at. 4
   • (c) Attempt any one
   • (i) Consider a system single particle (with zero spin) inside a box. If 4 energy of the particle in the ground state is E, find energy and degenerancy of the particle in its fifth excited state IN PHYSICS/ THERMAL AND STATISTICAL PHYSICS. ( AL IN METHODS
   • (ii) A system is having 40 spin half particles fixed in Space and placed in 4 Magnetic field B. Find relative Probability of 10% deviation [R,, from the most probable macrostate,
   • (d) Attempt any one
   • (i) Consider distribution of 7 electrons in 10 cells. Find the number 3 of possible arrangements using : (1) B-E Statistics, (2) Statistics, Comment on the results if any,
   • (ii) Solar Spectrum shows that, maximum is emitted at wavelength 3 5500 AU, Assuming the sun as a black body, estimate its temperature,

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