BSc Physics SEM V ATKT May 2018-19 ATKT PHYSICS MATHEMATICAL THERMAL & STATISTICAL PHYSICS Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate full marks

1. Q1 Attempt any two:
   • (a) State and explain probability theorems. Using this theorem, find the chance 10 of throwing a 6 at least once in two throws of a single die
   • (b) Explain the terms 10 Laws of large number
   • (c) Explain the Poisson distribution and derive the required relations. 10
   • (a) State the second order non- homogeneous linear ordinary differential 10 equation with constant variable and solve the same
   • (b) you mean by partial differential equation? Hence Solve the 10
   • (c) What do you mean by Hyperbolic function in complex number. 10 Prove the following formulas
   • i) cosh? (z) = 1
   • ii) (z) = sinh
2. Q3 Attempt any two:
   • (a) . Derive an expression of root mean square deviation in occupation number 10 of dominate configuration
   • (b) State Boltzmann formula of entropy and derive its relation with Canonical 10
   • (c) Define partition. function. Derive expression for translation partition 10 function. Find translation partition function for Ar confine to a volume of 1L at 298k. (Given mar = 6.63 x kg)
3. Q4 Attempt any two:
   • (a) Consider a large box having area A is divided into k cells of area 10 — N identical balls are thrown in the box in a completely random manner. Hence find the condition for the most probable distribution of N balls
   • (b) What are Fermions? Derive Fermi-Dirac distribution law. 10
   • (c) Derive Rayleigh-Jean’s formula for the black body radiation. 10
4. Q5 Attempt any Four:
   • (i) A club consists of 50 members. In how many ways can a president, 05 vice-president, secretary and treasurer be chosen? In how many ways can a committee of 4 members be chosen?
   • (ii) Three coins tossed, the number of random variables x (say head) are 05
   • a) Mean value of x
   • b) Variance of x
   • c) Standard deviation of x (il) the value of sin + iln 3) 05
   • (iv) Solve = 2y’=3y=e* 05
   • (v) Write notes on Equipartition theorem 05
   • (vi) What is the difference in energy between the n = 2 and n= | states 05 for molecular oxygen constrained by a one-dimensional box having a length of 1.00 cm? (Given mass of O2 = 5.31 x kg.)
   • (vii) Ifthe r.m.s. velocity of the molecules of hydrogen at N.T.P. is 05 1.84 km/s, calculate the r.m.s. velocity of oxygen molecules at
   • N.T.P. Molecular weight of hydrogen and oxygen are 2 and 32
   • (viii) Three identical particles can be in any of the five states. What are the 05 number of possible ways of distributing them in various states
   • (a) M-B. Statistics. (b) B.E. (c) F.D. Statistics

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