BSc Physics SEM V 2018 19 2018-19 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) Explain the terms 10 Laws of large number
   • (b) Explain the following random variables 10
2. Q1 Probability functions for the random variables
   • ii) Mean value, Variance and Standard deviation of a random variable x
   • (c) Explain the Poisson distribution and derive the required relations. 10 2 Attempt any two:
   • (a) State the second order non- homogeneous linear ordinary differential 10 equation with constant variable and solve the same
   • (b) What is method of separation of variables for solving partial differential 10 equation? Explain the same by solving heat equation
   • (c) do mean by Hyperbolic function in complex number. 10 Prove the following formulas
   • i) cos 2 (z) = — sin? (z) Attempt any two:
   • (a) Derive an expression of probability of occupying a given energy for 10
   • (b) Define partition function. Derive expression for translation partition 10 function. If translation partition function for Ar is equal to 4.88 x Find the volume in which it confines at temperature of 298k (Given mar = 6.63 x
   • (c) Derive expressions of total energy E for two-level system. 10 Determine the total energy of an ensemble consisting of N particles that have only two energy levels separated by energy hv
3. Q4 Attempt any two:
   • (a) Using Maxwell-Boltzmann distribution law of velocities, derive the 10 expression for root mean square velocity, average velocity and most
   • (b) What are Fermions? Derive Fermi-Dirac distribution law. 10
   • (c) Obtain Wien’s displacement law and Stefan-Boltzmann law using Plank’s 10
4. Q5 Attempt any Four:
   • (i) Find the probability density function of exactly 54 heads in 100 05 tosses of a coin using Normal or Gaussian distribution
   • (ii) Three coins are tossed; what is the probability that two are heads 05 one tails? That the first two are heads and the third tails? If at least two are heads, what is the probability that all are heads?
   • (iii) path of particle in the (x, y) in plane is given by z = z(t) 05 find displacement and velocity
   • (iv) the value of cos z =2. 05
   • (v) What is the difference in energy between the and states for 05 molecular oxygen constrained by a one-dimensional box having a
   • (vi) | What is the weight associated with the configuration corresponding 05 to observing 40 heads after flipping a coin 100 times? How does this weight compare to that of the most probable outcome?
   • (vii) A box of area 1 m? is divided into 100 cells of equal areas. 300 balls 05 are thrown in this box. Calculate a priori probability that the three balls will fall in every cell
   • (viii) that the Plank’s law and the Rayleigh-Jeans’s law become 05 identical if the temperature becomes very high

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