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K.S ACADEMY, SALEM-QUESTION PAPER

K.S ACADEMY, SALEM PG TRB & TNSET COACHING CENTRE FOR PHYSICS CELL:9042976707 Page 1

PG TRB , POLYTECHNIC TRB & TNSET COACHING CENTRE FOR PHYSICS

Quantum & Statistical Mechanics model question paper

Time:1Hour Marks: 45

************************************************************************

Answer all the question:

1. For a self adjoined operator the eigen value and eigen functions belonging to

distinct eigen values are recpectively (PGTRB-2015)

a) Real , non orthogonal b) complex , non orthogonal

c) Real , orthogonal d) complex, orthogonal

2. For a system of 𝑁𝑖 particles with energy 𝐸𝑖 and chemical potential 𝜇, Maxwell –

Boltzman statistics function is (TRB ENGG COLLEGE ASST PROF-2016)

a) 𝑁𝑖 =𝑔𝑖

𝑒𝐾𝑇 𝐸𝑖−𝜇 b) 𝑁𝑖 =

𝑔𝑖

𝑒𝐸𝑖

𝐾𝑇

c) 𝑁𝑖 =𝑔𝑖

𝑒𝐾𝑇 𝐸𝑖 d) 𝑁𝑖 =

𝑔𝑖

𝑒𝐸𝑖−𝜇

𝐾𝑇

3. The microstate is defined by (PG TRB 2004-2005)

a) pressure and volume of the gas.

b) pressure and temp of the gas.

c) pressure, temp of the gas.

d) position & velocity component of the molecules

4. An object takes 5 minutes to cool from 80°𝐶 to 64°𝐶. And it will take 10 minutes

to cool to 52°𝐶 then the temperature of the surroundings is (TRB –JUNIOR

GRADUATE ASST 2003-2004)

a) 43°𝐶 b) 8.16°𝐶 c)16°𝐶 d) 20°𝐶 5. The certainty of finding a particle in a given volume is (PG TRB 2003-2004)

a) |Ψ|2 𝑑𝑣 = 0 b) |Ψ|2 𝑑𝑣 = 1

c) |Ψ|2 𝑑𝑣 ≤ 1 d) |Ψ|2 𝑑𝑣 > 1

6. In partial wave analysis the scattering cross section is maximum when the phase

shift 𝛿𝑙 is

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a) 0 𝑜𝑟 180˚ b) ±𝜋 2, ±3𝜋

2

c) ±𝜋 3, ±𝜋6 d)

2𝜋3

7. Thermodynamics mostly deals with (TNPSC-SCHOOL ASST)

a) Measurement of quantity of heat b) transfer of heat

c) conversion of heat to other forms of energy d) change of state

8. In van der Waals` equation the critical pressure 𝑃𝑐 is given by (TRB –BT ASST-

2005 – 2006)

a) 8a/27Rb b) 3b c) (a/27𝑏2) d) (27𝑏2/8𝑎)

9. which condition is to be satisfied by a normalized wave function ? (TRB BRTE

2008-09)

𝑎) Ψ2∗𝑏

𝑎 𝑥 Ψ1 𝑥 𝑑𝑥 = 0 b) Ψ Ψ

∗ 𝑑𝑥 𝑑𝑦 𝑑𝑧 = 1

c) Ψ2∗𝑏

𝑎 𝑥 Ψ1 𝑥 𝑑𝑥 = 1 d) Ψ Ψ

∗ 𝑑𝑥 𝑑𝑦 𝑑𝑧 = 0

10. The eigen value of the equation 𝑑2

𝑑𝑥 2 (sin 4 𝑥 ) is (TNPSC SCHOOL ASST)

a) -4 b) 4 c) 16 d) -16

11. The relation connecting slope of an isothermal (𝑠𝑖) and an adiabatic (𝑠𝑎) is if

𝛾 =𝐶𝑝

𝐶𝑣 (TRB-POLY COLLEGE LECTURER 2006-07)

a) 𝑠𝑖 = 𝛾𝑠𝑎 b) 𝑠𝑖 + 𝑠𝑎 = 𝛾 c) 𝑠𝑎 = 𝛾𝑠𝑖 d)

𝑠𝑖 − 𝑠𝑎 = 𝛾

12. The optical theorem relation

a) The imaginary part scattering cross – section to the forward differential

scattering cross – section

b) Scattering amplitude and differential scattering cross section

c) Scattering flux to the total scattering cross section

d) Forward scattering amplitude to the total scattering cross section

13. Momentum of a photon of wavelength 𝜆 is (TRB –JUNIOR GRADUATE ASST-

2002)

𝑎) 𝜆 b)

𝜆 c)

𝜆

d)

𝑐𝜆



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14. Which of the following have negligible potential energy and almost all of its

kinetic energy appear as internal energy? : (TRB –BT ASST-2001)

a) Solid substance b) liquid substance

c) gas substance d) soild, liquid & gas substance

15. The translational partition function Z for molecules of a perfect gas is given by:

(TRB SCERT LECTURER-2016)

a) 𝑉

3(2mkT)

3

2 b) 𝑉

3(2mkT)

1

2

c) 𝑉

3(2mkT) d)

𝑉

3(2mkT)

−1

2

16. The wave function of a particle in a box 𝑉 = ∞ 𝑓𝑜𝑟 𝑥 ≤ 0 𝑎𝑛𝑑 𝑥 ≥ 𝐿

𝑉 = 0 𝑓𝑜𝑟 0 < 𝑥 < 𝐿 PG TRB-2011-12

a) 𝐴 sin 𝑛𝜋

𝐿 𝑥 b) 𝐴 cos

𝑛𝜋

𝐿 𝑥

c) 𝐴 𝑒−𝑘𝑥 d) A sin kx + B cos kx

17. The value of [𝐿𝑦2 , 𝐿𝑥 ] is: (SCIENTIFIC ASST)

a) 0 b) -2iℏ𝐿𝑧

c) iℏ 𝐿𝑧𝐿𝑦 − 𝐿𝑦𝐿𝑧 d) 2iℏ𝐿𝑧

18. If 𝐸0 is the zero point energy of a harmonic oscillator of frequency 𝜈 and

plank’s constant h , then its energy in the n = 2 state will be (TNSET 2016)

a) 𝐸0 b) 𝐸0 + 2𝜈 c) 4𝐸0 d) 2𝐸0

19. A black body radiates energy at rate of E watt/𝑚2 at a high temperature

𝑇𝐾. when the temperature is reduced to 𝑇

2𝐾. the radiant energy will be. (TRB ENGG

COLLEGE ASST PROF 2012)

a) 𝐸

64 b)

𝐸

32

c) 𝐸

16 d)

𝐸

8

20. Correct identity is. (TRB POLY COLLEGE LECTURER 2012)

a) [𝐿𝑥 , 𝐿𝑦 ] = 0 b) [𝐿2, 𝐿𝑥] = 0

c) [𝐿𝑥 , 𝐿𝑦 ] = iℏ𝐿𝑦 d) [𝐿𝑦 , 𝐿𝑧] = iℏ𝐿𝑧

21. The statistics theory which supports the Zero point energy of a gas event at

absolute Zero is. (TRB POLY COLLEGE LECTURER 2006-07)

a) Classional statistics b) B. E statistics

c) F. D statistics d) all of these



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22. The phase-space consists of________dimensional space. (PGTRB-2013)

a) 2 b) 4 c) 6 d) 8

23. Which of the following is an acceptable wave function ? (PGTRB-2013)

a) Ψ = x b) Ψ = x2

c) Ψ = sinx d) Ψ = 𝑒𝑥

24. The dimensional formula of thermal conductivity K is (TRB-AEEO 2009-

2010)

a) 𝑀𝐿𝑇−2 𝜃 b) 𝑀𝐿𝑇−1 𝜃−1

c) 𝑀𝐿−1𝑇−3 𝜃 d) 𝑀𝐿𝑇−3 𝜃−1

25. A thermos flask containing tea is shaken vigorously. Considering tea as a

system, which one of the following is a false statement? (TRB-BRTE 2007-2008)

a) Heat has been added to tea b) work has been done on it

c) its internal energy has been changed d) its temperature rises.

26. The Fermi golden rule gives [TNSET 2012]

a) first order correction to energy b) average energy transfer

c) the transistion probability per unit time d) scattering cross section

27. The second order perturabation energy is

a) 𝐸𝐾" =

2

𝐸𝐾0−𝐸𝑙

0∞𝑙=0 b) 𝐸𝐾

" =


0∞𝑙=0

c) 𝐸𝐾" =


0

𝐻 ′∞𝑙=0 d) 𝐸𝐾

" = < 𝑙 𝐻′ 𝑙 > 2∞

𝑙=0

28. The value of 𝑃𝑦𝑦 − 𝑦𝑃𝑦 is [TNSET 2012]

a) 0 b) 𝑖ħ c) −𝑖ħ d) 1

29. If 𝜎𝑥 ,𝜎𝑦 𝑎𝑛𝑑 𝜎𝑧 are Pauli spin matrices and A & B any constant vectors then

𝜎 .𝐴 𝜎 .𝐵

a) 𝐴 × 𝐵 + 𝑖𝜎 . 𝐴.𝐵 b) 𝐴 × 𝐵 − 𝑖𝜎 . 𝐴.𝐵

c) 𝐴 .𝐵 + 𝑖𝜎 . 𝐴 × 𝐵 d) 𝐴 .𝐵 + 𝑖𝜎 . 𝐴 × 𝐵

30. What is the unit of volume element in phase space

a)𝑚3 b) (𝐽𝑜𝑢𝑙𝑒 − 𝑠𝑒𝑐)3 c) 𝐽𝑜𝑢𝑙𝑒 − 𝑠𝑒𝑐 d) 𝐽𝑜𝑢𝑙𝑒



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31. Heat cannot flow from a body at lower temperature to a body at higher

temperature. This statement comes from

a) First law of thermodynamics b) Second law of thermodynamics

c) conservation of energy d) conservation of matter

32. If K, 𝑄𝑁 & U are Boltzmann constant, partition function and internal energy

respectively then

a) 𝑈 = −𝐾𝑇2𝜕

𝜕𝑇 log 𝑄𝑁 b) 𝑈 = 𝐾𝑇

𝜕

𝜕𝑇 log𝑄𝑁

c) 𝑈 = −𝐾𝑇𝜕

𝜕𝑇 log 𝑄𝑁 d) 𝑈 = 𝐾𝑇

2 𝜕

𝜕𝑇 log 𝑄𝑁

33. In an irreversible process with T, V, N remaining constant which of the following

attains minimum under equilibrium? [TNSET 2012]

a) Gibbs free energy b) Helmholtz free energy

c) entropy d) chemical potential

34. The Gibbs phase rule is

a) 𝑃 = 𝐶 + 𝐹 + 1 b) 𝑃 + 𝐹 = 𝐶 − 2

c) 𝑃 = 𝐶 + 2 − 𝐹 d) 𝑃 + 2 = 𝐶 + 𝐹

35. For a free particle, energy and momentum are related as (PGTRB-2005-2006)

a) 𝐸 =𝑝2

𝑚 b) 𝐸 =

𝑝

2𝑚 c) 𝐸 =

𝑝2

2𝑚 d)

𝐸 =𝑝

𝑚

36. The energy of a particle in a square potential well is (PGTRB-2002-2003)

a) Proportional to the square of the quantum number,𝑛

b) inversely proportional to the square of 𝑛

c) proportional to the square of the width of the well

d) proportional to the mass of the particle.

37. Radius of first Bohr orbit of hydrogen atom is (TRB BT ASST-2005-2006)

a) 0.35𝐴° b) 5.321𝐴° c) 3.52𝐴° d) 0.53𝐴°

38. Entropy of the universe is (TRB –GRADUATE ASST-2006-2007)

a) decreases b) increases c) remains constant d) zero

39. According to M. B. statistics, the number of particles in the given energy range is

given by (PGTRB-2001)



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a) 𝑛𝑖 =𝑍𝑖

𝐴𝑒𝐸𝑖/𝐾𝑇 b) 𝑛𝑖 =

𝑍𝑖

𝐴𝑒𝐸𝑖/𝐾𝑇−1

c) 𝑛𝑖 =𝑍𝑖

𝐴𝑒𝐸𝑖/𝐾𝑇 +1 d) 𝑛𝑖 =

𝑍𝑖

𝐴𝑒𝐸𝑖/𝐾𝑇 ±1

40. For a self adjoined operator the eigen value and eigen functions belonging to

distinct eigen values are respectively (PGTRB-2015)

a) Real, non orthogonal b) complex , non orthogonal

c)Real , orthogonal d) complex, orthogonal

41. Rayleigh Jeans law for energy distribution of blackbody radiation is (TRB-BT

ASST 2004-2005)

a) 𝐸𝜆 =𝐾𝑇

𝜆4 b) 𝐸𝜆 =

8𝜋𝐾𝑇

𝜆4 c) 𝐸𝜆 =

8𝜋𝐾𝑇

𝜆5 d) 𝐸𝜆 = 8𝜋𝐾𝑇 × 𝜆

5

42. The change in entropy is (PG TRB 2006-07)

a) Positive in a reversible change b) Negative in an irreversible change

c) Positive in an irreversible change d) Negative in a reversible change

43. Which statistics will apply to deuterons and α – particles?

a) B – E b)F – D c) M – B d) either a (or) b

44. The number of ways 3 particles can be distributed in 4 energy states according

to Fermi – Dirac statics is

a) 2 b) 4 c) 6 d)16

45. The Eigen function of linear harmonic oscillator is found by using

a) Laguerre polynomial b) Legender polynomial

c) Hermite polynomial d) both a & b

ANSWER KEY GIVEN AT THE LAST PAGE

K.S ACADEMY – நடத்தும் முதுகலை பட்டதாரி ஆசிரியர் ( PG TRB )

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𝟑 rd PORTION TEST & HALF TEST

FULL TEST (MORE THAN 10)

DATE : 07.05.2017 (Demo Class) PLACE : JOTHI MATRIC HR.SEC SCHOOL, AMMAPET

COLONY, SALEM

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Answer key

Q.NO ANS Q.NO ANS Q.NO ANS Q.NO ANS Q.NO ANS 1 C 11 C 21 C 31 B 41 B 2 D 12 D 22 C 32 D 42 C 3 D 13 C 23 C 33 B 43 A 4 C 14 B 24 D 34 C 44 B 5 B 15 A 25 D 35 C 45 C 6 B 16 A 26 C 36 A 7 C 17 A 27 A 37 D 8 C 18 B 28 C 38 B 9 B 19 C 29 C 39 A 10 D 20 B 30 B 40 C



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