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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, ENG TRB, AEEO TRB TNPSC SCIENTIFIC ASSISTANT & TNSET
COACHING CENTRE FOR PHYSICS
Quantum & Statistical Mechanics model question paper
PG TRB AND POLYTECHNIC TRB
2nd BATCH DEMO CLASS ON 20 MAY 2018 (SUNDAY) EFFECTIVENESS OF CLASS WITNESSED ONLY BY
ATTENDING THE CLASS ************************************************************************
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)
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K.S ACADEMY, SALEM-QUESTION PAPER
K.S ACADEMY, SALEM PG TRB & TNSET COACHING CENTRE FOR PHYSICS CELL:9042976707 Page 2
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
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
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K.S ACADEMY, SALEM-QUESTION PAPER
K.S ACADEMY, SALEM PG TRB & TNSET COACHING CENTRE FOR PHYSICS CELL:9042976707 Page 3
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
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)
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K.S ACADEMY, SALEM-QUESTION PAPER
K.S ACADEMY, SALEM PG TRB & TNSET COACHING CENTRE FOR PHYSICS CELL:9042976707 Page 4
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
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
" =
𝐸𝐾0−𝐸𝑙
0∞𝑙=0
c) 𝐸𝐾" =
𝐸𝐾0−𝐸𝑙
0
𝐻 ′∞𝑙=0 d) 𝐸𝐾
" = < 𝑙 𝐻′ 𝑙 > 2∞
𝑙=0
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K.S ACADEMY, SALEM-QUESTION PAPER
K.S ACADEMY, SALEM PG TRB & TNSET COACHING CENTRE FOR PHYSICS CELL:9042976707 Page 5
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
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
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K.S ACADEMY, SALEM-QUESTION PAPER
K.S ACADEMY, SALEM PG TRB & TNSET COACHING CENTRE FOR PHYSICS CELL:9042976707 Page 6
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)
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
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K.S ACADEMY, SALEM-QUESTION PAPER
K.S ACADEMY, SALEM PG TRB & TNSET COACHING CENTRE FOR PHYSICS CELL:9042976707 Page 7
ANSWER KEY GIVEN AT THE LAST PAGE
****************************************************************************************
ீங்களும் ிச்சனம் அபசு ள்ி ஆசிரினபாக & ாிடெக்ிக் விரிவுரபனாபாக ணினாற்
K .S அகாெநினில் இரணந்து னன்டறுவரீ் ! (𝑬𝒙𝒄𝒍𝒖𝒔𝒊𝒗𝒆𝒍𝒚 𝒇𝒐𝒓 𝑷𝑯𝒀𝑺𝑰𝑪𝑺)
TRB தேர்வில் அனுபவம் ிக்க தபாசிரிரக் ககாண்டு நடத்ேப்படுகிமது.
ஒவ்கவாரு UNIT க்கும் SLIP TEST , UNIT TEST நடத்ேப்படும்.
ஒவ்கவாரு UNIT க்கும் 400 தகள்விகள் ககாடுக்கப்படும் ேினந்தோறும் தேர்வுகள் நடத்ேப்படும். 1/3 rd PORTION TEST , HALF PORTION TEST நடத்ேப்படும்.
பத்து முழு தேர்வுகள் (TEN FULL TEST) நடத்ேப்படும். காத்ோக 4000 வினாக்கரர ககாடுத்து பிற்சி
அரிக்கப்படும். 2001 ஆம் ஆண்டு முேல் நரடகபற்ம PG TRB வினாக்கள்
ககாடுக்கப்படும். 2006 ஆம் ஆண்டு முேல் நரடகபற்ம பாயிகடக்னிக் , DIET
விரிவுராரர் ற்றும் கபாமிில் கல்லூரி தபாசிரிர்
(Polytechnic , DIET & Engineering TRB ) வினாக்கள் ககாடுக்கப்படும்.
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K.S ACADEMY, SALEM-QUESTION PAPER
K.S ACADEMY, SALEM PG TRB & TNSET COACHING CENTRE FOR PHYSICS CELL:9042976707 Page 8
TNPSC நடத்ேி பள்ரி இரங்கரய ஆசிரிர் (BT SCHOOL ASST ) வினாக்கரில் PG TRB SYLLABUS வுடன் கோடர்புரட வினாக்கள் ககாடுக்கப்படும்.
தலும் இந்ே பிற்சி வகுப்பில் கயந்துககாள்வது TNSET ,CSIR – NET, DIET LECTURER TRB & ENGINEERING ASSISTANT PROFESSOR
TRB, SCIENTIFIC ASSISTANT (TNPSC ), DEO (TNPSC MAINS PAPER -3) ,
TNPSC SCHOOL ASSISTANT தேர்வுகலக்கு பன்படும். EDUCATION , PSYCHOLOGY & GK விற்கு ேனிாக
அனுபவம் ிக்க ஆசிரிரக் ககாண்டு பிற்சி ககாடுக்கப்படும்
TRB பிற்சி வகுப்பு 20.05.2018 முேல் கோடங்கப்படுகிமது
வாங்க படிக்கயாம் ! பிற்சி கபமயாம் !! கவற்மி நிச்சம் !!!
EXAM NO OF CANDITATE
SELECTED
PG TRB 2013 2 (100%)
PG TRB 2014 6 (86%)
TNSET 2016 5 (71%)
PG TRB 2017 26 (74%)
TNSET 2017 WE EXPECT -12
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K.S ACADEMY, SALEM-QUESTION PAPER
K.S ACADEMY, SALEM PG TRB & TNSET COACHING CENTRE FOR PHYSICS CELL:9042976707 Page 9
20.5.2018 முதல் வகுப்புகள் ஆபம்ம் K.S ACADEMY
சுப்பரீிர் அகாெநி
டவுன் ில்தவ ஸ்தடஷன் அருகில்
தசயம்-1
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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