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Syllabus

राष्ट्रीय शिक्षा नीति के नवीन पाठ्यक्रमानुसार
अतुल प्रोफेसर माइन्ड
Question Bank
बी. एस-सी. तृतीय वर्ष : सेमेस्टर-पंचम
भौतिक विज्ञान
प्रथम प्रश्न-पत्र : चिरसम्मत और सांख्यिकीय यांत्रिकी
(Classical and Statistical Mechanics)
(OMR)
पाठ्यक्रम
PART-A
INTRODUCTION TO CLASSICAL MECHANICS
UNIT-I: Constrained Motion
Constraints: Definition, Classification and Examples. Degrees of Freedom
and Configuration space. Constrained system, Forces of constraint and
Constrained motion. Generalised coordinates, Transformation equations
and Generalised notations & relations. Principle of Virtual work and
D’Alembert’s principle.
UNIT-II : Lagrangian Formalism
Lagrangian for conservative & non-conservative systems, Lagrange’s
equation of motion (no derivation ), Comparison of Newtonian & Lagrangian
formulations, Cyclic coordinates and Conservation laws (with proofs and
properties of kinetic energy function included). Simple examples based on
Lagrangian formulation.
UNIT-III : Hamiltonian Formalism
Phase space, Hamiltonian for conservative & non-conservative systems,
Physical significance of Hamiltonian, Hamilton’s equation of motion (no
derivation), Comparison of Lagrangian & Hamiltonian formulations, Cyclic
coordinates and Construction of Hamiltonian from Lagrangian. Simple
examples based on Hamiltonian formulation.

UNIT-IV: Central Force
Definition and properties (with prove) of central force. Equation of motion
and differential equation of orbit. Bound & unbound orbits, stable & non-
stable orbits, closed & open orbits and Bertrand’s theorem. Motion under
inverse square law of force and derivation of Kepler’s laws. Laplace-Runge-
Lenz vector (Runge-Lenz vector) and its applications.
PART-B
INTRODUCTION TO STATISTICAL MECHANICS
UNIT-V: Macrostate & Microstate
Macrostate, Microstate, Number of accessible microstates and Postulate
of equal a priori. Phase space, Phase trajectory, Volume element in phase
space, Quantisation of phase space and number of accessible microstates
for free particle in ID, free particle in 3D & harmonic oscillator in ID.
UNIT-VI: Concept of Ensemble
Problem with time average, concept of ensemble, postulate of ensemble
average and Liouville’s theorem (proof included). Micro Canonical, Canonical
& Grand Canonical ensembles. Thermodynamic Probability, Postulate of
Equilibrium and Boltzmann Entropy relation.
UNIT-VII Distribution Laws
Statistical Distribution Laws: Expressions for number of accessible
microstates, probability & number of particles in ith state at equilibrium for
Maxwell-Boltzmann, Bose-Einstein & Fermi- Dirac statistics. Comparison
of statistical distribution laws and their physical significance. Canonical
Distribution Law: Boltzmann’s Canonical Distribution Law, Boltzmann’s
Partition Function, Proof of Equipartition Theorem (Law of Equipartition of
energy) and relation between Partition function and Thermodynamic
potentials.
UNIT-VIII: Applications of Statistical Distribution Laws
Application of Bose-Einstein Distribution Law: Photons in a black body
cavity and derivation of Planck’s Distribution Law.
Application of Fermi-Dirac Distribution Law: Free electrons in a metal,
Definition of Fermi energy, Determination of Fermi energy at absolute zero,
Kinetic energy of Fermi gas at absolute zero and concept of Density of
States (Density of Orbitals).

पिछले साल का exam paper K QUESTIONS

B.Sc. (Semester-V) Examination, 2023-24
भौतिक विज्ञान (Physics-I)
प्रथम प्रश्न-पत्र
Classical & Statistical Mechanics
1. संरक्षी निकाय के लिए, गति की लागरेज समीकरण है-
d L
OL
+
dal
(अ)
=0
=0
dt q,
dq,
dt 0q,
dal aL
(स)
=0 (द) इनमें से कोई नहीं
dt da,
q,
g
उत्तर- (ब)
2. सरल लोलक पर उपस्थित द्रव्यमान बिन्दु की गति में कौन-सा प्रतिबंध नियत होता है।
(अ) होलोनोमिक
(स) रेयोनॉमिक
3. प्लांक नियतांक (11) का मान क्या होता है-
(31) 6.63 x 10
जूल-से.
(स) 6.63×10
-34.
जूल-से
4. बोल्ट्जमान विहित वितरण में विभाजन फलन है-
(अ) Zelk
E / T
i
(स)
-E,/kT
(ब) नॉनहोलोनोमिक
(द) इनमें से कोई नहीं
उत्तर- (स)
(ब) 6.63 × 10
30.
जूल-से.
() 6.63 x 10
-38.
जूल-से.
उत्तर- (स)
(ब) [g, ea/kt
Ze, g, ee//kt
(द)
28, eG/KT
उत्तर- (ब)
5. 3-D आकाश में मुक्त कण के लिए, ऊर्जा परास 0 से E, में उपलब्ध सूक्ष्म अवस्थाओं
की संख्या-
(31) n(E)=
4rV
3h3
-(2mE)/
(ब) n(E) =
4TV
3h
(2mE3/2/
(स) (E)= (2 mE) 5/2
4TV
3h3
(द) उपरोक्त में से कोई नहीं
उत्तर- (ब)
6. केन्द्रीय बल के कारक बनी कक्षा की उत्केन्द्रता होगी-
1/2
(अ) = {1+
El²
1/2
E/²
mk
mk2
1/2
(स) ε=<I+
E/²
1/2
(द) : = < 1
E/2
mk³
उत्तर- (ब)
mk