Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Mandi, Himachal Pradesh 175001

India

ph: +(91)1905-237930

achakrab

Engineering Chemistry

This course is a blend of some fundamental chemistry concepts and applied chemistry topics. The course along with CY101 P (Chemistry Practicum) is intended to give a flavor to the students about how the basic chemistry concepts can be applied in real life Engineering applications/problems.

Spectroscopy and classification, fundamental principles, instrumentation and applications of uv-visible spectroscopy, IR spectroscopy, Raman spectroscopy & NMR Spectroscopy.

**Module 2: Polymer Chemistry**

Polymer chemistry, polymerisation, properties, polymer processing, industrial polymers & conducting polymers.

**Module 3: Fules and Combustion**

Fuels and Combustion Properties of fuels, Calorific value, Petroleum and petrochemicals, biofuels.

**Module 4: Electrochemistry**

Electrochemistry, applications of electrochemistry at the interface of science & technology, batteries, fuel cells, biomedical devices, corrosion and its control.

Lubricants, mechanism of lubrication, types, properties & selection of lubricants.

**Text Books**

1. Applied Chemistry - A Textbook for Engineers and Technologists by H.D. Gesser, Springer.

2. Engineering Chemistry by Wiley India Editorial Team, Wiley India Pvt. Ltd., 2011.

3. Engineering Chemistry by Shashi Chawla.

**Physical Chemistry Lectures**

Lecture 1: Course Outline & The State of a System.

Lecture 2: Historical Review: Experiments and Theories.

Lecture 3: Waves vs. Particles, Probability waves.

Lecture 4: Double slit to infinite slit experiments.

Lecture 5: Heisenberg's Uncertainty Relation and de Broglie Hypothesis.

Lecture 6: Observables and Operators.

Lecture 7: Measuremeants in Quantum Mechanics.

Lecture 8: State Functions and Expectation Values.

Lecture 9: Time Development of the state function.

Lecture 10: Commutator Relations in Quantum Mechanics.

Lecture 11: Superposition Principle and Schrodinger's cat experiment.

Lecture 12: An introduction to the Hilber space.

Lecture 13: One dimensional potential step.

Lecture 14: One dimensional rectangular barrier.

Lecture 15: Dirac Delta potential barrier.

Lecture 16: Particle in a box problem (part-1).

Lecture 17: Particle in a box problem (part-2).

Lecture 18: Sudden perturbation & adiabatic perturbation.

Lecture 19: An introduction to wave packet dynamics.

Lecture 20: Born-Oppenheimer Approximation.

Lecture 21: Rigid rotor : quantum aspects.

Lecture 22: Harmonic Oscillator vs. Morse Oscillator.

Lecture 23: Light-Matter interactions.

Lecture 24: Experiment vs. Theory.

**Historical Review of Quantum Mechanics:** 1. Blackbody Radiation, 2. Compton Effect, 3. Photoelectric effect. Students are expected to study the above three introductory topics in detail and submit a short write-up on each topic.Key words: quantum theory, classical theory.Before the final examination, this assignment will be discussed in the class with all details.

**Quantum Mechanics of Hydrogen Atom**. Time Duration: One Month. Students are expected to solve this assignment with the help of Instructor, they are allowed to interact with the instructor by phone,e-mail, chat, tweitt and face to face interactions. Instructor will supply all study materials, help students to understand the concept, derivation,interpretation etc. (that is the reason for calling it 'interactive assignment'). Students will submit an elaborate solution of the problem within one month.Before the final examination, this problem will be discussed in detail in the class.

Topic: Phase Transitions. Students are expected to study the above topic in detail and submit a short write-up. Key word: Thermodynamics. Before the final examination, this assignment will be discussed in the class with all details.

1. Calculate the de Broglie wavelength of (a) an electron travelling at 1.00% of the speed of light & (b) a baseball (0.14 kg) travelling at 40m.s-1. Mass of Electron is 9.11 x 10 -31 kg; Speed of light is 3 x 108 m/s; Planck’s constant is 6.626x10-34 J.s. Is it possible to observe these waves experimentally?

2. What is the uncertainty in speed if we wish to locate an electron within an atom, say, so that uncertainty in position is approximately 50 pm. Mass of Electron is 9.11 x 10 -31 kg; Speed of light is 3 x 108 m/s; Planck’s constant is 6.626x10-34 J.s..

3. Show that Exp[ikx] is an eigenfunction of the (a) Momentum Operator and (b) free particle Hamiltonian Operator.

4. By acceptable eigenfunctions we mean that the eigenfunction is single valued, finite, and continuous and that the first derivative of eigenfunction is continuous. Which of the following eigenfunctions are acceptable and not acceptable, please indicate the reason.

(a) f(x)=Sin(x) & (b) f(x)= x^{2}.

**Quiz 2 : Physical Chemistry Questions**

1. A free particle of mass m is constrained to move along the x-direction. For all values of x the potential is zero. Show that the momentum operator commutes with the Hamiltonian Operator for free particle.

2. A linear operator **R** has the following properties **R** (u+v) = **R** u + **R** v and **R** (cu ) = c **R** u. Where c is a complex number, which of the following operators are linear? (a) u = λ u, where λ = constant (real)., (b) u =1/ u, (c) u = (d/dx) u & (d) u = u -10.

3. What is the flux associated with a particle described by the wave function Ψ(x) = u(x) Exp[i k x], where u(x) is a real function?

4. Why does Ψ(x) Ψ*(x) have to be everywhere real, non-negative, finite, and of definite value ?

5. In ordinary algebra, (P + Q ) ( P – Q ) = P^{ 2} - Q ^{2}. Expand (P + Q) (P – Q). Under what condition do we find the same result as in the case of ordinary algebra?

6. A particle in one dimension is in the energy eigen state Φk = A cos( k x). Measurement of energy finds the value E= E1. What is the state of the particle after measurement ?

7. A free particle of mass m moving in one dimension is known to be in the initial state Ψ(x, 0) = sin ( k x). What is Ψ(x, t)?

8. Consider a situation where it is equally likely that an electron has momentum ± p0. Measurement at a given instant of time finds the value + p0. A student concludes that the electron must had this value of momentum prior to measurement. Is the student correct?

**Final Exam. : Physical Chemistry Questions**

1. A particle of mass m moves in one dimension (x). It is known that the momentum of the particle is P_{x} = ħKo, where K_{0} is a known constant. What is the time-independent wave function of this particle?

2. Under what conditions is the expectation value of an operator Â (which does not contain the time explicitly) constant in time?

3. Can a harmonic oscillator can ever be dissociated? Explain.

4. What is Born-Oppenheimer approximation ?

6. Consider a particle with energy E = P^{2}/(2m) moving in one dimension (x). The uncertainty in its location is Δx. Show that of Δx Δp ≥ ħ/2, then ΔE Δt ≥ ħ/2, where (p/m) Δt = Δx.

7. What are the energy eigenfunctions and eigenvalues for the particle in an one dimensional box problem, if the ends of the box are at –L/2 and L/2 ?

8. Give an argument in support of the statement that one cannot measure the momentum of a particle in an one dimensional box, with absolute accuracy.

10. Calculate the probability that a particle in an one dimensional box of length a is found to be between 0 and a/2.

11. What are the units if any, for the wave function of a particle in an one dimensional box?

12. Consider a particle of mass m in an one dimensional box of length a. Its average energy is given by <E> = <p^{2}>/(2m). Because <p> = 0, <p^{2}> = (Δp)^{2}, where Δp can be called, the uncertainty in p. Using the uncertainty Principle, show that the energy must be at least as large as ħ^{2}/(8ma^{2}) because Δx, the uncertainty in x, cannot be larger than a.

**Make-up of Final Exam. : Physical Chemistry Questions**

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1. Show that Exp[- i k x] is an eigenfunction of the (a) Momentum Operator & (b) Free Particle Hamiltonian Operator.

2. By acceptable eigenfunctions we mean that the eigenfunction is single valued, finite, and continuous and that the first derivative of eigenfunction is continuous. Which of the following eigenfunctions are acceptable and not acceptable, please indicate the reason. (a) f(x)=1/x^{2}, (b) f(x)=x^{2}, (c) f(x)=1+ x^{2} & (d) f(x)= Exp[- x^{2}].

3. What is the flux associated with a particle described by the wave function Ψ(x) = Sin(k x)?

4. Show that momentum operator commutes with the Hamiltonian Operator for a free particle.

5. Why does Ψ(x) Ψ*(x) have to be everywhere real, non-negative, finite, and of definite value?

6. Find the reflection coefficient through the potential of the form V(x) = K_{0} δ(x), where K_{0 }is a positive number.

7. Calculate the probability that a particle in a one-dimensional box of length ‘a’ is found to be between 0 & a/2.

8. Consider the particle-in-box problem in which V(x)=0 inside the box and V(x)= ∞ otherwise. Derive expressions for energy levels and eigenfunctions.

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For IIT Mandi Students (B.Tech./M.Tech./M.S./M.Sc./Ph.D.) - You are always welcome to inquire about working on a project (irrespective of your discipline). For more details - visit my office!

Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Mandi, Himachal Pradesh 175001

India

ph: +(91)1905-237930

achakrab