Download PTU M-Sc -Chemistry 2nd Semester May 2019 75983 PHYSICAL CHEMISTRY II Question Paper

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Roll No.

Total No. of Questions : 11

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Total No. of Pages : 02

M.Sc (Chemistry) (2018 Batch) (Sem.-2)

PHYSICAL CHEMISTRY - II

Subject Code : CHL-413-18

M.Code: 75983

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Time: 3 Hrs.

Max. Marks : 70

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains EIGHT questions carrying FIVE marks each and students have to attempt any SIX questions.

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3. SECTION-C will comprise of two compulsory questions with internal choice in both these questions. Each question carries TEN marks.

SECTION-A

Answer Briefly

1. a. Write down time independent Schrödinger equation and explain all the terms.
   b. Check the acceptability of the following function :
   

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   ^{2 ?p?}/_L sin (in the range (0 to L))
   c. Determine whether the following operator ^d2/_dx² is linear or nonlinear.
   d. Determine whether the following functions are normizable or not over the indicated intervals :
   Sin x (0, p)
   e. Why the value of ?*? be finite everywhere?
   

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   f. Show that if the linear operators A and B have common complete set of eigen functions, then A and B commute.
   g. For a particle in a cubical box what is the degeneracy of the level that has energy 14/3 times that of the lowest level?
   h. Write the ground state term symbols for the following electronic configurations of 3d² and 2p³.
   i. Calculate the number of radial node and angular node of 5d orbital.
   j. Calculate the momentum of a photon having wavelength 200 nm.

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SECTION-B

2. The wave function ? of a certain system is a linear combination of following :
   ? = ³/₂ ?₁+ ?₂, where ?₁ and ?₂ are the eigen functions with eigen value E₁ and E₂.
   What is probability that the system energy will be observed to be E₂?
3. Show that the function y=xe^-ax2 is an eigen function of the operator ^d2/_dx²-4a²x². What is its eigen value?

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4. Calculate the probability that a particle in 1-D box of length L is found between 0 and L/2.
5. Determine the value of A_m so that the wave function (f) = Ae^imf, where, m = 0, ±1, ±2 (0 = f = 2p) are normalized.
6. A particle in one dimensional box simple harmonic oscillator in x-direction is perturbed by a potential x. What is the 1st order correction for ground state?
7. Find out <Px> for a harmonic oscillator in its ground state.
8. Write a short note on Russel-Saunders (R-S) coupling.

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9. Arrange the following states (term symbols) for p² configuration in the increasing order of energy: ¹D, ³P and ¹S. Justify the trend of the result.

10. The radial function for a 2s electron in hydrogen atom is given by :
    R_2s = ¹/_v2 (¹/_ao)^3/2 (2-^r/_ao)e^-r/2a_o
    Determine the number and location of node(s) in the 2s wave function. Plot the plot of R_2s against 'r' and also the radial distribution plot for R_2s.
    OR

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11. Write the electronic Hamiltonian of a hydrogen molecule ion (H₂⁺) and explain each term briefly and clearly with the help of a schematic diagram.

11. Derive the Huckel MO theory for ethylene. Draw simple schematics of the bonding and anti-bonding energy level diagrams.
    OR
12. Describe the variation theory and prove the same in detail.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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