M.Sc. (Semester III) (CBCS) Examination Mar/Apr-2018
Physical Chemistry
QUANTUM CHEMISTRY
Time: 2½ Hours
Max. Marks: 70
Instructions: Attempt in all 5 questions. Section I is compulsory. Attempt any two questions from Section II and any two from Section III. Answer to all Sections II and III) should be written in the one answer book. Figures to the right indicate full marks. All questions carry equal marks. Use of calculator and log-table is allowed.
SECTION I
Q.1
Answer the following:-
14
Give Rydberg formula for the estimation of all the lines in the hydrogen atomic spectrum.
With any trial function, the expectation value of the energy will be greater than the true value [True False)
Give the expression for zero point energy for a particle in a cubical box.
Calculate the de Broglie wavelength of 0.250 g particle moving with the speed of 40 m/s.
Write down the expression for bond integral.
Why is the wave nature of matter not more apparent in our daily observations?
Perform the operation  (6cos4x) where  d2/dx2
What do you mean by eigen value and eigen function?
Name any two approximate methods for determination of energy of a system.
Define free valence index.
Classical frequency of oscillation is given by the expression
Write the expression for operator in terms of spherical coordinates.
Sketch plots for particle moving in one dimensional box of length nm.
At the stopping potential, the initial kinetic energy of electron is equal to the potential energy. [True False]
SECTION II
Q.2
What is Hermitian type of operator? Write on the properties exhibited by the Hermitian operators.
07
Discuss the recursion formula for the hermit polynomials.
07
Q.3
Discuss in detail the semiempirical method; approximate method for estimation of energy.
07
Derive an expression for kinetic energy operator in three dimensions.
07
Q.4
Show using Huckel molecular orbital approach, butadiene is stabilized by a delocalization energy.
07
Explain the various observations of Compton effect. Derive the expression for Compton shift.
07

SECTION III
Q.5
Give the physical interpretation of and ψ2 for quantum mechanical harmonic oscillator.
05
Show graphically the first four energy levels illustrating the degeneracy and the zero point energy for particle in cubical box. Comment on it.
05
The total electron energy for naphthalene is Eπ=10α+13.68β
Calculate the delocalization energy of naphthalene.
04
Q.6
Evaluate average value for position for a particle is one dimensional box of length a Å.
05
Write on Schimdt orthogonalization process.
05
The work function for metallic Rb is 2.09 eV. Calculate kinetic energy and speed of electron ejected by light of wavelength 195 nm.
04
Q.7
Write short notes on any three:-
14
Acceptability conditions for a wave function.
Slater and Guassian type atomic orbitals
Heisenberg's uncertainty principle
Ladder operator