Chem 221-final 2005

(B. Sc. Biochemistry) Fourth Semester 2005 Subject: Chem 221 (Quantum Chemistry & Group Theory)

Full Marks: 100 Pass Marks: 45 Time: 3 hours

Candidates are required to give their answers in their own words as far as practicable. The figure in the margin indicates full marks. (3× ×14 = 42)

Group (A) Long Questions (Any three)

1. Determine the point group of H2O2 (transplanar configuration) and analyse the normal modes of vibration. Character Table is given as: C2h E C2 i σh Ag Bg Au Bu

1 1 1 1

1 -1 1 -1

1 1 -1 -1

1 -1 -1 1

Rz Rx, Ry z x, y

x2 , y2, z2, xy xz, yz

2. Deduce the energy for rigid rotor using wave equation. 3. Explain the rotational spectra observed for diatomic molecule considering it as a non-rigid rotor. 4. Explain the postulates of quantum mechanics. Group (B) Short Questions: (Any six) (6× ×7 = 42) 1. What is photoelectric effect? Mention the conclusions drawn . 2. Calculate the energy required for the transition from nx = ny = nz = 1 to nx = ny = nz = 3 for an electron in a cubic hole of a crystal having edge length = 2A0. 3. Explain in brief the vibrational spectra observed for a diatomic molecule. 4. The pure rotational spectrum of gaseous diatomic molecule contains a series of equally spaced lines separated by 40 cm-1. Calculate the inter-nuclear distance of the molecule. The atomic masses of atom A and B of a diatomic molecule are 1.678 x 10-27 kg. and 5.06 x 10-26 kg respectively. 5. What is a symmetry operation? Show your familiarity with all kinds of symmetry operations. 6. Define symmetry elements. Show that in C2v point group, every symmetry element is a class by itself. Group multiplication table for the element of C2V is given as: E C2 v' v'' E E C2 v' v'' C2 C2 E v'' v' ' ' '' E C v v v 2 C2 E v'' v'' v' 7. Show that maximum radial density occurs at ao in 1s atomic orbital. 8. Find the value of [Lx.Ly]. Group (C) Very Short Questions: (Any eight) (2× ×8 = 16) 1. What are the consequences of symmetry? 2. Find a. Snn = ? when n is even b. Snn = ? when n is Odd. 3. Find out the symmetry elements belonging to PF5 (trigonal bipyramidal). 4. Find the value of [L2x, Lz] 5. Calculate the zero-point energy of a mass of 1.67×10-24 g connected to a fixed point by a spring with a force constant of 104 dyne/cm. 6. Calculate the moment of inertia of a rigid rotor having energy 9.2 x 10-86 J for j = 2. 7. Calculate the wave length of an electron having kinetic energy equal to 15×10-25J. (h = 6.6× 10-34 kg m2 sec-1 and mass of an electron = 9.1 × 10-31 Kg) 8. What do you understand by Black Body radiation? 9. What do you understand by stoke's line and antistroke's line? 10. Why the intensity of line obtained from first vibrational level is very much less than that obtained from zero level? 11. Draw the spectra observed for a diatomic molecule considering it as a rigid rotor. 12. What is the significance of ψ. ***