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CH103: Mid-Semester Examination 21 February 2012

Use separate answer sheets for Part-A and Part-B. Answer each question in a new page. Calculators may be used. Use

PEN to write all answers, including sketches and figures. Read questions carefully and keep answers to-the-point.

Arguments are necessary to earn full credit.

PART-A (PHYSICAL CHEMISTRY) 24 Marks

h=6.626x10-34 Js;c=3x108 m s-1;me=9.1x10-31

kg;mp=1.672x10-27

kg; e=6x10-19 C; 1eV=1.6x10-19 J; kB =1.308 x 10-23

JK-1

1A. A hydrogen atom has kinetic energy corresponding to temperature T=300K. What is the approximate inter-planar

spacing of a crystal lattice in order to diffract such a beam of such hydrogen atoms? [2]

1B. The functions 1, 2 and 3 are the only possible eigenfunctions of an operator and the correspondingeigenvalues are a1 = 1, a2 = 2 and a3 = 3, respectively. There is a 50 percent chance that a measurement produces a 1

and equal chances for either a2 or a3. Calculate the average value . [2]1C. A particle detector having spatial resolution of 0.1 nm is placed at 2.5 nm from one of the walls of a 1-D potential

well of length L = 10 nm. When the particle jumps from n=2 to n=4 state, what will be the signal change at the

detector. Rationalize pictorially. [1]

2A. What is an orbital? [1]

2B. Under what condition energies of oribitals can be added? [1]

2C. Given

=

3 2

2

2

0

1 12

4 2

o

r

a

s

o

re

a a

find the region of r which has maximum probability density. [1]

2D. Draw in the SAME PLOT the radial parts of the wavefunctions [R(r) vs. r] for 2s and 2p orbitals of Boron andFluorine atoms. Label each curve appropriately. [3]

2E. Given

=

3 2

2

0

1 1sin cos

32

o

r

a

o

r

e

a a

Plot on a single polar-graph the angular parts { () and

()} of the wavefunction and label appropriately. [2]

3A. Write down the complete Hamiltonian for the triangular [H3]+ molecular ion. [1]

3B. Write the complete (space and spin) for the lowest energy MO for the triangular [H3]+

molecular ion. Note: This is

a 2-electron system. [2]

3C. Draw all the MOs of triangular[H3]+

molecular ion and comment on their energies. [2]

4. Draw the bonding and anti-bonding MOs formed due to overlap of2px and4dxz orbitals, when the inter-nuclear axisis along the z direction.Show the signs of the AOs and MOs. Also plot the overlap integral for both the bondingand anti-bonding MOs as a function of inter-nuclear distance. [3]

5. The three sp2 hybrid orbitals formed in the xz plane are shown in the figure.Evaluate the coefficients (including the signs) of the three hybrid orbitals h1, h2andh3. [3]

PART-B (INORGANIC CHEMISTRY) 06 Marks

1. Applying appropriate rules/energies, prove/confirm the following:(a) Element X (atomic number = 19) has the configuration 1s2 2s2 2p6 3s2 3p6 4s1 and not 1s2 2s2 2p6 3s2 3p6 3d1. [1](b) Element Y (atomic number = 64) has the configuration [ Xe] 4f7 5d1 6s2 and not [Xe] 4f8 5d0 6s2. [1]

2. Explain the following:(a) For element Z (atomic number = 77), the valence shell configuration is [Xe} 5d7 6s2 and not 5d9 6s0. [1](b) van der Waals radius [1]

3. Among metals up to atomic number 100, which metal/atomic number has the highest atomic volume per mole andwhy? [2]

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