Guru Nanak Dev University 2007-3rd Sem B.Sc Chemistry QUANTUM (CHEM-303) (, 2k7) - Question Paper
2117
B.Sc. (H.S.) 3rd Semester
CHEMISTRY
Paper - Chem-303
(Quantum Chemistry)
Time Allowed - 3 Hours
Maximum Marks - 75
Note :- All parts of any ques. should be attempted in continuation at 1 place.
(Refer to the attachment) 5413
2117
B.Sc. (H.S.) Third Semester CHEMISTRY PaperChem-303 (Quantum Chemistry)
5413Time allowedThree Hours] [Maximum Marks75
5413Note :All parts of any question should be attempted in continuation at one place.
SECTIONA
(Compulsory)
5413(iy E = h f (f is frequency) is known as ..........and
this term was given by.................
(#r Name the relation
8f2 kT
energy density a--.
C
{iii)'iiow many orbitals are there in a shell with n = 3 ?
rXWhat is the difference between a scalar matrix and unit matrix ?
Jy)What is the degeneracy of the state having the
h2
5413energy 17 in units of-j for a particle in two
8 ma
dimensional square box of each side a.
5413 1 (Contd.)
( ( ' )
H vT) w hat is orthogonality ?
fvii) Write the Hamiltonian for H2+ ion.
4a)-hat is the third postulate of quantum mechanics ?
(pt) Why the wave function should be antisymmetric ?
(x) What is Born-Oppenheimer approximation ?
1/2x10=15
SECTIONB Note :Attempt any EIGHT questions out of the twelve questions each question carry 414 marks.
If AB = -BA, the matrices A and B anti-commute. Show that the Pauli-Spin matrices
|
'0 |
r |
"0 |
-r |
'1 |
0N | |||
|
=r |
, CTV = |
, o7 = | ||||||
|
,1 |
o, |
9 > |
o, |
7 |
,0 |
-K |
(i2 = -1)
Anti-commute in pairs. Show only in one case.
The eigenvalues i.e. energy levels of each rotational level, of rigid rotator problem is given by :
'u2
J(J + 1)
E,=
8 7c2I
where I is the moment of inertia and J = 0, 1, 2, .......Calculate the energies of the first
four levels and find the energy difference between each level.
XT' The wave functions for a particle in a box of width' a is given by :
Vn ~1~ sin x-
V a a
Plot this function for n = 4 and explain how many, nodal points are there.
Show that sin 2x is not an eigen function of the operator d d2
but of t; what is the eigen value, dx dx2
/x J
--vt
\X j
<9
is a solution of the
5?) Prove that V = A cos 2ti
equation
dx X
What is the physical meaning of the Schrodinger equation ?
6. Explain the significance of particle in a box.
(Q The Hermite polynomial of degree n is given by :
n t2 dne~2
Obtain the Hermite polynomial H(),-H1 and H2.
Set up Schrodinger equation for the rigid rotor and separates into two equations.
(9.) Show that the reduced atomic mass is close to the. electronic mass.
10. Show that in atomic units
Set up the S.W.E. for hydrogen atom in polar coordinates.
What should be the characteristics of a well behaved function ?
SECTIONC
Note :Attempt any ,TWO questions from this section. Each question carries 12 marks.
Using the first order-time independent perturbation
theory solve the Schrodinger equation for the ground
state of Helium atom.
15
2. Outline the salient features of the Hartree-Fock self consistent field theory for solving the Schrodinger
wave equation for a many electron atom. 15
3. Starting from Planks distribution law for the energy density in a cavity containing black body radiation,
 3rd Sem (Dec, 2k7)_files/3717-10845-QUANTUM CHEMISTRY (CHEM-303) 3rd Sem (Dec, 2k7)-1.png) |
ehv/kT _ i dv |
(i) the Stefan-Boltzmann fourth-power law E = a T4 where a is the Stefan-Boltzmann constant,
C
(ii) the Wein displacement law, -max=Y where C is a constant and X is the wavelength where
max
energy density reaches a maximum at a given temperature.
(iii) Show that the Planck radiation law becomes identical with the Rayleigh-Jeans law if the size of the energy quantum is allowed to vanish or if the temperature is too high. 5+5+5=15
_v/2
4. (a) Verify that the function vy(x) = x e is an
d2 2
eigen function of the operator j - x . What
dx
is the corresponding eigen value ? 6
(b) On the basis of the particle in a box model verify that the 7i-electron density in butadiene is maximum between carbon atoms 1 and 2 (and 3 and 4) but minimum between carbon atoms
2 and 3. (average C-C bond length is 0-140 nm).
9
f
5413 5 100
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Attachment: |
| Earning: Approval pending. |
