Aligarh Muslim University (AMU) 2011 B.Sc Physics Quantum Mechanics - Question Paper
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2010-2011 B.Sc. (HONS.) (PART - III) EXAMINATION (PHYSICS)
QUANTUM MECHANICS
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(PH-313)
Maximum Marks : 40 Duration : Three Hours
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Note: Answer all questions. Use of Calculator is allowed.
Plancks constant h = 6.63 x 1034 J-sec,
Mass of electron m* = 9.1 x 10 kg.
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1. Answer any Six of the following:
(i) The work function of a metal is 4 x 10-19 J. Find the threshold frequency for [2] photoelectric effect.
(ii) Find the de Broglie wavelength for an electron of kinetic energy 10 eV. [2]
(iii)/ An X-ray of wavelength 0.5 Angstrom undergoes a 60 Compton scattering. Find the [2] wavelength of scattered photon.
(iv) The radius of an atomic nucleus is around 5 Fermi. Use the uncertainty principle to [2] place a lower limit on the energy of an electron if it is to be inside the nucleus (one
Fermi = 10'5 meters).
(v) The wave function of a particle in one dimensional box of length L is given by [2]
x L
Find the expectation value of x.
(yi) Evaluate [px,x] [2]
(vii) What is the spacing between two consecutive energy levels of a particle in a one [2] dimensional potential box?
(viii)/ What do you understand by zero point energy of a particle in a harmonic oscillator [2] potential?
(ix) The ground state wave function of an electron in hydrogen atom is given by [2]
1
Vnlm ~ VlOO
where ao is the Bolir radius, find the expectation value of the potential energy in the above state.
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'm machines [4]
&o
unction of a particle. [4]
,ion coefficient of a particle incident on a \J\ .iergy E of a particle is less than the barrier
X
xrodinger equation for the hydrogen atom and obtain vil as the energy eigenfunctions.
vperiment and its importance. [5]
OR
.spin singular momentum operators S2 and Sz for a spin - XA particle Jfi]
V ,oli matrices. Obtain the eigenfunctions of Sz operator.
/ quantum mechanical treatment of collisions and obtain the election [5]
a scattering amplitude and differential scattering cross section.
OR
Obtain the correction to energy and wave function in first order perturbation theory. -f5]
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