Download De Broglie Hypothesis - Intermediate Physics - Exam and more Exams Physics in PDF only on Docsity!
THE UNIVERSITY OF SYDNEY
FACULTY OF SCIENCE
INTERMEDIATE PHYSICS
PHYS 2002 PHYSICS 2B
NOVEMBER 2003 TIME ALLOWED: 3 HOURS
ALL QUESTIONS HAVE THE VALUE SHOWN
INSTRUCTIONS:
This paper consists of 2 sections.
Section A Quantum Physics 75 marks Section B Electromagnetic Properties of Matter 75 marks
Candidates should attempt all questions.
USE A SEPARATE ANSWER BOOK FOR EACH SECTION.
In answering the questions in this paper, it is particularly important to give rea- sons for your answer. Only partial marks will be awarded for correct answers with inadequate reasons.
No written material of any kind may be taken into the examination room. Calcu- lators are permitted.
Table of constants
Avogadro’s number =
speed of light =
electronic charge = C
electron rest mass = kg
electron rest energy energy = 511 keV
electron volt 1 eV = J
protron rest mass = kg
neutron rest mass = kg
Planck’s constant = J.s
Planck’s constant (reduced) = J.s
Boltzmann’s constant =
Stefan’s constant =
Coulomb constant =
permittivity of free space =
permeability of free space =
gravitational constant =
atomic mass constant =
Please use a separate book for this section.
Answer ALL QUESTIONS in this section.
- (a) State one piece of experimental evidence which suggests that the de Broglie postulate, , is valid for matter particles. Describe very briefly how this evidence supports the de Broglie hypothesis.
(b) The “seeing ability”, or resolution, of any optical instrument is roughly the same as the wavelength being used. If the size of an atom is of the order of 0.1 nm, how fast must an electron travel to have a wavelength small enough to “see” the atom?
(c) Explain in words what is meant by normalization of a wave function and why it is a useful procedure. (13 marks)
- A proton with total energy attempts to tunnel through a rectangular potential barrier of height and width.
(a) Using a model for this system in which a steady beam of protons is incident upon the left-hand side of the barrier, draw a carefully labelled diagram to show what the absolute value of the wave function for the proton beam should look like.
(b) Explain briefly how you might estimate the reflection coefficient from your diagram.
(c) A deuteron is a particle with the same charge as a proton, but twice the mass. If a beam of deuterons, each with energy , tried to tunnel through the same barrier (with height ), would the reflection co- efficient be less than, greater than or the same as that for the beam of protons? Explain. (12 marks)
- A rectangular potential well in one dimension is bounded by a wall of height on one side and a wall of height on the other, as shown in the figure.
Suppose that the well (Region II) is of such a width that the second energy eigenstate for a quantum particle of mass has energy exactly equal to
. (The state of lowest energy is defined to be the first state.)
(a) Make a qualitative plot of the energy eigenfunction. Indicate care- fully the relative rates of decrease of with in regions I and III.
(b) Let be the wavelength of that part of your wave function which is inside region II. It can be shown that and obey the relationship
(i) The first part of this relationship, that , should follow from your diagram. Explain.
(ii) In order to satisfy the boundary conditions (that the wave function must vanish at ), your wave function must be “headed” towards the -axis at the two ends of Region II. This fact is re- sponsible for the second part of the above relationship, that is, that
. Explain. (12 marks)
- (a) When an atom drops down from an excited quantum state (energy ) to a lower state (energy ) it must lose an amount of energy equal to ( ). Often it does this by emitting a photon of frequency
The emission process can be either spontaneous or stimulated.
(i) Explain what is meant by stimulated emission, paying particular attention to the ways in which it differs from spontaneous emis- sion.
(ii) Describe briefly the key role that stimulated emission plays in the operation of a laser.
(b) An important concept in laser operation is a population inversion.
(i) State what is meant by the term population inversion.
(ii) Explain why it is important in the operation of a laser. (13 marks)
SECTION B
ELECTROMAGNETIC PROPERTIES OF MATTER
FORMULAS
- (a) Sketch a graph showing hysteresis in a ferromagnetic material. Label the axes. On the graph, indicate remanence and coercivity.
(b) Briefly define remanence and coercivity.
(c) The sketch below shows an electromagnet. The length of the iron core is and the air gap is.
(i) Assuming that the permeability of the iron core is large, use Am- pere’s Law to obtain an expression for the field in the gap in terms of the number of turns and the current in each turn.
(ii) Copy the diagram and indicate the closed loop you used when ap- plying Ampere’s Law.
(iii) If you have made any further assumptions, say what they are. (15 marks)
- A conductor of width and thickness is placed in a magnetic field of strength. The field is directed parallel to the axis and into the page, as indicated in the figure below. When a current is passed through the conductor in the direction, a potential difference known as the Hall voltage appears across the conductor, which can be measured between the electrodes shown on either side of the specimen.
(a) Starting from formulas given on the formula sheet, show that the mag-
nitude of the Hall voltage developed across the conductor is
where is the density of charge carriers in the conductor and their individual charges. Carefully explain your working.
(b) Suppose that the magnitude of the Hall voltage for the conductor is measured to be. If the conductor is thick and mm wide, the magnetic field strength is and the current is , calculate the carrier density, assuming that each charge carrier carries the same magnitude of charge as an electron.
(c) Copy the above diagram twice, and indicate the direction of the electric field associated with the Hall voltage for the case of (i) negative charge carriers and (ii) positive charge carriers. (15 marks)
- Answer both of the following items. You may include equations if you wish, but do not derive them. You may answer in point form.
(a) Briefly describe the difference between diamagnetism and paramag- netism.
(b) Briefly describe the effect of temperature on the electrical resistance of conductors, and the reasons for this effect. (8 marks)
- (a) By adding an extra term which includes the “displacement current”, , Maxwell modified Ampere’s Law to give the equation be- low
(i) Explain qualitatively how this modified law implies that there are two ways to generate magnetic fields.
(ii) Write a brief qualitative explanation of the role of the displacement current in describing one of the following two phenomena: elec- tromagnetic waves or magnetic fields associated with a charging capacitor.
