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THE UNIVERSITY OF SYDNEY
FACULTY OF SCIENCE
INTERMEDIATE PHYSICS
PHYS 2901 PHYSICS 2A (ADVANCED)
JUNE 2004 TIME ALLOWED: 3 HOURS
ALL QUESTIONS HAVE THE VALUE SHOWN
INSTRUCTIONS:
This paper consists of 4 sections.
Section A Special Relativity 25 marks Section B Optics 45 marks Section C Nuclear and Particle Physics 40 marks Section D Introduction to Stellar Astrophysics 40 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 =
Universal gas constant = J.mol K
Stefan’s constant =
gravitational constant =
atomic mass constant =
Solar mass = kg
Solar radius = m
astronomical unit AU =
parsec pc =
light year ly =
Please use a separate book for this section.
Answer ALL QUESTIONS in this section.
- (a) According to Special Relativity, the concept of simultaneity is relative. Under what circumstances will two observers agree that two events are simultaneous? Hint: there are two possible circumstances.
(b) Sally is stationary on Earth and John is in a spaceship moving directly away from Earth and towards Jupiter at speed.
(i) According to Sally, it takes John 60 minutes to travel from Earth to Jupiter. How long does the trip take according to John?
(ii) What is the distance from Earth to Jupiter, as measured by John?
(iii) Sally has discovered a new asteroid that lies exactly half way be- tween Earth and Jupiter. When John passes the asteroid, he sends out a strong radio signal in all directions. According to Sally, whom will the signal reach first: Sally on Earth or her mother on Jupiter? Justify your answer.
(iv) According to John, whom will the signal reach first? Justify your answer. (13 marks)
- A particle with rest mass has kinetic energy equal to 3.00 times its rest energy. The particle then decays into two photons which travel in opposite directions.
(a) Briefly explain why it is impossible for the two photons to be travelling in the same direction.
(b) Calculate the Lorentz factor ( ) of the particle.
(c) Calculate the total energy of the two photons.
(d) Calculate the total momentum of the two photons.
(e) Calculate the individual energies of the two photons. (12 marks)
SECTION B
OPTICS
FORMULAS
Please use a separate book for this section.
Answer ALL QUESTIONS in this section.
- Ultraviolet light of wavelength 250 nm from two narrow apertures, 10. mm apart, illuminates a (side-on) length of optical fibre at a distance of 1.00 m from the apertures. It is intended that the illumination should result in a series of maxima and minima of intensity, and thereby create a perma- nent pattern of refractive index modulations along the fibre (a fibre Bragg grating).
(a) What condition must be satisfied by the light beams from the two aper- tures, in order for them to create such a pattern of maxima and minima of intensity in the region where the beams overlap?
(b) Calculate the separation of adjacent maxima of intensity in the overlap region. (10 marks)
- A transmission grating with slits separated by m is illuminated at normal incidence by a narrow parallel beam of red light ( nm) from a ruby laser. On a screen 2.00 m away from the grating, a row of spots of light appears.
(a) Briefly describe the reason why the pattern has this form.
(b) How far apart on the screen are adjacent spots near the centre of the pattern.
(c) What colour will an observer perceive for the various spots? Explain briefly. (10 marks)
- (a) The Jones matrix for a horizontal linear polarizer is
Explain what this element does to the polarization of an arbitrary input state. Why is its determinant zero?
(b) The Jones matrix for a quarter wave plate with its fast axis vertical is
Explain what this element does to the polarization of an arbitrary input state. What physically is the reason for the element? Why is the determinant of the Jones matrix not equal to zero?
(c) Define a rotation matrix by
Then if , denote a Jones vector and a Jones matrix respectively in the original coordinate system, and , denote corresponding entities in a coordinate system rotated through the angle ,
Use the second of these to convert from the Jones matrix for a horizon- tal linear polarizer to that for a general angle. (10 marks)
- A certain Fabry-Perot interferometer has a plate spacing of 1.00 mm and the intensity reflectance of the plates is 0.90. It is used to examine details of a spectrum at wavelengths near 560 nm.
(a) Find the order of interference for the bright ring closest to the central axis of the transmitted light.
(b) Find the contrast of the interferometer.
(c) The interferometer is to be used to separately examine two closely spaced spectral lines, in the vicinity of 560 nm.
(i) Find the interferometer’s spectral resolving power.
(ii) Find whether the resolving power is adequate to resolve two spec- tral lines separated by 0.010 nm.
(d) What is the largest difference in wavelength between two spectral lines (again near 560 nm) that can be examined by the interferometer with- out adjacent orders overlapping and becoming confused?
(e) Given that the interferometer is used in transmitted light, explain briefly why it is still beneficial to have partially reflecting plates, rather than plain (unsilvered) glass. (15 marks)
Please use a separate book for this section.
Answer ALL QUESTIONS in this section.
- (a) What is nuclear binding energy and how it is defined?
(b) For the nuclide Ni,
(i) Calculate the binding energy in MeV
(ii) Calculate the binding energy per nucleon in MeV
(c) Use the Figure shown below to explain why fission of U and fusion of H with H both release energy.
(d) Calculate the energy release in the fusion reaction H + H He + n
(e) Calculate the density of the Ni nucleus in kg m. (15 marks)
- (a) In which of the following decays are the three lepton numbers con- served? In each case, explain your reasoning.
(i)
(ii)
(iii)
(iv)
(b) The quark content of the neutron is udd ;
(i) What is the quark content of the antineutron? Explain your rea- soning.
(ii) Is the neutron its own antiparticle? Why or why not?
(c) The quark content of the particle is. Is the its own antiparticle? Explain your reasoning. (15 marks)
- Consider the nuclear reaction
H + Be X + He where X is a nuclide.
(a) What are the values of Z and A for nuclide X?
(b) How much energy is liberated in the reaction?
(c) Estimate the threshold energy for this reaction. (10 marks)
Please use a separate book for this section.
Answer ALL QUESTIONS in this section.
- (a) A star has its spectral and luminosity types determined to be A5V, im- plying an absolute magnitude.
(i) In no more than 5 lines, describe this star as completely as you can.
(ii) The apparent magnitude of the star is measured to be. Calculate the distance to this star.
(iii) The star is accompanied by a white dwarf companion 1.30 arc- seconds away. Observations over several years allow the size and period of the orbit to be determined as 43 AU and 153 years re- spectively. Use these values to make a new estimation of the dis- tance to the system.
(iv) How do you account for any difference between your two distance determinations?
(b) If we ignore statistical weight ( g ) factors, the Boltzmann equation has the form: (1)
(i) Explain why, for a given temperature, this equation predicts that hydrogen gas will have almost 10 times as many atoms excited above the ground state as helium gas.
(ii) As the temperature of the hydrogen gas increases, the number of excited atoms should continue to increase, resulting in stronger hy- drogen lines in the spectra of hotter stars. Explain what is actually observed and why. (15 marks)
- (a) A particular galactic star cluster contains 1000 stars. We assume that 900 of these stars are like our Sun ( ) and the remaining 100 have absolute magnitudes 3.0 magnitudes brighter than the Sun.
(i) What is the integrated absolute magnitude (measuring the total brightness) of the cluster?
(ii) If a certain bright star, previously assumed to be a foreground star, is also a cluster member and has , what will be the new integrated absolute magnitude of the cluster?
(iii) How bright will the cluster (with 1001 stars) appear in our skies if it lies at a distance of 1000 parsecs?
(b) The cluster described above is obviously unrealistic.
(i) Sketch an HR diagram for a more typical open galactic cluster, and clearly label all the main features of your diagram. (Make sure your diagram is large enough to be clear.)
(ii) On the same HR diagram , clearly mark the zero-age main se- quence (ZAMS). Draw an evolutionary track showing how a 1 solar mass star evolves after leaving the ZAMS, labelling the im- portant features along the track. Include approximate ages at im- portant points. (15 marks)
- (a) The equation of hydrostatic equilibrium for a spherically symmetric, gravitationally bound mass can be written as
(i) Assuming the density is constant and equal to throughout the star, show that the central pressure of a star can be approxi- mated as (3)
where the star has radius and mass
(ii) Use this crude approximation to estimate the central pressure of the sun. Comment on the reliability of this result.
(b) Explain briefly the essential elements of the “valve” mechanism for stellar oscillations.
(c) Explain how the “valve” mechanism accounts for the positions of dif- ferent types of variable stars in the HR diagram. (10 marks)
THERE ARE NO MORE QUESTIONS.
