SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO Annual Exam 2013 Subject: PHYSICS Level: ADVANCED Time: 3 hrs Take the acceleration due to gravity g = 10m/s 2 Section A Answer all questions in this section. 1. The total energy E of an electron in the orbit with quantum number n is: E = Where m is the mass of the electron in kg, e is the charge of the electron in C, is permittivity of free space in Fm -1, n is the number of orbits and h is Planck s constant in Js. Show that the equation is consistent with respect to its units. 5 marks 2. A muon is a particle which has the same charge as an electron but its mass is 207 times the mass of an electron. An unusual atom similar to hydrogen has been created, consisting of a muon orbiting a single proton. An energy level diagram for this atom is shown. a) State the ionisation energy of this atom. b) Calculate the maximum possible wavelength of a photon which, when absorbed, would be able to ionise this atom. c) Calculate the de Broglie wavelength of a muon travelling at 11% of the speed of light. Page 1 of 13
0eV -312eV -703eV -2810eV ground state 7 marks Mass of electron = 9.1 x 10-31 kg, Plank s constant = 6.6 x 10-34 Js, speed of light = 3 x 10 8 m/s 3. The diagram (not to scale) shows a ray of monochromatic light entering a multimode optical fibre at such an angle that it just undergoes total internal reflection at the boundary between the core and the cladding. The refractive index of the core is 1.48. a) Explain the terms in italics. b) Calculate the angles r and i. c) Hence estimate the refractive index of the cladding. 12 marks Page 2 of 13
4. The diagram shows a pendulum oscillating to and fro. At which position/positions: a) the acceleration is maximum, A C B b) the acceleration is zero, c) the velocity is maximum, d) the velocity is zero, e) the kinetic energy is maximum, f) the potential energy is maximum. Sketch three graphs for displacement against time, velocity against time and acceleration against time. 12 marks 5. Two identical table tennis balls, A and B each of mass 1.5g, are attached to non-conducting threads. The balls are charged to the same positive value. When the threads are fastened to a point P the balls hang as shown in the diagram. P 10.0cm 50 0 50 0 A B 15.3cm a) Draw a labelled free-body force diagram for A. b) Calculate the tension in one of the threads. c) Show that the electrostatic force between the two balls is 1.8 x 10-2 N. d) Calculate the charge on each ball. Permittivity of free space = 8.85 x 10-12 F/m 9 marks Page 3 of 13
6. The grid enables different nuclei to be represented by plotting the number of neutrons N against the number of protons Z in nucleus. The arrow shows a nucleus X decaying to a nucleus Y. a) What type of radioactivity decay is taking place? b) Write a nuclear equation for this decay. Include all the information possible. c) Copy the grid and add another arrow to the grid to represent what happens if nucleus Y subsequently decays by β - emission to nucleus W. d) Repeat (c) for a β + decay. Final nucleus is P. e) Mark a point Q on the grid that could represent the nucleus of an isotope of X. 9 marks 7. Define the tesla. Calculate the magnetic field strength 4.0cm from a straight wire carrying a current of 5A. a) Explain briefly how you would find the magnetic flux density at this point by using a Hall probe. Name any necessary apparatus (diagram of set up is not required). b) A second wire, 20cm long, carries a current of 8A. It is placed parallel to the first and 4.0cm away. The force between the wires is known to be repulsive. Calculate this repulsive force. State the direction of the current in the second wire relative to that in the first. Permeability of free space = 4π x 10-7 H/m 14 marks Page 4 of 13
8. What is meant by the emf of a cell? A voltmeter is connected in parallel with a variable resistance, R, which is in series with an ammeter and a cell. For one value of R the meters read 0.3A and 0.9V. For another value of R the readings are 0.25A and 1.0V. Find the values of: i. R, ii. the emf of the cell, and iii. the internal resistance of the cell. What assumptions are made about the resistance of the meters in the calculation? 10 marks 9. a) State three differences between a stationary and a progressive wave. b) Two waves travelling in opposite directions produce a stationary wave. The individual wave functions are, y 1 = 4sin(3x 2t) and y 2 = 4sin(3x + 2t) Find the maximum displacement of motion at x = 2.3cm and determine the positions of the nodes and antinodes. (Hint: The equation of a stationary wave is y = 2asin wt cos kx ) 7 marks 10. State Lenz s law of electromagnetic induction. Describe the apparatus you would use and the observations you would make to verify your statement. Define self inductance. A 12V battery of negligible internal resistance is connected in series with a coil of resistance 1.0Ω and inductance L. When switched on the current in the circuit grows from zero. When the current is 10A the rate of growth of the current is 500A/s. What is the value of L? 10 marks Page 5 of 13
Section B Answer any three questions from this section 11. Radiocarbon dating is possible because of the presence of radioactive carbon-14 caused by the collision of neutrons with nitrogen-14 in the upper atmosphere. The equation for the reaction is: + = C + X The half-life of carbon-14 is 5.7 x 10 3 years. a) i. Write down the above equation, adding the proton and nucleon numbers of the particle X. ii. Identify the particle X. b) The mass of carbon-14 produced by this reaction in one year is 7.5kg. 14 g of carbon-14 contains 6.0 x 10 23 atoms. i. Show that the number of carbon-14 atoms produced each year is approximately 3.0 x 10 26. ii. Calculate the decay constant of carbon-14 in year -1. c) Two elements A and B have the following properties. Element Atomic mass Total mass of the separate protons and neutrons. A 15.9994u 16.1320u B 17.0049u 17.1407u i. Explain why the mass of the separated nucleons is different from the mass of the nucleus. ii. Calculate the binding energy in joules of a nucleus of element A and the binding energy in joules of a nucleus of element B. Page 6 of 13
iii. Which of these two elements would you expect to be more stable? Explain your answer. d) i. Sketch a graph showing the relationship between binding energy per nucleon and nucleon number. Label the approximate positions of hydrogen, iron and uranium. ii. State the difference between nuclear fission and nuclear fusion. iii. With reference to your graph explain why both processes release energy. 1 atomic mass unit = 1.67 x 10-27 kg 30 marks 12. a) An electrolytic capacitor is marked 15V 2200 µf. i. Describe the internal structure of this capacitor. ii. Explain the terms in italics. b) Examine the circuit and calculate i. the potential difference across capacitor X ii. the charge on the plates of capacitor Y, iii. the energy associated with the charge stored in capacitor Z. c) In an experiment to measure the speed of a revolver bullet, the circuit shown below is set up so that when the revolver is fired the bullet first breaks conductor A and then conductor B, 0.02m behind A, before being stopped in the block behind B. Page 7 of 13
Before the revolver is fired, the reading on the voltmeter, whose resistance is much higher than that of R, is 200V. After firing, the voltmeter reading is found to have dropped to 150V. i. What is the current through R the instant the bullet has broken the first conductor? Show how you arrive at your answer. ii. Describe what happens to the current through R as the bullet travels from A to B and then breaks the conductor B. Give a reason for your answer. iii. How much charge is lost by the capacitor as the bullet travels from A to B? iv. Calculate an approximate value for the time it takes the bullet to pass from A to B. Show how you arrive at your answer. 30 marks 13. a) i. Explain the term interference. ii) Distinguish between constructive and destructive interference by writing the condition for each type of interference. iii) Describe an experimental set up involving interference, which may be used to measure the wavelength of a monochromatic source of light. Your answer should include a well labeled diagram, the measurements taken and how one can use the results to calculate the wavelength. b) White light is viewed normally through a diffraction grating. i) Explain what is observed and why. ii) The grating has 2.00 x 10 5 lines/m. For which wavelength would the first order be seen at an angle of 5 0 to the normal? iii) A sodium source emits two yellow lines with wavelengths 5.890 x 10-7 m and 5.896 x 10-7 m. The source is viewed through a grating with 1.0 x 10 6 lines/m. - Find the angular separation in degrees between the two lines in the first order spectrum. - Express the angular separation in radians. - Find the linear separation between the two lines when viewed at a distance of 1.0m. c) i) Sketch a graph of intensity against angular distance from the centre of light diffracted through a single slit. Page 8 of 13
ii) Using this graph explain what is meant when we say that two stars are just resolved when using a given telescope. iii) What do you understand by the resolving power of a telescope. iv) State how the resolution of a telescope is affected by changing its aperture. 30 marks 14. a) Describe in detail an experiment to measure the Planck constant using the photoelectric effect. b) Explain the dual nature of light by appropriate examples. c) A strip of clean magnesium ribbon, surrounded by a cylinder of copper gauze maintained at a positive potential of 6.0V with respect to the magnesium, is connected to the input of an amplifier which measures the p.d. across the resistor R as shown. When the magnesium is illuminated with mercury light of wavelength 254nm the amplifier detects a current flowing in R. State the origin of this current. Why is this process different from thermionic emission. Calculate the energies of photons of mercury light of wavelengths 2564nm and 546nm. Using these values and the data at the end of the question, describe and explain in detail what you would observe when each of the following experiments is carried out separately. a) The polarity of the 6.0V battery is reversed. Page 9 of 13
b) The mercury lamp is moved farther away from the magnesium ribbon. c) A filter selects mercury light of wavelength 546nm in place of that of wavelength 254nm. d) The emf of the battery is increased to 10V. e) The magnesium ribbon is replaced by a strip of copper. Work function magnesium = 2.8eV copper = 5.05eV. Page 10 of 13
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