# Larbert High School. Quanta and Waves. Homework Exercises ADVANCED HIGHER PHYSICS

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1 Larbert High School ADVANCED HIGHER PHYSICS Quanta and Waves Homework Exercises

2 3.1 Intro to Quantum Theory HW 1. (a) Explain what is meant by term black body. (1) (b) State two observations that can be made from the black body radiation curve below. Intensity / W m K 5000 K 4000 K wavelength / nm 2. Electrons are known to exhibit wave properties. Electromagnetic radiation is known to exhibit particle properties. What experimental evidence is there to support these two statements? (3) 3. An electron has a de Broglie wavelength of 0.20nm. (a) Calculate the momentum of this electron? (3) (b) Calculate the kinetic energy of this electron. (3)

3 4. Calculate the de Broglie wavelength of: (a) an electron travelling at ms 1. (3) (b) a 20g bullet travelling at 300ms -1 passing through a 500mm gap in a target. (3) (c) Using the data from part (b) explain why no diffraction pattern is observed. 5. In the n = 3 orbit of the hydrogen atom, the electron can be considered as a particle travelling with a speed of 7.28 x 10 5 ms -1. Calculate: (a) The angular momentum of the electron. (3) (b) The de Broglie wavelength of the electron. (3) (c) The radius of the electron s orbit. (3) 6. (a) Describe the Bohr model of the hydrogen atom. (b) Calculate the principal quantum number for an electron with an angular momentum of 4.22 x kgm 2 s -1 in the hydrogen atom. (3) Total Marks = 34

4 3.2 - Uncertainty Principle and Particles from Space HW 1. Calculate the minimum uncertainty in the linear momentum of an electron travelling at a speed of 3.2 x 10 6 ms -1. (4) 2. Polonium-212 decays by alpha emission. The energy required for an alpha particle to escape from the polonium nucleus is 26 MeV. Prior to emission, alpha particles in the nucleus have an energy of 8 78 MeV. With reference to the Uncertainty Principle, explain how this process can occur. 3. In a scanning tunnelling microscope (STM) a sharp metallic tip is brought very close to the surface of a conductor. As the tip is moved back and forth, an electric current can be detected due to the movement ( tunnelling ) of electrons across the air gap between the tip and the conductor. According to classical physics, electrons should not be able to cross the gap as the kinetic energy of each electron is insufficient to overcome the repulsion between electrons in the STM tip and the surface. Explain why an electron is able to cross the gap. (3) 4. An electron enters a uniform magnetic field of magnetic induction 1.2 T with a linear velocity of 3.0 x 10 6 ms -1 at an angle of 30 to the direction of the magnetic field. (a) Calculate the magnitude of the magnetic force that acts on the electron. (3) (b) If a proton instead of an electron enters the same magnetic field with the same velocity, what difference, if any, would there be to the force experienced by the proton?

5 5. Explain how a charged particle in a magnetic field moves at a constant speed yet is constantly changing velocity. 6. An electron enters a uniform magnetic field of magnetic induction 1.2 T with a linear velocity of 3.0 x 10 6 ms -1 perpendicular to the direction of the magnetic field. (a) Calculate the radius of the circular path followed by the electron. (3) (b) If a proton instead of an electron enters the same magnetic field with the same velocity, what difference, if any, would there be to the path followed by the proton? 7. Explain how a charged particle in a magnetic field moves in a helical path. 8. Detailed observations of sunspots have been obtained by the Royal Greenwich Observatory since These observations include information on the sizes and positions of sunspots as well as their numbers. The number of sunspots is an indication of solar activity. A graph of the average number of sunspots since 1950 is shown below. Coronal mass ejections (CME) are one type of solar activity. CMEs are huge magnetic bubbles of plasma that expand away from the Sun at speeds as high as 2000 km s 1. A single CME can carry up to ten million tonnes (10 10 kg) of plasma away from the Sun. Use your knowledge of physics to discuss the potential effects that solar activity could have on Earth over the next few years. (3) Total Marks = 26

6 3.3 - Simple Harmonic Motion HW 1. (a) The displacement y of a particle at time t may be given by y = A cos ωt Where A and ω are constants. (i) (ii) Using this equation, derive the relationship between the acceleration of the particle and its displacement. Explain how the relationship derived in (a)(i) indicates that the motion of the particle is simple harmonic. (b) When a 0.60kg mass is attached to the lower end of a spiral of negligible mass, the spring increases in length by 200mm. The mass is then pulled down a little further, released, and allowed to oscillate. A motion detector records how the displacement of the mass from the detector varies with time. A graph of the motion is shown below. (i) The motion of the mass can be described by the equation y = A cos ωt, where A and ω have their usual meanings. Use the graph to calculate the magnitude of: (A) A. (1) (B) ω. (1)

7 (ii) Calculate the maximum acceleration of the oscillating mass. (3) (iii) The period of oscillation of the mass m is given by the expression T = 2π m k where k is the spring constant (measured in Nm -1 ). Use this expression and information from the graph to find the value for the spring constant k. (4) (iv) (A) Show how measurements made during the experiment and the value of k obtained in (iii) may be used to calculate a value for g, the acceleration due to gravity. (B) Calculate the value given for g by this experiment. (3) 2. A test tube contains lead shot. The combined mass of the test tube and the lead shot is 0.250kg. The test tube is gently dropped into a container of water and oscillates above and below its equilibrium position with simple harmonic motion. The displacement y of the test tube from its equilibrium position is described by the equation y = 0.05 cos 6t where y is in metres and t is in seconds. (a) Show that the kinetic energy of the test tube, in joules, is given by the equation E k = 4.5 (2.5x10-3 y 2 ) (3) (b) Calculate the maximum value of the kinetic energy of the test tube. (1) (c) Calculate the potential energy of the test tube when it is 40mm above its equilibrium position. (3)

8 3. A simple pendulum consists of a lead ball on the end of a long string. The ball moves with simple harmonic motion. At time t the displacement s of the ball is given by the expression where s is in metres and t in seconds. s = 2.0x10-2 cos4.3t (a) Calculate the period of the pendulum. (3) (b) Calculate the maximum speed of the ball. (3) (c) The mass of the ball is 5.0x10-2 kg and the string has negligible mass. Calculate the total energy of the pendulum. (3) (d) The period T of a pendulum is given by the expression Calculate the length of the pendulum L. (3) (e) In the above case, the assumption has been made that the motion is not subject to damping. State what is meant by damping. (1) Total Marks = 38

9 3.4 - Waves HW 1. (a) The displacement y of a wave can be represented by y = A sin 2π (ft x λ ) where the symbols have their usual meaning. Show that the displacement y of the wave can be given by y = A sin 2π (vt x ) λ where v is the speed of the wave. (3) (b) A loudspeaker emits a constant note which has a displacement given by y = sin (6800πt 20πx) Determine (i) the wavelength (ii) the frequency (iii) the wave speed of this note (5) 2. One form of the wave equation for a travelling sine wave moving from left to right is y = A sin 2πf ( x v t) (a) Show that this can be written in the form y = A sin 2π ( x λ t T ) where λ is the wavelength and T is the wave period (b) Such a wave has a frequency of 60Hz, an amplitude of 0.10m and a wavelength of 0.25m. Write down the equation of this particular wave.

10 3. A wave travelling along a horizontal string is represented by the equation y = 25 sin 2π (55t x 16 ) where x and y are in millimetres and t in seconds. (a) State the amplitude of the wave. (1) (b) Calculate the speed of the wave. (4) (c) (d) Two points on the string are separated by a horizontal distance of 24mm. Calculate the phase difference between these points. (3) The wave is reflected and loses some energy. State a possible equation for the reflected wave. 4. Figure 14 shows a standing wave experiment involving microwaves. Waves sent out by the transmitter are reflected by a reflector, with nodes and antinodes being detected by means of a probe and meter. A node is detected with the probe at the 21.2cm mark on the metre stick. A further 20 nodes are detected as the probe is moved along the metre stick with the last node occurring at the 49.8cm mark. For these microwaves, calculate: (i) the wavelength (ii) the frequency Total Marks = 26

11 3.5 - Interference HW 1. Young s interference fringes are produced using sodium light of wavelength 589nm and the two slits are 0.2mm apart. If the screen on which the images are formed is 6.5m from the slits, how far apart are the fringes? (3) 2. In an interference experiment the fringes of monochromatic green light, produced by the two slits 1.04 mm apart are viewed by a micrometer eyepiece which is 80 cm from the slits. If the distance across 20 fringes is 8.20 mm, what is the wavelength of the green light? (3) 3. A narrow wedge of air is enclosed between two glass plates. When the wedge is illuminated by a beam of monochromatic light of wavelength 640 nm, parallel fringes are produced which are 0.30 mm apart. Find the angle of the wedge. (4) 4. Two microscope slides are arranged as below to enclose a wedge shaped air film. a) Describe how you would use this to obtain interference fringes by reflection. b) Explain how these fringes are formed and describe their appearance. c) If the distance occupied by 20 fringe-spacings was measured and found to be 5.50mm, and the wavelength of light used was 589nm, what was the thickness of the metal foil. (4) d) Describe and explain what would be seen if the metal foil was moved very slowly in the direction of the arrow.

12 5. Magnesium fluoride is used as a coating to provide a non-reflecting surface. (a) Show that light of wavelength, λ, is not reflected when the thickness, d, of the coating is such that d = λ 4n Where n = refractive index of the coating material used. (b) Manufacturers choose a coating so that light of wavelength 550nm is not reflected. Calculate the required thickness of magnesium fluoride of refractive index (3) (c) Explain why coated camera lenses appear purplish in colour Total Marks = 27

13 3.6 Polarisation HW 1. (a) Explain what happens when a light beam is incident at 54.5 o on a sheet of plane glass of refractive index n = (b) How would you show one difference between the reflected and refracted rays? 2. (a) Explain the difference between a longitudinal and a transverse wave and give one example of each of these. (3) (b) What is plane polarisation and with which of these types of waves can it occur? 3. A plate of refractive index n = 1.50 is used as a polariser. (a) What is the polarising angle? (3) (b) What is the angle of refraction? (3) 4. (a) Explain the terms polariser and analyser in plane polarisation. (b) Under what arrangement of the polariser and the analyser will no light be seen by the eye? 5. (a) Name one practical application of polarised light. (1) (b) Explain how this practical application would operate. Total Marks = 22

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