80 Physics Essentials Workbook Stage 2 Physics

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Clementine Morrison
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1 80 Physics Essentials Workbook Stage 2 Physics the thickness of the tissue: Obviously, the thicker the tissue through which the X-rays have to pass the more they will be absorbed from the beam passing through the photographic plate. Thus the greater the attenuation of the X-rays. the atomic number of the elements that make up the tissue: In addition to the density of the tissue, the attenuation of the X-rays also depends on the atomic number (number of protons in the nucleus) of the material through they pass. The tissues of the human body are not made up of pure elements but of mixtures of complex organic compounds. Thus each type of tissue is assigned an "effective atomic number", which takes into account the atomic numbers of the atoms of the elements that constitute these compounds and the proportion to which these atoms are represented in the compound. The greater the atomic number, the greater the attenuation of the X-rays. Penetrating Power or Hardness To be able to expose the photographic plate the X-rays must first of all penetrate (i.e. pass through) the tissues which are being photographed. The ability of the X-rays to do so is called their penetrating power. The greater the energy of the X-ray photons, the further they will be able to penetrate through a material before being completely absorbed. Remember that the maxirnum frequency of the X-ray photons emitted from an X-ray tube, and thus the maximum energy, is proportional to the operating voltage of the tube. Em, = hfm, = ea V X-rays are often described in terms of their hardness. Hard X-rays are X-rays with high penetrating power and, hence, high photon energies and frequencies. Therefore hard X-rays are produced in tubes of high operating voltage, typically kV. Soft X-rays are X-rays of much lower pen~trating power and, hence, relatively low photon energies and frequencies. Soft X-rays, for medical imaging purposes, are produced by tubes operating at voltages of the order of 50kV. Exposure Time Once the hardness of the X-rays to be used to create a certain image has been determined (from consideration of the type of tissue to be imaged), then the exposure time for the photograph needs to be decided. To create an image on the photographic plate, we could have a long exposure with low intensity X- rays or a short exposure with high intensity X-rays. It is advisable to keep exposure times short, so that the patient does not move an blur the image. The intensity of the X-rays depends on the current in the X-ray tube. A larger current means a larger number of electrons accelerating across the tube and so a larger number of photons being generated. Knowledge and Skills Checklist e o a Do I know that, in interacting with matter, light behaves like particles? Can I describe how images build up in low light situations? Do I know how to calculate the energy and momentum of a photon? Do I know what the photoelectric effect is and can I describe its properties? Can I describe how Einstein explained the photoelectric effect in terms of photons? Can I explain how the Maximum kinetic energy of the photoelectrons is measured experimentally? Can I deduce Einstein's photoelectric equation and use it in solving problems? Can I relate the graph of maximum kinetic energy to the various parameters associated with the photoelectric effect? Can I describe the main features of an X-ray tube? Can I describe the three main features of the X-ray spectrum? Can I explain how the continuous X-radiation is produced and why there is a maximum frequency? Can I deduce the formula for maximum frequency and use it in problem solving? Do I understand what is meant by the attenuation ox X-rays? Can I relate the attenuation of X rays the three factors that affect it an hence to the type of body tissue? Do I understand that the penetrating power or hardness of X-rays depends on the energy and hence the frequency of the photons and hence on the voltage of the X-ray tube? Do I understand that the exposure time in a n X-ray image depends on the intensity of the X-radiation and hence on the current in the X-ray tube?

2 Photons "1.6 Exercises 1 Calculate the energy of a yellow light photon of wavelength 590m. 2 Calculate the energy and momentum of an ultra-violet photon of wavelength 9 lnrn. 3 Find the momentum of a photon of energy 13.6eV. """" A gamma photon has momentum p = 2-3 x 1 o-~~sn. Calculate its wavelength, frequency and energy (in MeV). 5 A photon of wavelength 45m is reflected normally off a shiny metal surface. Calculate its change in momentum on reflection. 6 Determine the range of the momenta of photons of visible light.

3 I82 PhysicsEssentials Workbook Stage 2 Physics 7 A photon of frequency 7.0~ 1014~z is absorbed by an unbound (free) electron, which is initially stationary. (1) What is the wavelength of this photon? (2) What is the momentum of this photon? --- (3) Use conservation of momentum considerations to determine the velocity of the electron after this interaction. 8 How is the intensity of a light source explained in terms of photons? 9 A 60W globe ernits monochromatic red light of wavelength 700nm. How many photons does it emit in every hour? 10 Explain what is meant by the photoelectric effect.

4 Photons Explain what is meant by the term "threshold frequency" of a metal. Is the threshold frequency of all rnetals the same? 12 A metal has a work hnction W = 2.leV. If light of wavelength 38 lnrn is incident on the surface of the metal, will photoelectrons be emitted? Support your answer with calculations. 13 Sodium has a work function W = 2-32eV. (1) Find the threshold frequency& of sodium. (2) If sodium is irradiated by light of wavelength h = 390nm, fmd the maximum kinetic energy of the emitted electrons. 14 White light is shone on a sodium surface with work function W = 2.32eV. Calculate the maximum speed of the emitted photoelectrons.

5 15 A metal has a work function W = 4.2eV. It is irradiated by ultra-violet light of wavelength h = 90nm. (1) What is the threshold frequency of the metal? (2) What is the maxirnum kinetic energy of the electrons emitted from the surface? - "-" "... " (3) Explain why some electrons are emitted with a kinetic energy lower than that calculated in (2). (4) What will be the stopping voltage required to stop the emitted electrons? 16 Explain how A. Einstein used the conservation of energy to derive the photo-electric equation Km, = hf -W 17 Show that the photoelectric effect will not occur if light of wavelength h = 580nm is shone on a surface with work function W = 2-3eV.

6 Photons 18 (1) Explain why changing the intensity of the light source has no effect on whether electrons are emitted from a metal surface nor on the maximum kinetic energy of the electrons if they are emitted. (2) What aspect of the emission of the electrons does the intensity of the radiation affect? Explain. 19 The graph below shows the maximum kinetic energy of photo-electrons that are emitted when a metal surface is irradiated by light of various frequencies (mainly UV) frequency (x 1 014Hz) (1) On the graph indicate the threshold fiequencyfl and the work function W of the metal surface and their approximate values. (2) Use the graph to fmd a value for Planck's constant

7 186 Physics Essentials Workbook Stage 2 Physics 20 (1) Sketch an X-ray tube labelling its main features. (2) Describe and explain two factors that need to be considered in choosing the target material. (3) Explain why the tube needs to be cooled. 211 (1) Sketch a typical X-ray emission spectrum showing, and labelling, the continuous radiation, the maximum frequency and the characteristic X-radiation. (2) Explain how the continuous X-radiation is produced.

8 Photons 22 An X-ray tube operates at a voltage of 60kV. (1) Find the kinetic energy (in Joules) of the electrons as they strike the target. (2) Find the maximum frequency of the emitted X-rays. (3) Find the maximum momentum of the emitted X-ray photons. 23 The accelerating voltage of an X-ray tube is 50,000V. (1) Find the speed of the electrons just before they hit the target. (2) 1015 electrons hit the target every second and 98% of the energy of the tube is lost as heat. What is the power dissipated as heat? (3) Explain what change we could make to the operating parameters of the tube in order to increase the intensity of the emitted X-rays.

9 188 PhysicsEssentials Workbook Stage 2 Physics 24 (1) Use the law of conservation of energy to show that the maximum frequency of the X-rays e AV emitted is given by fmax = -, where AV is the accelerating voltage. h (2) If you were to draw a graph of the maxirnum frequency against the accelerating voltage, explain carefully the type of graph that you expect. (3) Determine the slope of the above graph. 25 (1) Explain the term hardness as applied to X-rays. (2) What factors affect the hardness of the X-rays generated by an X-ray tube. (3) Explain what is meant by the term attenuation as applied to the passage of X-rays through tissues.

Explain what is meant by a photon and state one of its main properties [2]

1 (a) A patient has an X-ray scan taken in hospital. The high-energy X-ray photons interact with the atoms inside the body of the patient. Explain what is meant by a photon and state one of its main properties....