Chapter 30 X Rays GOALS When you have mastered the material in this chapter, you will be able to: Definitions Define each of the following terms, and use it in an operational definition: hard and soft x rays Bremsstrahlung characteristic x rays absorption coefficient X-ray Problems Solve problems involving the generation, absorption, and detection of x rays. X-ray Interactions List and discuss the interactions of x rays with matter- particularly those with humans. PREREQUISITES Before beginning this chapter you should have achieved the goals of Chapter 21, Electrical Properties of Matter, Chapter 27, Quantum and Relativistic Physics, and Chapter 28, Atomic Physics. 245
Chapter 30 X Rays OVERVIEW When high speed electrons (greater than 10,000 ev) strike a solid target (e.g., copper) high energy, short wavelength photons are produced. These photons are called "x rays." Because of their high energy, x rays have remarkable penetrating power. In this chapter you will read about the production, absorption, and detection of x rays. Also, because x rays can produce damage to biological tissue, the biological effects of x rays will be discussed. SUGGESTED STUDY PROCEDURE Before you begin your study of this chapter, be familiar with the following Chapter Goals: Definitions, X-Ray Problems, and X-Ray Interactions. An extended discussion of each of the terms listed under the Definitions goal are included in the first section of this Study Guide chapter. Next, read chapter sections 30.1-30.9. As you read please keep in mind that X rays are not electrons, but high-energy photons. Thus, from the photon theory, x rays have both particle and wave characteristics. Also, be cautious of equation 30.3. If you do not recognize the exponential nature of the equation, look at Appendix, Section A9. Now turn to the end of the chapter and read the Chapter Summary and complete Summary Exercises 1-9. Now, do Algorithmic Problems 1-3 and Exercises and Problems 1-3, 5, 6, 11-14, and 16. Be sure that you compare your answers to each of these problems to those given. If you need assistance with any part, turn back to a portion of the text or to this Study Guide chapter. This study procedure is outlined below. --------------------------------------------------------------------------------------------------------------------- Chapter Goals Suggested Summary Algorithmic Exercises Text Readings Exercises Problems & Problems --------------------------------------------------------------------------------------------------------------------- Definitions 30.1,30.2,30.6 1,2,3, 14, 16 30.7,30.8 4,5,6 X-Ray 30.2,30.8 7,8 1,2,3, 1,2,3, Problems 5, 6 X-Ray 30.3,30.4,30.5 9 11,12,13 Interactions 246
DEFINITIONS HARD X RAYS - The higher energy and greater penetrating x rays. SOFT X RAYS - The lower energy and lesser penetrating x rays. BREMSSTRAHLUNG - "Break radiation" is the name given to the continuous x-ray spectrum from an x-ray source. In most medical uses of x rays a metal plate such as an aluminum disc is used to absorb the low energy Bremsstrahlung radiation as it leaves the x- ray tube. CHARACTERISTIC X RAYS - The x ray production due to inner electron energy state transitions that result in x-ray photons. The inner electron energy shells are often labeled by the letters K, L, M, N,... instead of the value of the principle quantum number n = 1, 2, 3, 4,... respectively. Thus the various characteristic x-rays are sometimes labeled by the final state of the electron after x-ray production, such as Kα where the K means the final state of the electron is the K or n=1 state and alpha means the electron originated at the first level above K, i.e. the L or n=2 state. Hence, when an electron goes down from an n = 2 state to an n = 1 state of an atom a Kα characteristic x ray is emitted. ABSORPTION COEFFICIENT - The physical parameter that characterizes the absorption of electromagnetic radiation (x rays) per unit length of absorber. Typical values of absorption coefficients for x rays from ~10-3 cm -1 for air to 1 cm -1 for water to ~10 3 cm - 1 for gold, platinum and lead. ANSWERS TO QUESTIONS FOUND IN THE TEXT SECTION 30.1 Introduction The fact that x rays penetrate body tissue while being absorbed by bone and that x rays will expose photographic emulsions enable us to use x rays to photograph the interior portions of human beings. Since x rays are photons of a few thousand electron volts and since the electrons in color television sets are accelerated through electric potentials of several thousands of volts, x rays will be produced whenever the high energy electrons strike suitable targets. The detection of x rays first occurred because they expose photographic emulsions. Now more quantitative measurements of x-ray intensities are made using ionization chambers and scintillation counters. 247
EXAMPLES X- RAY PROBLEMS 1. An x- ray tube is operated at a peak voltage of 250 kv and a current of 1.0mA. Then the exposure rate is 2.5 R/hr at a distance of 1.5 m from the target. (a) What is the minimum wavelength of x-ray radiation emitted from this tube? (b) If the current is increased to 20.0 ma what is the exposure rate at 1.5 m from the target. (c) At what distance for the increased current can the exposure be reduced back to 2.5 R/hr. What data are given? Accelerating voltage = 250 kv = 2.5 x 10 5 V Current = 1.0 ma = 1.0 x 10-3 A Exposure = 2.5 R/hr at a distance of 1.5 m. What data are implied? We will assume an inverse square law relationship between exposure and distance. What physics principles are involved? The conservation of energy as expressed in Equation 30.1 can be used. The definitions of radiation units (Section 30.6) and the inverse square law will also be used. What equations are to be used? λv = 1240 ev nm (30.2) I (1/d 2 ) (16.12) Solutions (a) λ min = 1240eV nm / 2.5 x 10 5 V λ min = 4.96 x 10-3 nm 5.0 x 10-12 m. (b) If the current is increased to 20 ma then the power of the tube is increased by a factor of 20, so the intensity of x-ray radiation from the tube is increased by a factor of 20, so the exposure rate is increased by a factor of 20 to a value of 50 R/hr. (c) In order to reduce the exposure rate back to 2.5 R/hr the distance from the target must be increased (Dose) (distance) 2 = constant (50 R/hr) (1.5m) 2 = 2.5 R/hr (X 2 ) (SQR RT(20)) (1.5 m) = x 6.7 meters = x Thinking about the answers Remember dose rates increase linearly with the tube current. High current, high voltage x-ray sources ought to be avoided. If you can keep a large distance away from sources of radiation you can reduce your exposure. 248
PRACTICE TEST 1. A target of copper will produce X-rays when bombarded with high speed electrons. A typical graph showing the X-ray spectrum produced is shown below. a) What approximate electron energy (in ev's) is required to produce X-rays from a target like copper? b) What produces the Bremsstrahlung? What is the origin of the two "peaks" called the characteristic X-ray spectral lines? 2. A technician operates an X-ray machine at 200 kv peak for therapeutic purposes. a) Find the energy and wavelength of the most energetic x-rays emitted. b) This machine operates at an exposure rate of 1.0 R/min at a distance of 1.0 meter from the machine. The recommended dosage for the technician (for a 40 hour week) is 1.0 x 10-4 R/min. How thick should the lead shield be for protecting the technician? (Given: The density of lead (ρ) = 11.4 gram/cm 3. The ratio (µ/ρ) for lead at 200 KeV = 0.80 cm 2 /gm.) 3. The interactions of radiation with living matter depends upon many factors and are therefore complex. In general, absorbed radiation produces changes in cells. a) Rate the following as most sensitive (MS), sensitive (S) or less sensitive (LS) to the effects of radiation. bone marrow cells lymphoid cells bone cells blood vessel cells muscle cells b) What properties of cells and their response to radiation allows the radiation treatment of cancer to be effective? ANSWERS: 1. 20-50 KeV (The accelerating voltage must be approximately 20,000 to 50,000 volts.) The Bremsstrahlung is white noise or background radiation produced by the deceleration of the electrons upon impact with the target. The "peaks" are produced by the excited target atoms. This energy allows target electrons to return to a ground state after excitement and produce similar radiation frequencies. 2. a) 200 KeV, 6.2 x 10-12 m, b) 1.0 cm 3. MS, LS, LS, MS, LS. Radiation treatment has shown that cells which reproduce rapidly are the most sensitive to obstruction. Thus rapid growing cancerous cells can be selected for destruction with proper levels of radiation which can allow healthy cells to survive. 249