INTRODUCTION TO MEDICAL PHYSICS 1 Quiz #1 Solutions October 6, 2017

Transcription

1 INTRODUCTION TO MEDICAL PHYSICS 1 Quiz #1 Solutions October 6, 2017 This is a closed book examination. Adequate information is provided you to solve all problems. Be sure to show all work, as partial credit is likely to be given. If you need extra paper, please use the sheets affixed to this exam. Neatness counts! 1. (8 points) Identify each of the following quantities as (F) fundamental or (D) derived and give the SI units for the quantity. Quantity F or D SI unit Kerma Electric current Mass D F F Gy amp kg Velocity D m sec (2 points) A set of five measurements of a length yields values of cm, cm, cm, cm, and cm. Upon analysis of the experimental method, it was found that these measurements were all approximately 15% too large. This measurement is an example of a. High accuracy and low precision b. High accuracy and high precision c. Low accuracy and low precision d. Low accuracy and high precision 3. (6 points) The following is a list of observations of radiation effects on humans. Identify each effect as pertaining to stochastic (S) or deterministic (D). Observation The formation of cataracts typically occurs with a threshold acute dose of 2 Gy. The frequency of radiation-induced mutations usually increases in a dose-dependent manner. Most models for radiation protection are based on an assumption that there is no threshold for radiation-induced malignancies. S or D D S S

2 4. (12 points) A photon beam coming from a linear accelerator has the following energy spectrum: Energy Fraction of photons 1 MeV MeV MeV MeV MeV MeV If the photon fluence rate is photons m -2 s -1, what is the energy fluence rate in J m -2 s -1? To calculate the energy fluence rate, weight the energy by the photon fluence rate and sum over the energy spectrum. Energy fluence rate = photons m -2 s -1 ( ) MeV photon -1 = MeV m -2 s -1 ( ) = MeV m -2 s J ev ev MeV -1 = 46 J m -2 s (4 points) Indicate whether the following radiation is x-rays (x) or gamma rays (γ): a. Radiation emitted from a change in a nuclear energy level γ b. Radiation emitted from a change in an electronic energy level x c. Radiation emitted from positron-electron annihilation. γ d. Radiation emitted when an electron changes direction x

3 6. (4 points) What two pieces of evidence appear to validate the shell model of the nucleus? a. Existence of discrete energy transitions between energy levels b. Stability of certain nuclei suggesting filled nuclear shells 7. (10 points) If the atomic mass of 16 O is amu, calculate the binding energy per nucleon of 16 O. 16 O nucleus has 8 protons and 8 neutrons mass of 8 protons = amu = amu mass of 8 neutrons = amu = amu total mass of nucleons in 16 O nucleus = amu mass of 16 O nucleus mass defect = amu = amu energy equivalent = amu Mev amu -1 = MeV binding energy per nucleon = /16 = MeV/nucleon

4 8. (5 points) An electron has energy of 10 MeV. Calculate the speed of this electron relative to the speed of light. Total energy is given by E = mc 2 = = m 0 c 2 1 β 2 E 0 1 β 2 1 β 2 = E 0 E 1 β 2 = E 0 E 2 β 2 = 1 E 0 E 2 β = 1 E 0 E 2 Since E 0 = MeV, E 0 /E = , and β = (8 points) Radiation energy spectra can be categorized into two main groups: those that consist of one or more discrete energies (line spectra) and those that consist of a broad distribution of energies (continuous spectra). For each of the radiation sources listed below, indicate whether line or continuous is a better description: Radiation Source Spectra Line Continuous a) Alpha particles X b) Beta particles X c) Gamma rays X d) Characteristic x-rays X e) Conversion electrons X f) Auger electrons X g) Bremsstrahlung X h) Annihilation radiation X

5 (12 points) 29Cu has a mass of amu. It decays to 30Zn (mass = amu). a. What is the decay process? The atomic number increases by 1 and the mass number remains the same, so the decay process is beta-minus decay b. What is the maximum energy of the emitted particle? (Do not forget the units) = amu x 931 MeV/amu = MeV c. ESTIMATE the mean (average) energy of the emitted particle. (Use your brain, not your calculator) Mean energy is approximately 1/3 the maximum energy 1/ MeV = MeV 11. (2 points) 133 Cs is the stable isotope of cesium. The decay of 137 Cs is most likely via a. Alpha decay b. Beta-minus emission c. Beta-plus emission d. Isomeric transition (8 points) 5 grams of 97Au is placed in a reactor (ϕ = neutron cm -2 s -1 ). The thermal neutron cross section for 197 Au is 99 barns/atom. a. What isotope is produced? Au b. What is the rate of production of this isotope (neglecting decay)? rate of production = neutron flux thermal cross section number of target atoms = neutron cm -2 s cm 2 atom -1 5 g g mole atoms mole 1 = neutron s -1 = neutron s -1

6 13. (10 points) In an x-ray target, electron interactions result in three identifiable end products. List these three end products, list the component of the atom with which the electron interacts. Is the end product useful or a waste product? Interaction end product Component of atom Useful or waste product? Heat is/are produced Outer shell electrons waste Characteristic x-rays when an electron Inner shell electrons useful Bremsstrahlung interacts with Nuclei useful In a diagnostic x-ray tube, the bulk of the energy results in which end product? Heat 14. (6 points) Characteristic x-rays are produced when an outer shell electron falls into an inner shell vacancy. Give three mechanisms for producing an inner shell vacancy. a. Photoelectric effect b. Electron capture c. Electron collisions (also internal conversion) 15. (3 points) In the figure below, two x-ray tube spectra are compared. What single parameter was changed between the acquisitions of the spectra? 1. a. filtration b. target material c. tube current d. tube potential

7

8 Useful physical constants: Speed of light in vacuum c m s -1 Avogadro s number N A mol -1 Planck s constant h J s Electron charge e C Electron mass m kg = amu Proton mass kg = amu Neutron mass Average energy deposited in air by liberated charge kg = amu W J C -1 = ev IP -1 Density of air ρ kg m -3 (0 C, kpa) Density of lead g cm -3 Roentgen R C kg -1 Energy conversion factors: Some binding energies: 1 amu = MeV 1 ev = J Shell Hydrogen Tin Tungsten Lead K ev -29,200 kv -69,500 ev -88,005 ev L ev -4,180 ev -12,100 ev -15,861 ev M ev -2,820 ev -3,851 ev N ev -594 ev -892 ev O ev -76 ev -147 ev Energy considerations in Compton scatter: Thomson scatter cross section: ( 1 cosθ ) ( 1 cosθ ) α E = hν 1+ α 1 hν ' = hν 1+ α cosθ ( 1 ) hc λ = cosθ 2 m c o 2 ( 1+ cos ) ( 1 ) 2 2 ds r m = o θ dω 2 e steradian

9 A useful integral: sin x dx = - cos x Energy transfer in a billiard-ball collision: i - incident particle t - target E t = E i 2 M ( M + M ) 2 t t M i i

10 This page may be used for calculations. If you wish me to consider material on this page for partial credit, please indicate which problem(s) are being solved.