11 Gamma Ray Energy and Absorption
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1 11 Gamma Ray Energy and Absorption Before starting this laboratory, we must review the physiological effects and the proper use of the radioactive samples you will be using during the experiment. Physiological Effects of Ionizing Radiation In this lab, we will be using weak radioactive sources to produce gamma particles. These particles or 'radiations' are classified as ionizing radiation, since they are sufficiently energetic to break chemical bonds and produce ions in tissue they pass through. There are a number of ways to measure the strength of the radiation, each with corresponding units. Radioactive sources are measured in Curies, C. A Curie is defined as a source with 3.70x10 10 nuclear disintegrations per second. Thus, the 1µC sources used in this laboratory have 3.7 x10 4 disintegrations per second and will produce approximately an equal number of particles per second. Since each particle might have roughly 1MeV of energy (an MeV is a commonly used unit of energy in nuclear physics and equals 1.6 x Joules) we would expect a total energy of 6 x 10-9 J/s. A rad is a measure of the energy absorbed from ionizing radiation in a unit of mass of tissue and is defined by 1 rad = 0.01 J/kg. A slightly different unit is the rem that tries to correct for the varying damage done by the different types of particles (alpha, beta, gamma, neutrons, etc) and at different angles and is defined as: Dose ( in rems) = RBE x dose (in rads), where RBE is the correction factor and equals one for medium energy x-rays and 25 for 1 MeV alpha particles. There are units for these quantities in the SI system. The SI activity units is the Becquerel (Bq) where 1 Bq = 1 disintegration/sec; the SI absorbed dose unit is the Gray (Gy) where 1 Gr = 100 rads; and the SI dose equivalent unit is the Sievert (Sv) which equals Grays times RBE. We might estimate the dose a 150 lb. (68kg) student would receive in one hour if he or she absorbed 1/10th the rays from the 1µC source above (approximate the RBE to be 1): Dose ( rem) = ( 10 & ( 6' 10 ) $ 3600 % & J # $ 0.01! % kg " s h #! " ( 68kg) The 1/10th absorption fraction corresponds to the student being a foot or two from the source. Since it varies as the inverse distance squared, this fraction and the resulting dose would be even smaller if the distance were greater. A person normally receives 1/10th of a rem per year from natural sources (cosmic rays, etc.). 1
2 Ingestion of radioactive material in the body is a particularly important consideration since it can be much more damaging than exposure to exterior sources. The radioactive material will often remain (or even be concentrated) in one small area of the body and apply an intense, prolonged radiation to that part. Furthermore, radioactive materials often concentrate in the very organs that are most sensitive to radiation like the liver, kidneys, bone marrow, etc. In addition, alpha emitters inflict their maximum damage in the body when incorporated in its tissue. Thus, experimenters should take utmost care to avoid ingesting even trace amount of radioactive materials into their bodies. Working with Radioactive Sources: The radioactive sources used in this lab are sealed in brightly colored plastic disks about the size of a quarter. In order to maintain some record as to source usage, the instructor will require each group of students to sign out for the source they will use and to check off their returning of the source. In use, the gamma sources radiate in all directions. Even though these are weak sources, it is a good idea to stand a meter or so away from the sources when possible to further minimize exposure. To safeguard against the possibility of a leaky plastic disk and the ingestion of radioactive material, students should handle the sources as little as possible, refrain from eating or smoking until hands are washed at the conclusion of the laboratory. Gamma-ray emissions from a radioactive source are energetic photons. The nucleus of an atom undergoes radioactive decay, and in the process is left in an excited energy state. It can then go through an additional decay, from the excited state to a lower or ground state, emitting a photon. These photons are the gamma-ray emissions. They have energy in the range of a few kev to several MeV. If we recall what was learned about transitions of electrons from different energy states (Atomic Spectra experiment), the energy of the emitted photon was equal to the change in the electron energy levels. The same is true for the nucleus, therefore, the nucleus appears the same as far as its constituent parts are concerned, and it simply loses energy to the photon. The energy lost is equal to the energy difference between the energy states of the nucleus. Theory The purpose of this experiment is to observe the statistical nature of certain physical laws. In particular, we will measure the radioactive decay rate of a naturally radioactive element, Cesium, and observe the statistical distribution of the decay rate. Certain elements are naturally radioactive. They spontaneously change into other elements by emitting radiation. The law governing the rate of this disintegration, the radioactive decay law, varies from element to element and is characteristic of a given element.! N The radioactive decay rate is defined as, where! N is the number of nuclei! T disintegrating in the time interval.! T. In general, the decay rate is a function of time. Thus, if we took a given sample of radioactive material and measured its decay rate today, and then repeated the measurement a month from today we would get different 2
3 values. However, for some elements the decay is so slow that the quantity regarded as a constant over a short time interval.! N! T can be The radioactive decay law is of a statistical nature. The law cannot predict when the nucleus of a single radioactive atom will disintegrate. For a very large number of atoms the law accurately predicts how many of these will disintegrate in a given time interval but it cannot be used to determine which atoms will disintegrate and which will not. It can only state the probability that a given atom will decay in a given time interval. The law is accurate for a large number of atoms. It becomes less and less accurate as the number of atoms decreases. The statistical nature of the decay law can also be described in another way. Suppose we count the number of atoms decaying in a given time interval in both parts of this experiment. We will refer to the number of counts recorded in a given sample period as N. We then repeat the measurement. We then repeat it again and again. We will find that the values of N will vary from measurement to measurement. However some values will occur more frequently than others. If we plot the number of times a given value occurs versus the value for the decay rate we obtain a bell shaped curve, like the one seen in Fig The radioactive decay law gives only the most probable count N avg that will occur most frequently provided a sufficiently large number of measurements are taken. Statistics predicts that σ = N avg 1/2. 3
4 Procedure. Figure 13.1: Data Studio Histogram Screen Capture In this experiment the radioactive material is Cesium. It decays slowly enough so that its decay rate can be regarded as constant for the duration of the experiment. (It takes 30 years for half of the cesium initially present to disintegrate.) The Geiger counter is used to detect the radiation accompanying the radioactive decay and thus to count the number of atoms decaying in a given time interval. The image above serves as a hint in exploring the probabilistic nature of cesium decay. Make sure to analyze all graphs measuring pertinent values and comparing these values to theory. Cesium decay follows a Poisson distribution where sigma = sqrt(avg. # of decays over a time period). Remember a 2 &' ( N ' N ) # Gaussian curve is given by P = Pmax exp ave $ 2! % 2( " Absorption of Gamma Radiation For gamma rays, the processes by which they interact with matter are such that a single event will remove the gamma ray from the beam. It follows that the intensity of the gamma rays will decrease exponentially as the thickness of an absorbing material such as lead is increased. N " n! x "µ x = N 0 e = N 0e 4
5 The constant : is called the absorption coefficient and has dimensions of length -1. Find the absorption coefficient for the lead sheets provided. You may assume each sheet is 1 mm thick. 5
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