note1 - Med Phys 4R06/6R03 Radioisotopes and Radiation...

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Med Phys 4R06/6R03 Radioisotopes and Radiation Methodology Lecture Notes (Version 2009-10)
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Med Phys 4R06/6R03 Radioisotopes and Radiation Methodology 1-2 Chapter 1 Radioactivity The radiations investigated in this course are ionizing radiations. In general, they are classified into Charged particles Fast electrons Ions Neutral radiations Photons in ionizing region Neutrons 1.1. Radioactive decay law We will start with the concept of radioactivity and the radioactive decay law is the most fundamental principle. What do we mean by a transition (or decay) ? A transition occurs when a system changes spontaneously from one state to another. For our purposes this can be Radioactive Decay 226 Ra 222 Rn + α Atomic de-excitation Na* Na + h ν The decay (or disintegration) constant λ is defined as the decay probability of a nucleus per unit time and its unit is [s -1 ] or [yr -1 ]. One important assumption of radioactive decay is that the decay constant is independent of the age of the nuclei. For a single isolated system, such as one atom, there is little more to say: if we observe the atom over unit time, λ will be the probability per unit time that it will decay. However, for a group, or an ensemble of atoms, λ becomes a useful quantity. We have a group of atoms which start off as nuclide i They decay to nuclide f with a decay constant λ If we start with N 0 radioactive nuclei i at t = 0 and N i (t) nuclei are present at time t = t, the number of decay in an time interval dt is ) ( ) ( t dN dt t N i i = λ ¨ t i e N t N = 0 ) ( This is the well-known radioactive decay law. The governing equation for the number of nuclei of type f is ) ( ) ( t N dt t dN i f =
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Med Phys 4R06/6R03 Radioisotopes and Radiation Methodology 1-3 The half-life t ½ gives the time required for half of nuclei to decay. From its definition, t ½ is related to the decay constant by λ / 693 . 0 / 2 ln 2 / 1 = = t Another useful life quantity in decay is the mean life (or lifetime ) τ , which is defined as the average time that a nucleus can survive before decay. From its definition the mean life becomes τ 1 = = dt e dt te t t Therefore, the mean life is simply the inverse of the decay constant. After one mean life, the number of nuclei becomes 1/e of the initial number as shown in Fig. 1.1. 0.00 2.24 4.48 6.72 0.00 0.25 0.50 0.75 1.00 28 Al, t 1/2 : 2.24 min τ : 3.23 min Time [min] Number of nuclei [Rel. unit] Fig. 1.1. Radioactive decay: 28 Al. From the decay law, we can determine the number of undecayed nuclei at a time t . However, measuring N is a very difficult work while measuring the number of decay is much easier since we can detect radiations emitted through decay. If the number of nuclei at time t 1 is 1 0 1 ) ( t e N t N = and the number at time t 2 is 2 0 2 ) ( t e N t N = , the total number of disintegrations in ( t 1 , t 2 ) can be expressed as ) ( ) ( ) ( 2 1 0 2 1 t t e e N t N t N = When the time interval t becomes short, the number of disintegrations in ( t , t t + ) interval is given by ) 1 ( ) ( ) ( 0 t t e e N t t N t N N = + = If the interval t is much shorter than the mean life τ , then the t e
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This note was uploaded on 03/03/2011 for the course ECON 3 taught by Professor Costescu during the Spring '11 term at Faculty of English Commerce Ain Shams University.

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note1 - Med Phys 4R06/6R03 Radioisotopes and Radiation...

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