Lecture on Nuclear Decay PDF

Radionuclides are unstable and decay by emission of particle or gamma radiation to achieve stable configuration of protons and neutrons in the nucleus. Radionuclides can decay by one or more of the six modes: Spontaneous fission (SF) Isomeric transition (IT) Alpha decay Beta decay (ꞵ...

Radionuclides are unstable and decay by emission of particle or gamma radiation to achieve stable configuration of protons and neutrons in the nucleus. Radionuclides can decay by one or more of the six modes: Spontaneous fission (SF) Isomeric transition (IT) Alpha decay Beta decay (ꞵ-) Positron decay (ꞵ+) Electron capture (EC) decay  Spontaneous Fission (SF)  Fission : is a process in which a heavy nucleus breaks into two fragments accompanied by the emission of two or three neutrons.  Cause: The nuclear binding energy of the elements reaches its maximum at an atomic mass number of about 58; spontaneous breakdown into smaller nuclei and a few isolated nuclear particles becomes possible at greater atomic mass numbers.  Nuclides that undergo spontaneous fission also are subject to alpha decay (emission from the nucleus of a helium nucleus). In uranium-238, alpha decay is about 2 million times more probable than is spontaneous fission. The probability is low. Fission Neutrons Neutrons Spontaneo Nuclide Half-life prob. per per gram- Z2/A per fission us half life decay second 235U 7.04×108 3.5×1017 2.0×10−9 1.86 3.0×10−4 36.0 years years 238U 4.47×109 8.4×1015 5.4×10−7 2.07 0.0136 35.6 years years Alpha decay ()  The  decay occurs mostly in heavy nuclides such as uranium the heaviest element in nature (92 protons) and radon.  The  particles are basically helium ions with two protons and two neutrons in the nucleus. After  decay, the atomic number is reduced by 2 and the mass number by 4. 222 86 Rn Po   218 84   particles energy ranges from 1 to 10 MeV  The range of  particles is very short in matter. Beta decay (-)  Atoms do radioactivity to become stable. Problem: the atom has too many neutrons and not enough protons. Solution: lowering the number of neutrons and increasing the number of protons by converting the neutron into proton. n → p + - + – Simultaneously, a neutron undergoes conversion to a proton. The result of beta emission therefore is to increase the atomic number by one (Z → Z + 1), while the atomic mass number remains the same (A = constant). This nuclear transformation results in the changing of an atom from one type of element to another (Figure 2-12). The difference in energy between the parent and daughter nuclides is called the transition or decay energy (Emax).  β- particles often carry only a part of Emax (about one-third), so a particle called antineutrino with no charge and a negligible mass has been postulated to carry the remainder of Emax and satisfy the law of energy conservation.  Positron decay (+) When a radionuclide is proton rich, a proton converted to a neutron, and + particle and a neutrino are emitted, thus decreasing the atomic number Z of the daughter nuclide by 1: p → n + β ++ ν This process takes place only when the energy difference between the parent and daughter nuclides is greater than 1.02 MeV.  Positron decay (+) β+ particle loses energy whle passing through matter. When it loses almost all of its energy , it combines with an atomic electron of the medium and is annihilated giving rise to two photons of 511 keV, these photons are called annihilation radiations. 15 8O N    15 7   Electron Capture (EC) This process is an alternative to the β +- decay for proton rich radionuclide. In EC decay, an electron from an extra nuclear shell, particularly the K shell, is captured by a proton in the nucleus, forming a neutron and a neutrino. Thus P+β-→n+ν In this process the atomic number Z of the daughter nuclide is lowered by 1.  Electron Capture (EC) The EC process occurs usually in nuclides having excitation energy less than 1.02 MeV. But if the nuclides have excitation energy greater than 1.02 MeV, both EC and β +-decay can occur, although the probability of β +-decay increases with higher excitation energy. 57 27 Co  e Fe   57 26  Radioactivity  Radioactivity or nuclear decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, such as an alpha particle, beta particle with neutrino or only a neutrino in the case of electron capture, or a gamma ray or electron in the case of internal conversion.  A material containing such unstable nuclei is considered radioactive.  Laws and Definitions in Radioactivity  The radioactive decay is described by: A=Aoe- λt Where A = activity present after time t Ao = initial activity at time = zero λ = decay constant in time-1 t = time taken to transform activity from Ao to A.  Also activity A=λN N is the number of radioactive atoms.  Half life time T1/2  The time needed for all of the radioactive nuclei to decay to its half activity. A=Aoe- λt -------------------- (1) At t = T1/2 ----------- A=1/2 Ao subst. in eqn. (1) ------ ½ Ao=Ao e- λT1/2 2= e λT1/2 ln 2 = λ T1/2 T1/2 = 0.693/λ Effective Half-Life Te It is defined as the time needed for half of the radiopharmaceutical to disappear from the biologic system. Average (mean) life time Ƭ  Average time required to all radioactive atoms to decay. Ƭ = 1/ λ Ƭ = 1.44 T1/2 Units of radioactivity. Curie 1 Ci=3.7x1010 disintegration/sec. Bequral Bq= 1 disintegration/sec. 1 Ci = 3.7x1010 Bq.  The concept of half-life is essential to radiologic science.  It is used daily in nuclear medicine and has an exact parallel in x-ray terminology, the half-value layer.  The better you understand half-life now, the better you will understand the meaning of half-value layer later. Obviously, in any biologic system, the loss of a radiopharmaceutical is due to both the physical decay of the radionuclide and the biologic elimination of the radiopharmaceutical. The net or effective rate (e) of loss of radioactivity is then related to p and b by e = p + b and then 1/Te = 1/Tp + 1/Tb T p  Tb Or T e  p T Tb