Nature of Radioactive Decay

Nature of Radioactive Decay Radiochemistry Nomenclature nuclide - This refers to a nucleus with a specific number of protons and neutrons. The composition of a nuclide is completely described by using the notation: A Z X radionuclide - This is a nuclide that undergoes spontaneous emission of particles and/or electromagnetic radiation because the nucleus is energetically unstable. Chart of the Nuclides - isotopes - where Z = atomic number = number of protons A = mass number = N + Z = total number of neutrons and protons (N = neutron number) This is a compilation of the nuclear/radiochemical properties of nuclides organized as a plot of Z (y-axis) vs N (x-axis); see figure below. An on-line version is available at: http://www.nndc.bnl.gov/chart/reZoom.jsp?newZoom=1 These are nuclides with the same Z but different A. They are found along horizontal lines on the Chart of the Nuclides (see figure below). Example: 8 known isotopes of carbon C, 9C, 10C, 11C (stable), 12C (stable), 13C, 14C, 15C, 16C, 17C, 18C, 19C, 20C, 21C, 22C isotones - These are nuclides with the same N but different A. They are found along vertical lines on the Chart of the Nuclides (see figure below). Example: 6 isobars - isotones with N = 5 H, 7He, 8Li, 9Be, 10B, 11C, 12N, 13O, 14F These are nuclides with the same A but different Z. They are found along diagonal lines running from the upper left to the lower right on the Chart of the Nuclides (see figure below). Example: 12 nuclear isomers - isobars with A = 12 Li, 12Be, 12B, 12C, 12N, 12O These are nuclides with the same A and Z found in different energy states, each with a measurable lifetime. The ground (lower energy) state nuclide may be stable or radioactive. The higher energy states are called metastable states and designated with an “m” by the mass number. Isomers are shown on the Chart of the Nuclides as divided boxes, with the ground state listed on the right. Examples: 77m Se (radioactive) 80m Br (radioactive) 116m1 In (radioactive) 77 80 Se (stable) Br (radioactive) 116m2 In (radioactive) 116 In (radioactive) Nuclear Stability Of the more than 3100 known nuclides, only 266 show no evidence of decay (i.e., are stable). Of the stable nuclides: ‚ about 60% have even Z, even N. This suggests that nucleon pairing is important for stability. ‚ there are about 20% with even Z, odd N and about 20% with odd Z, even N. This suggests that protons and neutrons interact in a similar way. ‚ there are only 4 stable nuclides with odd Z, odd N (2H, 6Li, 10B, 14N). ‚ the largest number of stable isotopes and isotones are for even values of Z and N (again suggesting the importance of nucleon pairing). ‚ elements of even Z are more abundant than odd Z by a factor of 10. For even Z, the isotopes of even N usually account for 70-100% of the element. ‚ there is special stability associated with Z or N equal to 2, 8, 20, 28, 50, 82, 126. ‚ above Z=28, the only nuclides with even Z that have an isotopic abundance larger than 60% are 88Sr (N=50), 138Ba (N=82) and 140Ce (N=82). ‚ there are no more than 5 stable isotones except for N=50 and N=82. ‚ the most stable isotopes occurs for Sn (Z=50). ‚ the naturally-occurring decay chains for U and Th end at Pb (Z=82). ‚ the heaviest stable nuclides are 208Pb (Z=82) and 209Bi‡ (N=126). ‚ there is very weak binding (absorption) of the first outside neutron at N= 50, 82 and 126. For example, 136Xe (N=82) has σ = 0.26 b. versus 135Xe with σ = 2.6 x 106 b. ‡ 209 Bi has recently been found to undergo alpha decay (t½ = 2 x 1019 y). One measure of nuclear stability is the binding energy (EB) of the nuclide. EB is the energy released if an atom is synthesized from its constituent protons, neutrons and electrons. The higher the binding energy, the more stable the nuclide. Mass defect (ΔMA) equals MA - ZMH - NMn where MA is the nuclide mass, MH is the mass of a hydrogen atom and Mn is the mass of a neutron, all in amu. ΔMA is a measure of how much less a nuclide mass is than the mass of its constituent protons, neutrons and electrons and is always a (-) quantity. Thus, one can calculate binding energy from the mass defect by: Mass excess (Δ) equals MA - A. Δ can be a positive or negative value and is frequently tabulated in energy units. This enables rather simple calculations of either Q or EB when Δ values have units of MeV. A better indicator of stability is the binding energy/nucleon (=EB/A). 56Fe has a binding energy of 492.26 MeV, thus EB/A = 492.26 MeV/56 nucleons = 8.790 MeV/nucleon. In fact, this is the highest binding energy per nucleon of any nuclide. A plot of EB/A vs A for stable nuclides is very revealing. Notice that for most nuclides the binding energy per nucleon is in the range 7-8 Mev/nucleon. Since EB/A ~ constant, then EB % A. This suggests that all nucleons do not interact with all others, which means that the nuclear force is different in this regard than the force of electrostatic attraction. Notice in the plot for A = 2-20 below that even A nuclides have higher EB/A values than neighboring odd A nuclides and that 4He, 12C and 16O have particularly high values. The fact that the EB/A vs A plot has a maximum and decreases both as A increases and decreases provides insight about the basis for using nuclear fission and fusion reactions as energy sources. When a heavy nucleus undergoes nuclear fission it splits into lighter nuclides. One possible fission reaction for 236U is: 236 U 6 140 Xe + 93 Sr + 3n Notice that the product nuclides have a higher binding energy/nucleon than the reactant. This means that energy is released as these more stable nuclides form. Conversely, if two very light (low A) nuclides are combined, as in nuclear fusion, the product that forms has a higher binding energy/nucleon and again energy is released. An example of a nuclear fusion reaction is: 2 H + 3 H 6 4He + n By looking at the stable nuclides on the Chart of the Nuclides, one can begin to understand what modes of radioactive decay might occur. α, SF n-deficient (β+, EC) n-rich (β-) Note that for A < 40, the stable nuclides have N/Z ~ 1. As A increases the stable nuclides have a higher N/Z (up to ~1.5) to compensate for the increased Coulomb repulsions between protons. However, even this is not sufficient for stability because for Z > 83 all nuclides are radioactive. For a given A, if N/Z is too high to form a stable nuclide it is referred to as n-rich. It can reach a stable nuclide (of same A) by undergoing β- decay. This involves the conversion of a neutron into a proton with the concurrent emission of a high-energy electron from the nucleus (note that A is constant and Z increases by 1). Examples of β- decay: 14 3 C H 38 Cl β- 6 14 N β- 6 3He β- 6 38 Ar Conversely, for a given A, if N/Z is too low to form a stable nuclide it is referred to as ndeficient. It can reach a stable nuclide (of same A) by undergoing β+ or electron capture (EC) decay. These decay modes involve the conversion of a proton into a neutron with the concurrent emission of a high-energy positron (e+) from the nucleus (β+ decay) or xrays (EC decay) . β+ decay is more likely at low Z whereas EC is favored at high Z. Both decay modes are characterized by constant A and a decrease in Z by 1. Examples of β+ and EC decay: β+ 6 13 N 22 Na 49 V 13 C β+, EC 22 6 EC 6 49 Ne Ti At very high Z (especially Z > 83) there are other common forms of decay - alpha decay (α) and spontaneous fission (SF). Alpha decay involves the emission of a packet of 2 neutrons and 2 protons from the nucleus and thus is characterized a decrease in A by 4 and a decrease in Z by 2. Examples of α decay: 224 Ra 238 U α 6 α 6 220 234 Rn Th