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Nuclear Stability 1 Nuclei containing a magic number of protons and or neutrons are stable The numbers 2 8 20 50 82 and 126 are called magic numbers There are many more stable nuclei with even numbers of protons and neutrons than with odd numbers of these particles All isotopes of the elements with atomic numbers higher than 83 are radioactive Number of Stable Isotopes Proton Number Neutron Number 157 53 50 5 Even Even Odd Odd Even Odd Even Odd Nuclear Stability 2 Figure 20 2 This plot shows the nuclides that are known to exist and those that are stable The stable nuclides are indicated in blue and this tight band is known as the band of stability Unstable nuclides are indicated in green and exhibit radioactivity Note that all isotopes of elements with atomic numbers greater than 83 are unstable The solid line is the line where n Z Radioisotopes Radioactive decay The disintegration of an unstable atomic nucleus with spontaneous emission of radiation Radioisotopes Nuclei that undergo radioactive decay mass neutrons protons atomic protons element symbol ZAE Types of Particles in Nuclear Reactions Although many species are encountered in nuclear reactions this table summarizes the names symbols representations and descriptions of the most common of these Types of Radioactive Decay Figure 20 7 This table summarizes the type nuclear equation representation and any changes in the mass or atomic numbers for various types of decay Balancing nuclear equations Balance total of all atomic numbers and all mass numbers We can identify mechanisms of decay in this way Example A stays the same 90 90 Z increases by one 38 39 3890 3990 3990 10 3890 emission Radioactive Decay Example Thorium 90228 decays to give radon 86220 via a two step process The element produced by the first alpha particle decay step must be The two steps are alpha emission A must decrease by 8 and Z by 4 over the two steps In the middle A will have decreased by 4 and Z by 2 Looking at a periodic table should show them that the element with Z 88 is radium B 90228 88224 24 Radioactive Half lives Figure 20 10 For cobalt 60 which has a half life of 5 27 years 50 remains after 5 27 years one half life 25 remains after 10 54 years two half lives 12 5 remains after 15 81 years three half lives and so on Radioactive Decay Obeys First Order Kinetics All radioactive decays obey first order kinetics ln A t kt ln A 0 The corresponding half life of the reaction is given by ln A t A 0 t 1 2 0 693 Half life Problem Example Plants constantly uptake the isotope 614 while they are alive but stop when they die Carbon dating works by determining the amount of 614 remaining compared to the level in living plants Carbon 14 has a half life of 5715 years What is the age of a piece of wood whose Carbon 14 content is 27 of the original concentration 1 2 0 693 k 1 21 10 4 ln0 271 1 21 10 4 10 000

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UMBC CMCS 471 - Nuclear Stability

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