Transcript nuclear sta
Nagehan Demirci 10-U What is nuclear stability and where does this come from? As we all know , the nucleus is composed of protons and neutrons and protons are positively charged particles and neutrons have no charge From Coulomb’s law we learned that like charges repel one another strongly , particularly in the nucleus when we consider how close they must be to each other. At first glance, the existence of several protons in the small space of a nucleus is puzzling. Why would not the protons be strongly repelled by their like electric charges? The existence of stable nuclei with more than one proton is due to the nuclear force. The nuclear force is a strong force of attraction between nucleons (protons and neutrons together called nucleons ) that acts only at very short distances. (about 10-15 m.) Beyond nuclear distances these forces become negligible. Insıde the nucleus however , two protons are close enough together for the nuclear force between them to be effective. This force can more than compensate for the repulsion of electric charges and thereby gives a stable nucleus. The fact that some nuclie are unstable (radioactive) ,and others are stable leads us to consider the reasons of stabilitiy. FACTORS DETERMINING NUCLEAR STABILITY Two important factors determine the nuclear stability. •The mass number (the total number of nucleons in the nucleus) •The neutron to proton ratio This is because in a nucleus , the positively charged protons repel each other and as the number of protons increases in a nucleus the forces of repulsion between the protons increases drastically. Thus a greater proportion of neutrons is required for a nucleus to remain stable as the atomic number increases. The Band Of Stability When you plot each stable nuclide on a graph with the number of protons (Z) on the horizantal axis and the number of neutrons (N) on the vertical axis , These stable nuclides fall into a certain region, or band , of the graph. The band of stability is the region in which nuclides lie in a plot of number of protons against number of neutrons. Slayt 14 The zone of stability. The dots in the blue area represents the nuclides that do not undergo radioactive decay. Note that as the number protons in a nuclide increases, the neutron/proton ratio required for stability also increases. The area above the blue area represents an unstable region in which there are too many neutrons, therefore beta decay. In the region below the blue area represents an unstable region in which there are too many protons therefore spontaneous positron decay A 1 to 1 neutron to proton ratio holds true for the stable nuclei of the first twenty elements in the periodic table. This ratio increases to 1.5 to 1 around atomic number 80. Elements above atomic number 83 with 209 nucleons do not exist as stable isotopes. Thus for polonium , with 84 protons , the repulsive forces due to the 84 protons are so large that regardless of the number of neutrons , its nuclides are unstable. When the neutron to proton ratio is too large or too small, the nucleus is unstable , the atom is called a radionuclide and undergoes radioactive decay. If a radionuclide has a higher neutron to proton ratio , that is it has An excess of neutrons and therefore a neutron disintegrates to form a proton with the emission of a beta particle. 1 p1 + e0 n 0 1 -1 This decreases the neutron to proton ratio and may be repeated until it reaches the stable value and no further radioactive decay takes place. An example of beta decay is; 239 e0 + Np 93 -1 239 Pu 94 If on the other hand , a radionuclide has a lower neutron to proton ratio , it has an excess of protons and therefore a proton is transformed to a neutron either by positron emmission or by electron capture. 30 Si30 + e0 ; positron emission P 15 14 -1 37 + e0 Cl37 ; electron capture Ar 18 -1 17 In both positron emmission and electron capture by a nucleus , the nucleus produced hass one less proton . If however , the number of nucleons exceeds 209, the limit to be a stable nuclide is over and lies beyond the stable value , so several decays are required in order to attain stability. MAGIC NUMBERS The protons and neutrons in a nucleus appear to have energy levels much as the electrons in an atom have energy levels. The shell model of the nucleus is a nuclear model in which protons and neutrons exist in levels, or shells analogous to the shell structure that exists for electrons in an atom. Filled shells of electrons are associated with the special stability of the noble gases. The total numbers of electrons for these stable atoms are 2,10,18,36,54,86. Experimentally it is noted that nuclie with certain numbers of protons or neutrons appear to be very stable. These numbers are called the magic numbers and associated with specially stable nuclei. According to this theory, a magic number is the number of nuclear particles in a completed shell of protons and neutrons. For protons the magic numbers are 2, 8,20, 28, 50, 82 . Neutrons have these same magic numbers , as well as the magic number 126. Some of the evidence for these magic numbers, and therefore for the shell model of the nucleus is as follows. Many radioactive nuclei decay by emmitting alpha particles or helium nuclei. There appears to be special stability in the helium nucleus. It contains two protons and two neutrons , which 2 is a magic number. Another piece of evidence is seen in the final products obtained in natural radioactive decay. For example uranium-238 decays to thorium-234, which in turn decays to protactinium- 234 and so forth. Each product is radioactive and decays to another nucleus until the final product 82Pb206 is reached. This nucleus is stable. Note that it cantains 82 protons, a magic number. Other some radioactive series end with 82Pb208 and note that it has magic number of neutrons (208-82=126). A nucleus with a completely filled shell of either protons or neutrons is said to be magic because it is relatively more stable than nuclei with either a larger or a smaller number of nucleons. Most magic nuclei are spherical in shape, but some nuclei can lower their energy somewhat, and hence increase their stability, by rearranging their protons and neutrons into deformed shells accommodating a different number of nucleons. The closing of these deformed shells leads to deformed magic numbers. Another rule that can be useful in predicting the nuclear stability is; Nuclei with even number of protons and even number of neutrons are more stable that those with any other combination. Conversely nuclei with odd numbers of both protons and neutron are the least stable. Remember that magic numbers are also even. The Odd-Even Rule In the odd-even rule, when the numbers of neutrons and protons in the nucleus are both even numbers, the isotopes tends to be far more stable than when they are both odd. Out of all the 264 stable isotopes, only 4 have both odd numbers of both, whereas 168 have even numbers of both, and the rest have a mixed number. This has to do with the spins of nucleons. Both protons and neutrons spin. When two protons or neutrons have paired spins (opposite spins), their combined energy is less than when they are unpaired. Number of protons Number of neutrons Stable Nuclides Example Even Even 168 Carbon12-6 Even Odd 57 Carbon13-6 Odd Even 50 Fluorine19-9 Odd Odd 4 Lithium6-3 Table 1:The table showing the number of stable isotopes according to the number of protons and neutrons being even or odd. Summary of the rules that are useful in predicting the nuclear stability : •All nuclides with 83 or more protons are unstable with respect to radioactive decay. •Light nuclides are stable when atomic number equals to the number of neutrons ; that is when the neutron to proton ratio is 1. However for heavier elements the neutron to proton ratio required for stability is more than 1 and increases with the increase in the atomic number. •Nuclides with even number of protons and neutrons are more stable compared to others. •Nuclei that contain a magic number of proton and neutron seems to be more stable.