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Nuclear Physics The Atomic Nucleus The nucleus of an atom consists of a collection of positively charged protons and neutral neutrons at the center of the atom. Protons and neutrons are called nucleons. The electrons surrounding the nucleus take part in chemical reactions, but not nuclear reactions. Protons and neutrons are made of smaller particles called quarks. The nucleus of an atom occupies 10-12 of the volume of the atom, yet it contains over 99% of its mass. Atoms are mostly empty space. Atomic Number and Mass Number The nucleus of an atom is described using atomic number(Z), mass number(A) and neutron number(N). The atomic number is equal to the number of protons in the nucleus and determines the identity of the atom. In a neutral atom, the number of electrons equals the number of protons and is also equal to Z. If electrons are gained or lost, the resulting particle is an ion of that element. If protons are gained or lost through nuclear reactions, we say we have formed a different element. The mass number is the total number of nucleons in the atom, and the neutron number is the number of neutrons in the atom. Mass number atomic number A ZX element symbol These numbers are related by the equation: A=Z+N Nuclear Forces There are 4 basic forces or types of interaction: • gravity • electromagnetic • strong interaction ("nuclear force") • weak interaction (causes some types of radioactive decay) In the nucleus protons repel each other with the electric Coulomb’s force and would make the nucleus split unless another force, the "nuclear force" or strong interaction, kept it together. The nuclear force is attractive at distances about the size of a nucleon and thereafter very quickly becomes weaker. Thus, for larger nuclei one tends to need more and more nucleons to keep them stable. At distances shorter than the size of a nucleon it becomes repulsive, preventing the nucleus from collapsing. The electromagnetic repulsive force is long range and all the protons in the atom affect each other. When the nucleus becomes very large (Z > 83), the repulsive force causes part of the nucleus to be expelled, and we say the nucleus is unstable (undergoes radioactive decay). Mass Defect If we add the mass of the nucleons and compare it to the mass of the nucleus, then we will find that some mass is missing. The difference in mass is called the mass defect (∆m): ∆m = mass of protons + mass of neutrons – mass of nucleus Einstein discovered that matter could be converted to energy (and vice-versa). The equation that expresses this mass-energy equivalency is: E = mc2 (c = 3.00*108 m/s) or ∆E = c2∆m This missing mass is then a form of energy which may be released if the atom, and especially the nucleus, changes in such a way that more energy is missing. The missing energy is called binding energy. The binding energy represents the amount of energy that must be supplied to break the nucleus into its individual protons and neutrons. Conversely, it is the energy released when the nucleus is formed from individual protons and neutrons. For a single nucleus, the magnitude of the binding energy is typically between 10-10 to 10-12 J. Nuclear Reactions Transmutation is the process of a nucleus changing into another nucleus. This can happen spontaneously, as in radioactive decay, or it can happen artificially when scientists add particle(s) to a nucleus causing it to change. All of the elements with atomic numbers greater than 92 are created artificially and do not exist in nature. They are called transuranium elements. In any nuclear reaction the following must always be true: • The total atomic number before the reaction must be the same as the total atomic number after the reaction. • The total atomic mass before the reaction must be the same as the total atomic mass after the reaction. The first requirement above is the statement of the conservation of charge in nuclear reactions. The second requirement is the statement of the conservation of nucleon number. Radioactive Decay In a nucleus, the repulsion between the positive protons is overcome by the nuclear force or strong interaction which is attractive at suitable distances. This leads to a certain relation between the number of protons and neutrons being most stable. The nuclei with less “favourable” ratio of neutrons to protons are unstable and can split forming nuclei of other elements. This process is called radioactive decay. Alpha decay of nucleus X: A ZX Æ A-4Z-2Y + 42He The helium nucleus atom is called alpha particle, sometimes 42α. Beta decay of nucleus X, type 1: β - -decay The most common type of beta decay is β- -decay where electrons are emitted as a neutron and the X-nucleus turns into a proton and the emitted electron. A ZX Æ AZ+1Y + 0-1e + 00ν Where the ν indicates an antineutrino, a massless particle whose existence was postulated since beta decay would violate the laws of momentum and energy conservation if X only split into Y and the electron. Beta decay of nucleus X, type 2 : β + -decay Another type of beta decay is one where a positron, the antiparticle of the electron is emitted; a particle with the same mass as the electron but the opposite electric charge. The third particle emitted here is an ordinary neutrino, not an antineutrino. A ZX Æ AZ-1Y + 0+1e + 00ν Beta decay of nucleus X, type 3 : Electron capture (EC) This is a case where the nucleus snatches an inner-shell electron. An ordinary neutrino, not an antineutrino, is also emitted. A ZX + 0-1e Æ AZ-1Y + 00ν Gamma decay of X Gamma decay occurs when the nucleus is left in an excited state by a previous step. The excited nucleus then emits a gamma photon when it relaxes. When the nucleus X has some of its parts in a higher energy state than the lowest possible—when it is "excited"—is denoted with the symbol X*. A * ZX Æ AZX + photon Nuclear Fission Nuclear fission is when an atomic nucleus splits into two or more pieces. This process is often triggered by the absorption of a neutron. Nuclides that are capable of undergoing nuclear fission are called fissile. When the nucleus splits, it also releases more neutrons and a large amount of energy. 1 0n 236 91 142 1 + 235 92 U→ 92 U→ 36 Kr + 56 Ba +3 0 n + energy Krypton-91 and barium-142 are known as the fission fragments. A uranium-235 nucleus can split in many different ways. An enormous amount of energy is released during each fission reaction. In any fission reaction, the combined mass of the incident neutron and the target nucleus is always greater than the combined mass of the fission fragments and the released neutrons. Only about 0.1% of the mass is converted into energy. 1 0 236 140 94 1 n + 235 92 U→ 92 U→ 54 Xe + 38 Sr +2 0 n + 160MeV 160MeV = 2.6*10-11J Since the reaction produces two new neutrons, these can be used again to split new U-nuclei; these can then split 4, 8, 16 and so on in an uncontrolled chain reaction (nuclear explosion). A controlled chain reaction can be obtained if the number of neutrons on average can cause a new fission = the multiplication factor =1.