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    29 NUCLEAR PHYSICSNUCLEAR PHYSICSNUCLEAR PHYSICSNUCLEAR PHYSICS The nucleus:  The tiny core of an atom known as the nucleus  is made up of protons and neutrons (collectively known as nucleons ) held together tightly by the short-range, but very strong nuclear force . The number of protons in the nucleus of an atom of an element is known as the atomic number  of that element,  Z  . The atomic number determines the chemical properties of the element. The total number of nucleons is known as the mass number  of the element,  A . Actual masses of atomic particles are measured in terms of the unified atomic mass unit , u, which is defined as exactly one twelfth of the mass of one whole atom (including electrons) of a particular isotope of carbon, C-12, whose molar mass is exactly 12,00 g. Instructional objectives:  At the end of this chapter you should be able to …   Define the terms: nucleus, nucleon, atomic number, mass number, atomic mass unit, isotopes, radio-isotope, radioactivity, nuclear reaction, transmutation reaction, parent nucleus and daughter nucleus, decay series, activity, decay constant, half-life, capture reaction, electron-volt, breeder reactor, binding energy, fission, fusion, chain reaction, multiplication factor, critical mass, enrichment, moderator, heavy water, control rod, thermonuclear conditions.   Write and interpret the correct notation for protons, neutrons, electrons, positrons, deuterons, alpha particles and neutrinos, as well as the general notation for nuclear isotopes.   List, and describe the characteristics of, the three types of radiation associated with radioactive decay. Illustrate α - and β -decay graphically on A-Z axes.   Write balanced nuclear equations, applying the principles of conservation of nucleon number and charge, in order to illustrate, inter alia  ,: the processes of α - and β -decay; the production and decay of 14 C; fission and fusion reactions. Identify such equations.   Perform numerical calculations using the radioactive decay law and its various derivatives, including calculations concerning the activity of a sample. Describe the process of radioactive dating, using 14 C dating as an example. Perform calculations involving half-life (particularly the half-life of 14 C, in order to determine the age of organic samples).   List several devices suitable for detecting radiation, describing briefly the basic mechanism involved in each.   List several uses of man-made radio-isotopes.   Describe and explain the biological dangers of nuclear radiation.   Perform numerical calculations using Einstein’s equation, E = m.c 2 , in order to calculate the binding energies (in electron-volts) of nuclei and/or the energies of reaction products as well as the energies required to instigate nuclear reactions and the energies released in fission and fusion reactions.   Describe thoroughly the processes and practicalities of nuclear fission and fusion and discuss briefly the advantages and disadvantages of each.    30 23 12,00g11u126,02210   =   ×    = 1,660 54 ×  10 -24  g = 1,660 54 ×  10 -27  kg  NUCLEAR PHYSICS 31   Isotopes:   Isotopes  are atoms of the same element with the same atomic number (and therefore the same chemical properties), but different mass numbers (because they contain different numbers of neutrons in their nuclei). Isotopic notation, shown alongside, is convenient both for distinguishing between different isotopes (where X is the chemical symbol, eg carbon-12 is written as 126 C ) and for representing other atomic particles, a selection of which is given (together with some of their properties) in the following table: Particle Notation Mass [u] Charge proton p p +   11 p   11 H  1,007 276 + e  Note: e  represents the elementary charge , 1,6 ×  10 -19  C   neutron n n 0   10 n  1,008 665 0 electron e e  –    01 e −   β  – 0,000 548 6 –  e  positron e +   01 e   β +  0,000 548 6 + e  deuteron d d +   21 H  2,013 55 + e  alpha particle α   42 He   α 2+ 4,001 5 +2 e  neutrino  ν  0,000 0 Some isotopes are more stable than others. Nuclear instability seems to be as a result of an imbalance between the number of protons and the number of neutrons present in a given nucleus. This instability can occur naturally (for example, elements with Z > 82, 40 K and a few others), or as a result of deliberately adding neutrons to the nuclei of stable isotopes, thereby creating radioactive isotopes, known as radio-isotopes . Radioactivity:  The instability of the nucleus implies there is excess energy present which will sooner or later be released (in the form of radiation). Def n : Radioactivity is the decay or disintegration of nuclei, with the emission of radiation There are three types of radiation, known as alpha, beta and gamma radiation: Radiation type αααα  (particles) ββββ  (particles) γ γγ γ   (rays) Consisting of... 42 He   01 e −  vhf e/m radiation Electric charge 2+ 1– nil Mass 4 u 11850th u nil Relative penetrating power 1 (absorbed within ≈ 2,5 cm in air)  100 10 000 (most difficult against which to shield)   Balancing nuclear equations:  Two simple rules govern the representation of nuclear reactions: 1. Conservation of charge:  The sum of the atomic numbers on the left of the equation must equal the sum of the atomic numbers on the right. 2. Conservation of nucleon number:  The sum of the mass numbers on the left of the equation must equal the sum of the mass numbers on the right. AZ X    32  NUCLEAR PHYSICS Decay types:   αααα -decay  eg: 238234492902 UThHe → +   parent   daughter   alpha particle  Since the srcinal element changes, or transmutes, into another element, this type of reaction is known as a transmutation  reaction. ββββ -decay  eg: 212212083841 BiPoe − → +   parent   daughter   beta particle   β  particles are essentially electrons emitted from the nucleus when a neutron transforms into a proton within the nucleus (by emitting an electron). Actually β -decay refers to any process in which the nucleus spontaneously emits or absorbs   an electron or a positron  . Furthermore, the process usually also produces a neutrino, a particle which, as a result of its lack of charge and virtual masslessness, interacts only very weakly with matter. eg: n →  p + e  –   +  ν   γ γγ γ  -decay  ( γ   radiation) Occurs along with α - and β -decay to further lower the energy of the nucleus. eg: 212212083841 BiPoe − → + + γ    Decay series:  The daughter nuclei formed by the decay of radioactive parents are themselves often radioactive. These then decay to form yet a third isotope, and so on. Such successive decays are known as a decay series . In this way, radioactive isotopes which should long ago have disappeared from the 5 billion-year-old Earth (such as 22688 Ra with a half-life of 1 600 yr) are continually replenished. For example, complete the adjacent diagram showing how 23892 U eventually becomes the stable lead isotope 20682 Pb by undergoing, sequentially: ã  an alpha decay ( α ) ã  two beta decays (2 ×   β ) ã  four alpha decays (4 ×   α ) ã  an alpha decay followed by a beta decay ( α , β ), OR a beta decay followed by an alpha decay ( β , α ) ã  ( α , β ) OR ( β , α ) ã   β   ã  ( α , β ) OR ( β , α ) 214 212 210 83 84 82 A Z
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