RI Chap 20 Nuclear Physics Lecture Notes

20 NUCLEAR PHYSICS H2 Physics 9478 Content Page 20.1 The Nuclear Atom 2 20.2 Radioactive Decay 10 20.3 Nuclear Processes and Conservation Laws 24 20.4 Mass Defect and Nuclear Binding Energy 26 20.5 Appendix 38 Learning Outcomes Candidates should be able to: (a) infer from the results of the Rutherford α -particle scattering experiment the existence and small size of the atomic nucleus. (b) distinguish between nucleon number (mass number) and proton number (atomic number). (c) show an understanding that an element can exist in various isotopic forms, each with a different number of neutrons in the nucleus, and use the notation XA Z for the representation of nuclides. (d) show an understanding of the spontaneous and random nature of nuclear decay. (e) infer the random nature of radioactive decay from the fluctuations in count rate. (f) show an understanding of the origin and significance of background radiation. (g) show an understanding of the nature and properties of α, β and γ radiations (knowledge of positron emission is not required). (h) define the terms activity and decay constant, and recall and solve problems using the equation AN λ= . (i) infer and sketch the exponential nature of radioactive decay and solve problems using the relationship ( )0 expxx t λ= − where x could represent activity, number of undecayed particles or received count rate. (j) define and use half-life as the time taken for a quantity x to reduce to half its initial value. (k) solve problems using the equation 1 2 ln2 tλ = . (l) discuss qualitatively the applications (e.g. medical and industrial uses) and hazards of radioactivity based on: (i) half-life of radioactive materials, (ii) penetrating abilities and ionising effects of radioactive emissions. (m) represent simple nuclear reactions by nuclear equations of the form 14 4 17 1 72 81N He O H+ →+ .

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 2 (n) state and apply to problem solving the concept that nucleon number, charge and mass-energy are all conserved in nuclear processes. (o) show an understanding of how the conservation laws for energy and momentum in 𝛽𝛽 decay were used to predict the existence of the (anti)neutrino [knowledge of the antineutrino and the zoo of particles is not required]. (p) show an understanding of the concept of mass defect. (q) recall and apply the equivalence between energy and mass as represented by 𝐸𝐸 =𝑚𝑚𝑚𝑚2 to solve problems. (r) show an understanding of the concept of nuclear binding energy and its relation to mass defect. (s) sketch the variation of binding energy per nucleon with nucleon number. (t) explain the relevance of binding energy per nucleon to nuclear fusion and to nuclear fission. 20.1 The Nuclear Atom  Introduction Just as the chemical energy liberated in fire can be used for good and evil, the energy in nuclear “fire” can also be put to benevolent or malevolent uses. A slow and controlled release of nuclear energy can be harnessed to sustainably power our megacities safely and efficiently, but the reckless deployment of weapons of mass destruction can obliterate the surface of the Earth many times over and effectively turn the clock back on progress made in civilisation. This topic provides opportunities to discuss a whole host of existential questions. There is also a strong argument to learn about nuclear physics as part of scientific literacy. We should appreciate that while the fallout from nuclear disaster can be extremely hazardous, life on Earth has coped with an environmental level of background r adiation. There are many creative applications that we have found to use nuclear radiation productively. Discussing such socio -scientific issues provides opportunities to situate scientific and technological understanding in the context of humanistic and economic concerns. In terms of the physics concepts, this topic builds from Electric Fields when discussing Rutherford scattering of α -particles from the atomic nucleus, as well as for understanding the characteristics of nuclear radiation. The rest of the topic is otherwise descriptive or involves data handling and simple mathematical modelling, such as the exponential curve in simple examples of radioactive decay, as well as applying conservation laws (including the famous mass -energy equivalence) in nuclear reactions and processes.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 3  Rutherford α-scattering Experiment Atoms, the basic building blocks of matter, were once thought to be the smallest indivisible particle. However, with his discovery of the electrons in 1897, J.J. Thomson concluded that electrons are part of an atom because his experiments consistently produced electrons regardless of the metal used. He further postulated that these very light and negatively charged electrons were distributed throughout a uniform sea of positive charges in an atom, much like the way that plums are evenly distributed in a pudding. He thus named this model as the ‘plum-pudding’ model. In 1909, under the direction of Ernest Rutherford, Hans Geiger and Ernest Marsden investigated the structure of an atom. As shown in Fig. 20.1, a beam of α-particles (helium nuclei ) having an energy of 7.7 MeV emitted by the decay of radium is directed towards a thin gold foil. Deflected α-particles were detected as flashes on the fluorescent screen. To minimise the scattering of the α-particles by air molecules, their experimental set up was enclosed in vacuum. beam of α-particles gold foil few α-particles scattered backwards radioactive source in lead box RafflesInstitution some α-particles deflected at larger angles most α-particles deflected at small angles Fig. 20.1 A schematic of the Rutherford α-particle scattering experiment. Almost all of the α-particle are deflected at small angles, but a small number are deflected at large angles. Based on the ‘plum-pudding’ model of the atom, they had expected the α-particles to be deflected by only a very small angle ( ~1 ° at most). Much to their surprise, a very small number of α-particles (1 in about 8000) were deflected at large angles ( 90>° ) and a few were even scattered backwards ( ~ 180° ). To explain the large deflections of some of the α-particles, Rutherford theorized in 1911 that all the positive charge of the atom and most of the mass was concentrated in a tiny space inside the atom called the nucleus and the electrons orbit around the nucleus (similar to planets revolving around the sun). When an α -particle (having a charge of 2e+ ) come s close to a gold nucleus (having a charge of 79e+ ), it experiences a strong Coulombic repulsion and suffers a large deflection due to the large mass of the nucleus. Modern variant of Rutherford’s experiment Models of the Atom Indivisible Atom An atom was thought to be the smallest component of matter and could not be further broken down into smaller constituents. Plum Pudding Model Atoms compose of the negatively charged electrons evenly distributed within a cloud of positive charges. Planetary Model Atoms consist of negatively charged electrons orbiting around a very small, dense, positively charged nucleus. Bohr Model Similar to Rutherford’s model but electrons are in stationary states and hence do not radiate EM energy. Quantum Model Electrons are distributed in region described by the electron density cloud around a positively charged nucleus. The greatest probability of locating the electron is at the densest region. Pre-1897 1897 1911 1913 Post-1926

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 4 The amount of deflection depends on how close the path of the incoming α-particle is to the gold nucleus. This distance is called the impact parameter b (Fig. 20.2). If the impac t parameter is large, (for instance,