EJC Physics H220 Nuclear Physics - 1. Notes (2024) - Full

Page 1 of 34 9749(2024) H2 Physics H220 Nuclear Physics – Notes H2 Topic 20 – Nuclear Physics The Sun is powered by nuclear fusion in its core. The core converts approximately 10 38 protons/second into helium at a temperature of 14 million K. This process releases energy in the form of photons, neutrinos, and other particles. (EIT - Extreme ultraviolet Imaging Telescope Consortium, The Solar and Heliospheric Observatory, NASA) Content • The nucleus • Isotopes • Nuclear processes • Mass defect and nuclear binding energy • Radioactive decay • Biological effects of radiation 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 (d) use the usual notation for the representation of nuclides and represent simple nuclear reactions by nuclear equations of the form 14 4 17 1 7 2 8 1N He O H+ → + (e) state and apply to problem solving the concept that nucleon number, charge and mass -energy are all conserved in nuclear processes (f) show an understanding of the concept of mass defect (g) recall and apply the equivalence relationship between energy and mass as represented by E = mc2 to solve problems (h) show an understanding of the concept of nuclear binding energy and its relation to mass defect (i) sketch the variation of binding energy per nucleon with nucleon number (j) explain the relevance of binding energy per nucleon to nuclear fusion and to nuclear fission (k) show an understanding of the spontaneous and random nature of nuclear decay (l) infer the random nature of radioactive decay from the fluctuations in count rate (m) show an understanding of the origin and significance of background radiation (n) show an understanding of the nature of α, β and γ radiations (knowledge of positron emission is not required) (o) show an understanding of how the conservation laws for energy and momentum in β decay were used to predict the existence of the neutrino (knowledge of antineutrino and antiparticles is not required) (p) define the terms activity and decay constant and recall and solve problems using the equation A = λN (q) infer and sketch the exponential nature of radioactive decay and solve problems using the relationship x = x0 exp(–λt) where x could represent activity, number of undecayed particles or received count rate (r) define and use half-life as the time taken for quantity x to reduce to half its initial value (s) solve problems using the relation 1/2 ln 2 t = (t) discuss qualitatively the effects, both direct and indirect, of ionising radiation on living tissues and cells.

Page 2 of 34 9749(2024) H2 Physics H220 Nuclear Physics – Notes 20.0 Introduction In our studies of Physics at the microscopic dimensions so far, we have remained at the atomic level, with the atomic electrons being the main participants in interactions. The nucleus, on the other hand, has been assumed to be dormant. This chapter on Nuclear Physics offers us a first look into the inner workings of a nucleus, and the interaction between nuclei . We will first look at the reactions between nuclei, and the changes in mass or energy involved . The spontaneous disintegration of a nucleus, which leads to the phenomena of radioactivity, will be discussed next. 20.1 The 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. He further postulated that these very li ght 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 the figure below, a beam of -particles ( 4 2He ) having an energy of 7.7 MeV is emitted by the decay of radium, and is directed towards a thin gold foil. [Gold was chosen because the element is stable (will not undergo radioactive decay with collisions), inert (will not chemically react with the alpha particles), and as a metal is malleable as well as ductile (so that it can be made to fewest possible layers of atoms).] The deflected -particles were detected as flashes on the fluorescent screen. To minimise the scattering of the -particles by air molecules, their experimental set up was enclosed in vacuum. Based on the ‘plum-pudding’ model of the atom, Rutherford and his collaborators had expected the -particles to be deflected by only a very small angle (~1 at most). The experimental results, as summarized in the table below, however, were much to their surprise. Plum Pudding Model Atoms compose of the negatively charged electrons evenly distributed within a cloud of positive charges. 1897 Planetary Model Atoms consists of negatively charged electrons orbiting around a very small, dense, positively charged nucleus. 1911 Bohr Model Similar to Rutherford s model but electrons are in stationary states and hence do not radiate EM energy. 1913 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. Current Models of Atom Indivisible Atom An atom was thought to be the smallest component of matter and could not be further broken down into smaller constituents. Pre-1897 source of alpha particles thin gold foil (vacuum environment) fluorescent screen lead shield α-particles detected as flashes on screen 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 Atom Atoms compose d 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, hence do not radiate EM energy. Quantum Model Electrons are distributed in space described by a probability density function around a positively charged nucleus. The greatest probability of locating the electron is at the densest region.

Page 3 of 34 9749(2024) H2 Physics H220 Nuclear Physics – Notes Experimental Observations Deductions Majority of -particles went straight through or were deviated by small angles of less than 10° - most of atom is empty space, mass of atom is concentrated in a very small nucleus. (size of atom  10-10 m, size of nucleus  10-15 m) - nucleus is positively charged, majority of -particles pass through atom far enough from nucleus to experience negligible electrostatic repulsion a small proportion (about 1 in 8000) of the α-particles deflected through large angles of more than 90° or came straight back - a small number of -particles that come close enough to the positively charged nucleus experienced significant electrostatic repulsion and are deflected through large angles Note that i n Physics, to scatter means to change in the direction of motion of a particle due to a collision with another particle. The “collision” need not involve direct contact between the particles, e.g. in this case the collision is due to electrostatic repulsion