ACJC Nuclear Physics Lecture Notes

Anglo-Chinese Junior College Lecture Notes Nuclear Physics H2 (9478) JC2 2026 Page 1 of 45 Nuclear Physics Guiding Questions Learning Objectives 1. What is an atomic nucleus? (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 XZ A for the representation of nuclides. 2. How is energy related to mass? (p) show an understanding of the concept of mass defect. (q) recall and apply the equivalence between energy and mass as represented by E=mc2 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. 3. How do nuclei react? (m) represent simple nuclear reactions by nuclear equations of the form N7 14 + He2 4 → O8 17 + H1 1 (n) state and apply to problem solving the concept that nucleon number, charge and mass-energy are all conserved in nuclear processes. (t) explain the relevance of binding energy per nucleon to nuclear fusion and to nuclear fission. 4. What is radioactive decay? (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 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 (anti)neutrino (knowledge of antineutrino and the zoo of particles is not required). (h) define the terms activity and decay constant and recall and solve problems using the equation A = 𝜆N. (i) 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. (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 relation 𝜆 = ln 2 t1 2 .

Anglo-Chinese Junior College Lecture Notes Nuclear Physics H2 (9478) JC2 2026 Page 2 of 45 5. How does radiation affect us? (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. 1. Atomic Structure and Nuclear Physics Terminology What is an atomic nucleus? Nature of Science Moment – From Plum Pudding to the Nuclear Atom At the turn of the 20th century, J. J. Thomson proposed the plum pudding model of the atom. Based on his discovery of the electron, he suggested that atoms were positively charged “puddings” with negatively charged electrons embedded within them. Importantly, this model was not a wild guess —it was the best explanation supported by experimental evidence available at the time. However, science does not stop at accepted ideas. When Ernest Rutherford and his team carried out the alpha-particle scattering experiment with gold foils , they observed results that the plum pudding model could not explain: most alpha particles passed straight through the foil, but a few were deflected at large angles. This led to a radical new conclusion—the atom is mostly empty space with a small, dense, positively charged nucleus at its centre. This shift from the plum pudding model to Rutherford’s nuclear model highlights a key feature of the Nature of Science: Scientific models are tentative and change when new evidence emerges. Thomson’s model was not “wrong” in a careless sense —it was limited by the evidence and technology of its time. Rutherford’s work did not simply reject earlier ideas; it refined and replaced them using stronger experimental support. This episode reminds us that scientific knowledge grows through questioning, testing, and being open to change when observations demand it. Thomson’s Plum Pudding Model Plum Pudding

Anglo-Chinese Junior College Lecture Notes Nuclear Physics H2 (9478) JC2 2026 Page 3 of 45 1.1 Rutherford’s Alpha-Particle Scattering Experiment Between 1909-11, Rutherford and two of his students, Hans Geiger and Ernest Marsden investigated the scattering of alpha () - particles by a thin film of heavy metal, notably gold Au79 197 , in a vacuum. The aim was to probe the interior structure of the atom. Using the simulation above, sketch the paths of ten alpha-particles emitted from a radioactive source (alpha-particle is a helium nucleus which has 2 protons and 2 neutrons) approaching the gold atoms in a thin foil (the nuclei in the atoms are actually smaller than shown). In the simulation, press the blue button to "turn on" the alpha source. You may wish to click the "Traces" checkbox to visualise the trails of the alpha particles. Rough perspective of a nucleus’ size: If the nucleus in an atom is the size of a baseball, the diameter of the atom would be the distance from ACJC to City Hall Area. Interact with this simulation to observe how the alpha particles scatter off the nucleus in Rutherford’s alpha-particle scattering experiment.

Anglo-Chinese Junior College Lecture Notes Nuclear Physics H2 (9478) JC2 2026 Page 4 of 45 Observations Interpretations (i) Majority of the alpha -particles pass through the gold foil undeflected. - Large numbers of high energy alpha-particles (travelling about one tenth of the speed of light) just pass almost straight through this very thin gold layer which was only about a thousandth of a millimetre thick. - This observation suggests that an atom consists of a large amount of empty space. (ii) A small number of alpha-particles were deflected through an angle greater than 90o. About 1 in 8000 alpha-particles was deflected back to where it came from. - When the positive charges are concentrated in a small volume, some of the alpha-particles could get near it to experience a large electric force to be deflected at larger angles (greater than 90o). - The atom must have all of its positive charges and most of its mass concentrated at its centre; the atom must have a positively charged nucleus that could deflect the alpha-particles through large angles. Conclusions 1. The nucleus occupies a small volume of the atom. It is no larger than 10-15 m in diameter. An atom has a typical diameter of 10-10 m. 2. The nucleus contains a large proportion of the mass of an atom. It accounts for at least 99.5% of the total mass of the atom. 3. The nucleus is positively charged.

Anglo-Chinese Junior College Lecture Notes Nuclear Physics