DHS 20 Nuclear Physics (Notes & Tutorial)

Dunman High School (Senior High Physics Department) For Internal Use Only Page 1 of 33 Guiding Questions • Why are some nuclei radioactive? What happens during radioactive decay? Where does the energy come from? • What is emitted during radioactive decay, and is it harmful? How do decay products interact with matter? • What are the uses of radioactivity? • How are nuclear reactions different from chemical reactions? How are they similar? • What can conservation laws tell us about nuclear processes? Content • The nucleus • Isotopes • Mass defect and nuclear binding energy • Nuclear processes • Radioactive decay • Biological effect of radiation 9749 H2 Physics Topic 20 Nuclear Physics Year 6 (2025) DUNMAN HIGH SCHOOL

Dunman High School (Senior High Physics Department) For Internal Use Only Page 2 of 33 (a) infer from the results of the Rutherford α-particle scattering experiment the existence and small size of the nucleus Rutherford’s α-particle scattering experiment: Setup Rutherford's experiment consisted of a beam of alpha particles ( ) 4 2 He , generated by the radioactive decay of radium, directed normally onto a sheet of very thin gold foil (~ 4×10–7 m thick) in an evacuated chamber (Fig. 1). Alpha particles produce a tiny, but visible flash of light when they strike the fluorescent zinc sulphide screen, which is used as a detector, at the focus of a microscope; the screen and microscope could be swivelled around the foil to observe particles deflected at any given angle. Figure 1: (Left) Schematic diagram of the apparatus used by Geiger and Marsden to test Ernest Rutherford’s atomic model. (Right) The actual apparatus. Figure 2: Possible paths of scattered α-particles most of the α- particles deviated through small angles α-particle deviated through angles > 90o [very small percentage (0.01%)] gold nucleus scatter angle θ b d

Dunman High School (Senior High Physics Department) For Internal Use Only Page 3 of 33 Rutherford’s α-particle scattering experiment: Observations 1 Most of the α-particles were deviated through small angles. 2 A small but significant percentage of the α-particles were deviated through angles larger than 90o, (Fig. 2). Rutherford’s α-particle scattering experiment: Inferences Observation Inference Most of the α-particles were deviated through small angles. A smaller but significant percentage of the α- particles deviated through large angles greater than 90°. Models for the atom Figure 3a: The quantum mechanical model of an atom, in this case, helium. The quantum mechanical model is based on mathematics. Although it is more difficult to understand than the Bohr model, it can be used to explain observations made on complex atoms. Figure 3b: The Bohr model of an atom. It can make accurate predictions for the behaviour of simple atoms such as hydrogen. The currently accepted model of an atom (Fig. 3a) consists of a dense central nucleus surrounded by a cloud of negatively charged electrons: • Over 99.94% of an atom's mass is concentrated in the nucleus with protons and neutrons having roughly equal mass. • The protons are positively charged while the neutrons have no charge. • The electrons determine the chemical properties of an element, and strongly influence an atom's magnetic properties. Example 1 (2013 P1 Q40) Two α-particles with equal energies are fired towards the nucleus of a gold atom. Which diagram could represent their paths?

Dunman High School (Senior High Physics Department) For Internal Use Only Page 4 of 33 Solution: (Answer: ………. ) ……….. : Both α-particle and the gold nucleus are positively charged and should …………….. each other instead of …………….. each other. The α-particle travelling closer to the gold nucleus should undergo greater deflection. Thus, the answer is …….... instead of …….... Example 2 (2002 P1 Q30) In an α-particle scattering experiment, a student determined the number n of α-particles incident per unit time on a detector held at various angular positions θ. Which graph best represents the variation of n with θ? A B C D Solution: (Answer: ………. ) Refer to “Rutherford’s α-particle scattering experiment: Observations - Point 1”. 0 n +90 -90 -170 +170 θ/° 0 n +90 -90 -170 +170 θ/° 0 n +90 -90 -170 +170 θ/° 0 n +90 -90 -170 +170 θ/° thin gold foil detector +90° −90° −170° +170° θ 0° α-particles

Dunman High School (Senior High Physics Department) For Internal Use Only Page 5 of 33 (b) distinguish between nucleon number (mass number) and proton number (atomic number) Atomic Structure Protons and neutrons in a nucleus are collectively known as nucleons. The total number of protons and neutrons in a nucleus is equal to its nucleon number A (which is an integer, without unit). Nucleon number is also known as mass number. Proton number Z of a nucleus is equal to the number of protons in it. Each element in the Periodic Table has a unique proton number in the nucleus of its atom, starting with hydrogen having proton number = 1, helium having proton number = 2, etc. It is the proton number in the nucleus of its atom that determines the element. Hence, proton number is also known as atomic number of the nucleus of the atom of that element. All atoms are neutral. In an atom, the proton number of its nucleus and the number of electrons orbiting this nucleus must be the same. Why is A also known as the mass number? Charge Mass Proton +1.60 × 10−19 C or +e (e is elementary charge) 1.6726 × 10–27 kg Neutron 0 1.6749 × 10–27 kg As the mass of protons and neutrons is small, it is more convenient to write the mass of a nucleus or atom in unified atomic mass constant (symbol u) rather than in kg. The unified atomic mass constant, u, is defined as 1 12 of the mass of a carbon-12 atom. Thus 1 u = 1.66 × 10–27 kg Nucleons have masses of approximately 1 u (proton mass = 1.007 u , neutron mass = 1.008 u, electron mass = 0.00055 u). Since the mass of protons and neutrons are approximately the same and the electron is much less massive (about 1840 times lighter), the mass of a nucleus (or an atom) is approximately A u. This is why A is called the mass number. (c) show an understanding that an element can exist in various isotopic forms each with a different number of neutrons in the nucleus Isotopes Isotopes are atoms of the same element with the ……………………………………….. but ……………………………………….. in the nucleus. Quite a number of elements have isotopes. Hydrogen, for instance, has 3 naturally occurring isotopes. The most common isotope of h ydrogen has 1 proton in its nucleus, with no neutron , and is known as protium or hydrogen-1 (i.e. it has 1 nucleon) . Another isotope which has 2

Dunman High School (Senior High Physics Department) For Internal Use Only Page 6 of 33 nucleons is known as deuterium or hydrogen-2, and yet another which has 3 nucleons is known as tritium or hydrogen-3. Chemically, these isotopes are identical (since chemical reactions only involve orbital electrons, and all isotopes of the same element have the same number of orbital electrons), but their nuclei have different masses. Physically, isotopes exhibit different characteristics. (d) use the usua