AQA A Level Physics: Atomic Structure & Decay Equations PDF

Head to www.savemyexams.com for more awesome resources AQA A Level Physics Your notes Atomic Structure & Decay Equations Contents Atomic Structure Nucleon & Proton Number Strong Nuclear Force Alpha & Beta...

Head to www.savemyexams.com for more awesome resources AQA A Level Physics Your notes Atomic Structure & Decay Equations Contents Atomic Structure Nucleon & Proton Number Strong Nuclear Force Alpha & Beta Decay Particles, Antiparticles & Photons Page 1 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Atomic Structure Your notes Atomic Structure All matter is made from atoms Atoms are made up of three types of particles: Protons Neutrons Electrons Protons and neutrons are found in the nucleus of an atom while electrons orbit the nucleus The properties of each particle in SI units are shown in the table below: Page 2 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes The relative properties of each particle are shown in the table below: A stable atom is neutral (it has no charge) Since protons and electrons have the same charge, but opposite signs, a stable atom has an equal number of both for the overall charge to remain neutral Examiner Tips and Tricks Remember not to mix up the ‘atom’ and the ‘nucleus’. The ‘atom’ consists of the nucleus and electrons. The ‘nucleus’ just consists of the protons and neutrons in the middle of the atom, not the electrons. Specific Charge In physics, ‘specific’ refers to the characteristic of a property of a substance Page 3 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources It is usually stated as a ratio i.e. per unit mass, length, area, volume etc. For example, specific heat capacity refers to the thermal energy per unit mass of a substance Your notes In atomic physics, specific charge is defined as: The ratio of the total charge of a particle to its mass It can be calculated using the equation: charge Q specific charge = = mass m Specific charge is measured in units of coulombs per kilogram (C kg–1) Values for the specific charge of the electron and proton are given on the datasheet as the ‘charge / mass ratio’ The specific charge of the electron = (e / me) = 1.76 × 1011 C kg–1 The specific charge of the proton = (e / mp) = 9.58 × 107 C kg–1 Calculating Specific Charge You may be asked to find the specific charge of an ion or a nucleus Charge of a proton or electron, e = 1.60 × 10–19C Mass of a proton, mp (or neutron, mn) = 1.67 × 10–27 kg To calculate the specific charge of an ion: Charge = Total number of electrons added / removed × (1.60 × 10–19 C) Mass = Total number of nucleons × (1.67 × 10–27 kg) To calculate the specific charge of a nucleus: Charge = Total charge of the protons × (1.60 × 10–19 C) Mass = Total number of nucleons × (1.67 × 10–27 kg) The number of nucleons is given by the mass number of the ion or nucleus Page 4 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes How the total charge and mass are calculated depends on whether you are calculating the specific charge for an ion or a nucleus Worked Example An atom of 24 Mg gains 2 electrons. 12 What is the specific charge of the ion? Answer: Step 1: List the relevant quantities from the data booklet: Charge of an electron = −1.60 × 10−19 C Mass of a proton = 1.67 × 10−27 C Step 2: Write the specific charge equation: Q specific charge = m Step 3: Calculate the total mass of the ion: Page 5 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources The notation for the magnesium ion can be written as: 24 Mg2 − 12 Your notes This tells us the ion contains 24 nucleons in total So, the total mass can be calculated using: Total mass = nucleon (mass) number × mass of one nucleon 24 × (1.67 × 10−27) = 4.0 × 10−26 kg Step 4: Calculate the total charge on the ion: Before gaining 2 electrons, the magnesium atom was electrically neutral So, the total charge on the ion is equal to the charge of 2 electrons, which is: Total charge = number of electrons × (−1.60 × 10−19) 2 × (−1.60 × 10−19) = −3.2 × 10−19 C Step 5: Substitute the values into the equation: −3. 2 × 10−19 Specific charge = = − 8. 0 × 106 C kg−1 (2 s.f) 4. 0 × 10−26 Examiner Tips and Tricks Sometimes you might be asked if the specific charge is positive or negative for an ion. Since the electron has a negative charge, the rules are as follows: If there is a gain in electrons, the specific charge will be negative. If there is a loss of electrons, the specific charge will be positive. Page 6 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Nucleon & Proton Number Your notes AZX Notation A nucleus can be described using AX notation Z AX notation is used to describe the constituents of a nucleus Z The top number A represents the nucleon number or the mass number Nucleon number (A) = total number of protons and neutrons in the nucleus The lower number Z represents the proton or atomic number Proton number (Z) = total number of protons in the nucleus Examiner Tips and Tricks In Chemistry, you may see nucleon number referred to as mass number and proton number as atomic number. Both of these are valid, just make sure you don't mistake mass number for atomic number, or vice versa. Make sure you know that the periodic table is ordered by atomic number Isotopes Elements are defined by a fixed number of protons in their atoms For example, all hydrogen atoms have 1 proton, and all carbon atoms have 6 protons Page 7 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources However, atoms of an element can have different numbers of neutrons These different versions of elements are called isotopes Your notes An isotope is defined as: Nuclei that have the same number of protons but different numbers of neutrons For example, hydrogen has two isotopes, deuterium and tritium All three isotopes contain 1 proton, but different numbers of neutrons The three atoms shown above are all forms of hydrogen, but they each have different numbers of neutrons Since nucleon number A includes the number of protons and neutrons, an isotope of an element will have A fixed proton number, Z A different nucleon number, A Page 8 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Some isotopes have an imbalance of neutrons and protons which makes them unstable This means they constantly decay and emit radiation to achieve a more stable form Your notes This can happen from anywhere between a few nanoseconds to 100,000 years Isotopic Data Isotopic data is defined as: The relative amounts of different isotopes of an element present within a substance The mass of an element is often given as relative atomic mass The relative atomic mass of an element can be calculated using the relative abundance values The percentage abundance of different isotopes in a sample can be obtained using a mass spectrometer Table of isotopic data for a sample of oxygen For example, a sample of oxygen may contain three isotopes: 16 O , 17 O and 18 O 8 8 8 The relative atomic mass of this sample of oxygen can be calculated using: (16 × 0.9976) + (17 × 0.0004) + (18 × 0.002) = 16.0044 To two decimal places, the relative atomic mass of the sample of oxygen is 16.00 A common use of isotopic data is carbon dating of archaeological artefacts This involves using the ratio of the amount of stable isotope carbon-12, to the amount of unstable isotope, carbon-14 Page 9 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources The age of a sample of dead tissue can be determined by comparing the ratio of these isotopes to the ratio in a sample of living tissue Your notes Worked Example One of the rows in the table shows a pair of nuclei that are isotopes of one another. Which row is correct? Answer: B Step 1: Properties of isotopes Isotopes are nuclei with the same number of protons but different number of neutrons The nucleon number is the sum of the protons and neutron Therefore, an isotope has a different nucleon number too Step 2: Calculate protons in the first nucleus Nucleon number: 37 Neutrons: 20 Protons = 37 − 20 = 17 Step 3: Calculate protons in the second nucleus Page 10 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Nucleon number: 35 Neutrons: 18 Your notes Protons = 35 − 18 = 17 Step 4: Conclusion Therefore, they have the same number of protons but different numbers of neutrons and are isotopes of each other The correct answer is therefore option B Page 11 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Strong Nuclear Force Your notes Strong Nuclear Force In a nucleus, there are Repulsive electrostatic forces between protons due to their positive charge Attractive gravitational forces due to the mass of the nucleons Gravity is the weakest of the fundamental forces, so it has a negligible effect compared to the electrostatic repulsion between protons If these were the only forces acting, the nucleus would not hold together Therefore, there must be an attractive force acting between all nucleons which is stronger than the electrostatic force This is known as the strong nuclear force The strong nuclear force acts between particles called quarks Protons and neutrons are made up of quarks, so the interaction between the quarks in the nucleons keeps them bound within a nucleus Whilst the electrostatic force is a repulsive force in the nucleus, the strong nuclear force holds the nucleus together Page 12 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Properties of the Strong Nuclear Force The strength of the strong nuclear force between two nucleons varies with the separation between Your notes them This can be plotted on a graph which shows how the force changes with separation The strong nuclear force is repulsive below a separation of 0.5 fm and attractive up to 3.0 fm The key features of the graph are: The strong force is highly repulsive at separations below 0.5 fm The strong force is very attractive up to a nuclear separation of 3.0 fm The maximum attractive value occurs at around 1.0 fm, which is a typical value for nucleon separation The equilibrium position, where the resultant force is zero, occurs at a separation of about 0.5 fm In comparison to other fundamental forces, the strong nuclear force has a very small range (from 0.5 to 3.0 fm) Comparison of Electrostatic and Strong Forces Page 13 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources The graph below shows how the strength of the electrostatic and strong forces between two nucleons vary with the separation between them Your notes The red curve represents the strong nuclear force between nucleons The blue curve represents the electrostatic repulsion between protons At separations between 0.5 and 3.0 fm, the attraction of the strong force is far more powerful than the repulsion of the electrostatic force The repulsive electrostatic force between protons has a much larger range than the strong nuclear force However, it only becomes significant when the proton separation is more than around 2.5 fm The electrostatic force is influenced by charge, whereas the strong nuclear force is not This means the strength of the strong nuclear force is roughly the same between all types of nucleon (i.e. proton-proton, neutron-neutron and proton-neutron) This only applies for separations between 0.5 and 3.0 fm (where the electrostatic force between protons is insignificant) Page 14 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources The equilibrium position for protons, where the electrostatic repulsive and strong attractive forces are equal, occurs at a separation of around 0.7 fm Your notes Examiner Tips and Tricks You may see the strong nuclear force also referred to as the strong interaction Make sure you can describe how the strong nuclear force varies with the separation of nucleons - make sure you remember the key values: range = 0.5 to 3.0 fm and typical nuclear separation ≈ 1.0 fm. Remember to write that after 3 fm, the strong force becomes 'zero' or 'has no effect' rather than it is ‘negligible’. Recall that 1 fm, or 1 femtometre, is 1 × 10–15 m Page 15 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Alpha & Beta Decay Your notes α & β Decay Equations When nuclei are unstable, they can become more stable through the process of radioactive decay Three of the most common decay mechanisms are: Alpha decay Beta-minus decay Beta-plus decay Alpha Decay Alpha decay is common in large, unstable nuclei with too many nucleons (protons and neutrons) The decay involves a nucleus emitting an alpha particle and decaying into a different nucleus An alpha particle consists of 2 protons and 2 neutrons This is equivalent to a helium nucleus During alpha decay, a parent nucleus becomes a daughter nucleus by emitting an alpha particle (helium nucleus) Page 16 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources When an unstable nucleus (the parent nucleus) emits radiation, the constitution of its nucleus changes As a result, the isotope will change into a different element (the daughter nucleus) Your notes Alpha decay can be represented by the following radioactive decay equation: When an alpha particle is emitted from a nucleus: The nucleus loses 2 protons: proton number decreases by 2 The nucleus loses 4 nucleons: nucleon number decreases by 4 Beta-Minus Decay A beta-minus, β-, particle is a high energy electron emitted from the nucleus β- decay is when a neutron turns into a proton emitting an electron and an anti-electron neutrino Page 17 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources During beta-minus decay, a neutron in a parent nucleus becomes a proton in a daughter nucleus by emitting a beta-minus particle (an electron) and an anti-electron neutrino Your notes When a β- particle is emitted from a nucleus: The number of protons increases by 1: proton number increases by 1 The total number of nucleons stays the same: nucleon number remains the same The new nucleus formed from the decay is called the “daughter” nucleus (nitrogen in the example above) Beta-Plus Decay A beta-plus, β+, particle is a high energy positron emitted from the nucleus β+ decay is when a proton turns into a neutron emitting a positron (anti-electron) and an electron neutrino Page 18 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes During beta-plus decay, a proton in a parent nucleus becomes a neutron in a daughter nucleus by emitting a beta-plus particle (a positron) and an electron neutrino When a β+ particle is emitted from a nucleus: The number of protons decreases by 1: proton number decreases by 1 The total number of nucleons stays the same: nucleon number remains the same Worked Example Page 19 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources The radioactive nucleus 222 Rn undergoes alpha decay into a daughter nucleus Po. 86 Your notes (a) Which letter in the diagram represents the daughter product? (b) What is the nucleon number and proton number of Po? Answer: Part (a) Letter C represents the daughter product The number of neutrons in 222 Rn is 222 − 86 = 136 86 In alpha decay, the parent nucleus loses a helium nucleus (2 protons, 2 neutrons) Proton number: 86 decreases to 84 Neutron number: 136 decreases to 134 Page 20 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Therefore, the correct answer is C Part (b) The equation for alpha decay is as follows: Hence the daughter nucleus Po has Nucleon number = 222 − 4 = 218 Proton number = 86 − 2 = 84 Worked Example A radioactive substance with a nucleon number of 212 and a proton number of 82 decays by β-plus emission into a daughter product which further decays by β-plus emission into a granddaughter product. Page 21 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Which letter in the diagram represents the granddaughter product? Answer: A The number of neutrons in the parent nucleus is 212 − 82 = 130 In beta-plus decay, a proton turns into a neutron Proton number: 82 decreases to 80 Neutron number: 130 increases to 132 Page 22 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Therefore, the correct answer is A Your notes Examiner Tips and Tricks Remember to avoid the common mistake of confusing the number of neutrons with the nucleon number. In alpha decay, the nucleon (protons and neutrons) number decreases by 4 but the number of neutrons only decreases by 2. Neutrino Emission An electron neutrino is a type of subatomic particle with no charge and negligible mass which is also emitted from the nucleus The anti-neutrino is the antiparticle of a neutrino Electron anti-neutrinos are produced during β– decay Electron neutrinos are produced during β+ decay Although the neutrino has no charge and negligible mass, its existence was hypothesised to account for the conservation of energy in beta decay When the number of α particles is plotted against kinetic energy, there are clear spikes that appear on the graph This demonstrates that α-particles have discrete energies (only certain values) Page 23 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Alpha particles have discrete energy levels whilst beta particles have a continuous range of energies When the number of β particles is plotted against kinetic energy, the graph shows a curve This demonstrates that beta particles (electrons or positrons) have a continuous range of energies This is because the energy released in beta decay is shared between the beta particles (electrons or positrons) and neutrinos (or anti-neutrinos) This was one of the first clues of the neutrino’s existence The principle of conservation of momentum and energy applies in both alpha and beta emission Examiner Tips and Tricks One way to remember which particle decays into which depends on the type of beta emission, think of beta ‘plus’ as the ‘proton’ that turns into the neutron (plus an electron neutrino) Page 24 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Particles, Antiparticles & Photons Your notes Antimatter The Universe consists of matter in the form of particles i.e. protons, neutrons, electrons etc. All particles of matter have an antimatter counterpart Antimatter particles are identical to their matter counterpart but have an opposite charge This means if a particle is positive, its antimatter particle is negative and vice versa Common matter-antimatter pairs are shown in the table below: Matter-Antimatter Table Apart from electrons, the corresponding antiparticle has The same name with the prefix ‘anti-’ A line above its corresponding matter particle symbol Properties of Antiparticles Corresponding matter and antimatter particles have Opposite charges Page 25 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources The same mass The same rest mass-energy Your notes The rest mass-energy of a particle is the energy equivalent to the mass of the particle when it is at rest Some values of common particle masses and rest mass-energies are shown in the table below: Mass & Rest Mass Energy Table Examiner Tips and Tricks In the exam, don't forget that the datasheet provides masses in kg and rest-mass energies in MeV for a proton, neutron, electron and neutrino The Photon Model Photons are fundamental particles which make up all forms of electromagnetic radiation Page 26 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources A photon is defined as: A massless “packet” or a “quantum” of electromagnetic energy Your notes This means that energy is not transferred continuously but as discrete packets of energy In other words, each photon carries a specific amount of energy, or "quanta", and transfers it all in one go, rather than supplying it consistently Calculating Photon Energy The energy of a photon can be calculated using the formula: E = hf Using the wave equation, photon energy can also be written: hc E= λ Where: E = energy of the photon (J) h = Planck's constant (J s) c = the speed of light (m s-1) f = frequency (Hz) λ = wavelength (m) This equation tells us: The higher the frequency of EM radiation, the higher the energy of the photon The energy of a photon is inversely proportional to the wavelength A long-wavelength photon of light has a lower energy than a shorter-wavelength photon Page 27 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes The energy of a photon is linked to the frequency of the light wave by the Planck constant, h Worked Example Light of wavelength 490 nm is incident normally on a surface, as shown in the diagram. The power of the light is 3.6 mW. The light is completely absorbed by the surface. Calculate the number of photons incident on the surface in 2.0 s. Answer: Step 1: Write the known quantities Page 28 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Wavelength, =490nm=490 Your notes Examiner Tips and Tricks Make sure you learn the definition for a photon: discrete quantity / packet / quantum of electromagnetic energy are all acceptable definitions.The values of Planck’s constant and the Page 29 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources speed of light will always be available on the datasheet, however, it helps to memorise them to speed up calculation questions! Your notes Annihilation & Pair Production Two important interactions involving particles, antiparticles and photons are: Annihilation Pair production Annihilation When a particle meets its corresponding antiparticle, the two will annihilate Annihilation is defined as: When a particle meets its corresponding antiparticle they both are destroyed and their mass is converted into energy in the form of two gamma-ray photons The two most common particle-antiparticle pairs that are seen are: Proton-antiproton annihilation Electron-positron annihilation When an electron and positron collide, their mass is converted into energy in the form of two photons emitted in opposite directions Page 30 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources The minimum energy of one photon after annihilation is the total rest mass energy of one of the particles: Your notes E min = hf min = E Where: E min = minimum energy of one of the photons produced (J) h = Planck's Constant (J s) f min = minimum frequency of one of the photons produced (Hz) E = rest mass energy of one of the particles (J) To conserve momentum, the two photons will move apart in opposite directions As with all collisions, the mass and energy is still conserved Pair Production Pair production is the opposite of annihilation, it is defined as: When a photon interacts with a nucleus or atom and the energy of the photon is used to create a particle–antiparticle pair In order to achieve the creation of a particle-antiparticle pair, a single photon must have enough energy to create both particles When a photon with enough energy interacts with a nucleus it can produce an electron-positron pair Page 31 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources The minimum energy required for a photon to undergo pair production is equal to the total rest mass energy of the particles produced: Your notes E min = hf min = 2E Where: E min = minimum energy of the incident photon (J) h = Planck's Constant (J s) f min = minimum frequency of the photon (Hz) E = rest mass energy of one of the particles (J) To conserve momentum, the particle and anti-particle pair move apart in opposite directions Worked Example Calculate the maximum wavelength of one of the photons produced when a proton and antiproton annihilate each other. Page 32 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Examiner Tips and Tricks Since the Planck constant is in Joules (J) remember to always convert the rest mass-energy from MeV to J. Page 33 of 33 © 2015-2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers