H1 Physics Summary Notes (A-Level, 8867, 2021) PDF

These summary notes are valid for examination in 2023 and 2024. However, a new edition will be published in 2024 to reflect a revised syllabus for the 2025 examination. H1 Physics (Syllabus 8867) Section I: Measurement Topic 1: Measurement Physical quantities and SI units Base quantities and t...

These summary notes are valid for examination in 2023 and 2024. However, a new edition will be published in 2024 to reflect a revised syllabus for the 2025 examination. H1 Physics (Syllabus 8867) Section I: Measurement Topic 1: Measurement Physical quantities and SI units Base quantities and their SI units: ○ Mass – kilogram (kg) ○ Length – metre (m) ○ Time – second (s) ○ Current – ampere (A) ○ Temperature – kelvin (K) ○ Amount of substance – mole (mol) One mole of any substance contains 6.02 × 1023 particles – the Avogadro number NA = 6.02 × 1023 mol−1 can be used to calculate the number of particles in a substance given the number of moles or vice versa. A derived unit can be expressed as a combination of products or quotients of any of the base units. Using SI base units to check the homogeneity of physical equations: ○ A physical equation is homogeneous if all the terms in the equation have the same units ○ If the equation involves addition or subtraction of quantities, the quantities that are added or subtracted must also have the same units ○ Equations that are valid must be homogeneous, but equations that are homogeneous are not necessarily valid Conventions for labelling graph axes and table columns: ○ The table headers and graph axes must show the quantity and its corresponding unit (e.g. L / m) ○ The numerical labels for each axis should have the same number of decimal places Prefixes and symbols to indicate decimal sub-multiples or multiples of both base and derived units: ○ Pico (p) – 10−12 ○ Nano (n) – 10−9 ○ Micro (µ) – 10−6 ○ Milli (m) – 10−3 ○ Centi (c) – 10−2 ○ Deci (d) – 10−1 ○ Kilo (k) – 103 ○ Mega (M) – 106 ○ Giga (G) – 109 ○ Tera (T) – 1012  Estimates of physical quantities are made to judge the plausibility of any given quantity and estimate the sizes of further quantities, and are generally expressed to one significant figure. Scalars and vectors Distinction between scalar and vector quantities: ○ A scalar quantity is a quantity that has magnitude only ○ A vector quantity is a quantity that has both magnitude and direction ○ Examples of scalar quantities include mass, time, length, volume, temperature, density, speed, energy, pressure and current ○ Examples of vector quantities include displacement, velocity, acceleration, force and momentum Addition and subtraction of coplanar vectors: ○ Parallel vectors can be added or subtracted using simple addition or subtraction ○ Non-parallel vectors can be added using either the parallelogram or triangle of vectors ○ Resultant vectors can be computed using scale drawing, Pythagoras theorem, sine and cosine rule or resolution and recombination of vectors Representation of a vector as two perpendicular components: ○ |Rx| = |R| cosθ ○ |Ry| = |R| sinθ ○ θ is the angle between Rx and R Errors and uncertainties Distinction between systematic errors and random errors: ○ A systematic error is an error that has a constant magnitude and is either always positive or always negative ○ A random error is an error that has a varying magnitude and has an equal chance of being negative or positive ○ A zero error is an example of a systematic error Distinction between precision and accuracy: ○ Precision refers to how close individual measurements are to one another, without reference to any true value ○ Accuracy refers to how close a measured value is to the true value Assessing the uncertainty in a derived quantity: ○ When quantities are added or subtracted, the actual uncertainties of each quantity are added, i.e. z = x ± y ⇒ Δz = Δx + Δy ○ When quantities are multiplied or divided, the fractional / percentage uncertainty of the quantity to be calculated is the sum of the fractional / percentage uncertainties of each individual quantity, i.e. z = xy or z = x / y ⇒ Δz / z = Δx / x + Δy / y ○ If a quantity is multiplied by a constant, its actual uncertainty is also multiplied by the constant, i.e. z = kx ⇒ Δz = k Δx 2  ○ If a quantity is raised to the nth power, its fractional uncertainty is given by the fractional / percentage uncertainty of the quantity multiplied by the absolute value of the index, i.e. z = xn ⇒ Δz / z = |n| (Δx / x) ○ For quantities calculated using other mathematical functions, the error can be estimated using numerical substitution, taking the difference between the largest or smallest possible value and the calculated value, whichever is greater Section II: Newtonian Mechanics Topic 2: Kinematics Rectilinear motion Displacement, speed, velocity and acceleration: ○ The displacement of a body is its distance from a defined reference point in a defined direction ○ The speed of a body is the rate of change of its distance travelled ○ The velocity of a body is the rate of change of its displacement ○ The acceleration of a body is the rate of change of its velocity ○ Speed is a scalar quantity while displacement, velocity and acceleration are vector quantities Distance, displacement, speed, velocity and acceleration can be represented using distance-time, displacement-time, speed-time, velocity-time and acceleration-time graphs respectively. Properties of displacement-time and velocity-time graphs: ○ The gradient of a displacement-time graph is the velocity of the body ○ The gradient of a velocity-time graph is the acceleration of the body ○ The area under a velocity-time graph is the change in displacement of the body ○ In cases of non-uniform acceleration, the velocity-time graph is a curve (i.e. the gradient is not constant) Derivation of equations which represent uniformly accelerated motion in a straight line: ○ From the definition of acceleration, a = (v − u) / t ⇒ v = u + at --- (1) ○ Displacement is the area under the velocity-time graph, thus s = ½ (v − u) t + ut ○ From (1), v − u = at, hence s = ut + ½at2 --- (2) ○ Using the trapezoid formula for calculating area, s = (v + u) t / 2 ○ From (1), t = (v − u) / a, hence v2 = u2 + 2as --- (3) Solving problems using equations which represent uniformly accelerated motion in a straight line: ○ The equations can be used to solve problems such as the motion of bodies falling in a uniform gravitational field without air resistance ○ Sketch a diagram showing the path of the object, and select one direction as positive 3  ○ Select appropriate initial and final points for calculation, and determine the values of u, v, a, s and t ○ Use the equations to solve the problem Motion of bodies falling in a uniform gravitational field with air resistance: ○ At low speed with no turbulence, drag force is approximately proportional to speed ○ At higher speeds with turbulence, drag force is approximately proportional to the square of the speed ○ With air resistance, a body’s acceleration would be less than g when it is falling downward, causing it to take a longer time to reach the ground ○ After falling for some time, the air resistance becomes equal to the weight of the body and the body falls at terminal velocity Non-linear motion Motion due to a uniform velocity in one direction and uniform acceleration in a perpendicular direction: ○ The equations for uniformly accelerated motion in a straight line apply to such scenarios when the displacement and velocity of the body are resolved in the direction of acceleration and the direction of uniform velocity ○ From these equations, the body’s displacement in the direction of acceleration is a quadratic function of time while that in the direction of uniform velocity is a linear function of time ○ The body’s velocity in the direction of acceleration is a linear function of time ○ Thus, the trajectory of the body is parabolic ○ If the acceleration is caused by gravity alone, the motion is known as projectile motion Topic 3: Dynamics Newton’s laws of motion Newton’s laws of motion: ○ Newton’s First Law states that in the absence of a resultant force acting on a body, a body at rest will remain at rest and a body in motion will continue in motion at constant velocity ○ Newton’s Second Law states that the rate of change of momentum of a body is proportional to the resultant force acting on the body, and that the momentum change takes place in the direction of the resultant force ○ Newton’s Third Law states that when a body A exerts a force on a body B, body B exerts an equal and opposite force on body A ○ Newton’s laws of motion can be applied to solve problems involving forces and motion Mass is the property of a body which resists a change in motion (inertia) – the more mass a body has, the harder it is to start it moving from rest, bring it to rest or change its direction of motion. Concept of weight: 4  ○ The weight of a body is the gravitational force experienced by a mass in a gravitational field ○ The apparent weight of a body is the force exerted on the body by the body that is freely supporting it ○ The weight of a body is the product of its mass and the gravitational field strength, i.e. W = mg Linear momentum and its conservation The linear momentum of a body is defined as the product of the mass and the linear velocity of the body, and is a vector quantity in the direction of the body’s velocity. The impulse of a force is defined as the product of the net force and the time of impact, and is equal to the change in momentum of the body caused by the impact. The resultant force on a body is equal to the rate of change of momentum of the body, and the momentum change takes place in the direction of the resultant force. The relationship F = ma, where resultant force and acceleration are always in the same direction, can be used to solve problems involving forces acting on an object. The principle of conservation of momentum states that when bodies in a system interact, the total momentum remains constant provided no resultant external force acts on the system. Application of the principle of conservation of momentum to solve collision problems: ○ A (perfectly) elastic collision is one in which both kinetic energy and momentum is conserved ○ An inelastic collision is one in which momentum is conserved but kinetic energy is not conserved ○ A completely inelastic collision is a form of inelastic collision in which the bodies coalesce after the collision and kinetic energy loss is maximum ○ Collision problems can be solved by applying the appropriate conservation laws For a (perfectly) elastic collision between two bodies, the relative speed of approach is equal to the relative speed of separation. Whilst the momentum of a closed system is always conserved in interactions between bodies, some change in kinetic energy usually takes place, converted to other forms of energy such as internal energy or potential energy of deformation. Topic 4: Forces Types of force Hooke’s Law states that the applied force is proportional to the amount of extension or compression it produces in an elastic object, i.e. F = kx, where k is the force constant – it can be used to solve problems involving compression or extension of an elastic object. Forces on a mass, charge and current-carrying conductor in gravitational, electric and magnetic fields: ○ Two masses experience a gravitational force in the direction of their centre of mass, in the direction of the gravitational field 5  ○ Two like charges experience a repulsive electric force while two opposite charges experience an attractive electric force towards each other, in the direction of the electric field (positive charge) or in the direction opposite to the electric field (negative charge) ○ A current-carrying conductor experiences an electromagnetic force that is perpendicular to both the direction of the magnetic field and the direction of current in the conductor, in accordance with Fleming’s left-hand rule Normal contact forces, frictional forces and viscous forces: ○ A normal contact force is a force that two surfaces exert on each other, perpendicular to the surfaces in contact ○ A frictional force is a force that two rough surfaces exert on each other when there is motion or tendency to motion between them, opposite to the direction of motion or impending motion and parallel to the surfaces ○ A viscous force is a force exerted on a body moving through a fluid, opposite to its direction of motion relative to the fluid ○ Air resistance is a type of viscous force experienced by a body moving in air Centre of gravity The weight of a body may be taken as acting at a single point known as its centre of gravity. Turning effects of forces Moment of a force and the torque of a couple: ○ The moment of a force about a point is defined as the product of the force and the perpendicular distance from the line of action of the force to that point ○ The torque of a couple is defined as the product of either force and the perpendicular distance between the forces ○ The moment of a force and the torque of a couple can be applied to solve problems involving rotational motion A couple is a pair of forces which tends to produce rotation only, having no translational effect. The principle of moments states that if a body is in rotational equilibrium, the sum of clockwise moments about any point must be equal to the sum of anticlockwise moments about the same point – the principle is used to solve problems involving bodies in static equilibrium. Equilibrium of forces When there is no resultant force and no resultant torque, a system is in equilibrium – this means that their lines of action must intersect at a common point. Forces in static equilibrium can be represented by a closed vector triangle. Topic 5: Work, Energy and Power Work The work done by a force on a body is defined as the product of the force and the displacement of the body in the direction of the force. 6  Calculation of work done: ○ The work done by a constant force is given by W = Fs cos θ, where θ is the angle between the force vector and the displacement vector ○ The work done by a varying force is given by the area under the force-displacement graph Energy conversion and conservation Examples of energy in different forms, its conversion and conservation, and the principle of energy conservation: ○ Kinetic energy – a sprinting student ○ Potential energy – a satellite in orbit around a planet with multiple satellites ○ Internal energy – a body at any temperature above absolute zero ○ Photon energy – a quanta of light from a laser pointer ○ Mass energy – anything with mass ○ Nuclear binding energy – bound nucleons in an atom ○ Ionisation energy – an electron in a hydrogen atom being liberated ○ Work function – electron release from a gold plate in vacuum due to the photoelectric effect ○ Electromotive force – a mobile charger or power bank ○ Energy conversion – kinetic energy is converted to gravitational potential energy when a ball is being thrown upwards ○ Energy conservation – the total energy of the ball remains constant provided there is no air resistance ○ The principle of energy conservation states that energy can neither be created nor destroyed but it can be converted from one form to another, and the total energy in an isolated system remains constant ○ The principle of energy conservation can be applied to solve problems involving energy conversion Efficiency Implications of energy losses in practical devices and the concept of efficiency: ○ For all practical devices, the useful energy output is always less than the useful energy input as a result of energy loss to the environment ○ The efficiency η of a device is the ratio of useful energy output to the energy input, i.e. η = useful energy output / energy input ○ The concept of efficiency can be used to solve problems involving practical devices Potential energy and kinetic energy Derivation of the equation Ek = ½mv2: ○ The kinetic energy Ek of a body is the work done to accelerate it from rest to a speed v, i.e. Ek = Fs = mas ○ From the equations for uniformly accelerated motion in a straight line, v2 = u2 + 2as ○ Since the body was accelerated from rest, u = 0 ⇒ as = ½v2 ○ Hence Ek = ½mv2 7  The equation Ek = ½mv2 can be used to solve problems involving moving bodies. Distinction between gravitational potential energy, electric potential energy and elastic potential energy: ○ Gravitational potential energy is the energy possessed by a body due to its mass and its position in a gravitational field ○ Electric potential energy is the energy possessed by a body due to its charge and its position in an electric field ○ Elastic potential energy is the energy possessed by a body due to its deformation Elastic potential energy in a deformed material: ○ The elastic potential energy in a deformed material is the work done to deform the material by an extension x from its natural length ○ Since work done is the area under the force-displacement graph, the elastic potential energy of the deformed material is the area under the force-extension graph In a uniform field, the magnitude of the force acting on an object is equal to the change in potential energy of the object per unit distance travelled, i.e. F = ΔU / Δs – this relationship can be used to solve problems involving force and potential energy. Derivation of the equation Ep = mgh for gravitational potential energy changes near the Earth’s surface: ○ When a body is being lifted a displacement h, the gain in gravitational potential energy Ep of the body is equivalent to the work done by an external force F ○ From the definition of work done, Ep = W = Fh ○ Since the body of mass m is lifted without a change in velocity, by Newton’s Second Law, mg − F = 0 ⇒ F = mg ○ Hence Ep = mgh The equation Ep = mgh can be used to solve problems involving gravitational potential energy changes near the Earth’s surface. Power Definition of power and derivation of power as the product of a force and velocity in the direction of the force: ○ Power is defined as the work done per unit time, i.e. P = ΔW / Δt ○ Instantaneous power at a point in time is given by P = dW / dt = d(Fs) / dt, where F is constant ○ Thus P = F ds / dt = Fv (since dF / dt = 0) ○ Hence, instantaneous power is given by the product of the force and the velocity in the direction of the force Topic 6: Motion in a Circle and Orbits Kinematics of uniform circular motion Angular displacement can be expressed in radians, where one radian is the angle subtended at the centre of the circle by an arc equal in length to the radius of the circle. 8  Concept of angular velocity: ○ Angular velocity is the rate of change of angular displacement of a body, i.e. ω = Δθ / Δt ○ ω = 2π / T = 2πf, where T is the period of rotation and f is the frequency of rotation ○ All points on a rotating body have the same angular velocity ○ This concept can be used to solve problems involving rotational motion v = rω, where r is the radius of circular motion, can be used to convert angular velocity ω to linear velocity v and vice versa. Centripetal acceleration Motion in a curved path due to a perpendicular force and centripetal acceleration in the case of uniform motion in a circle: ○ By Newton’s Second Law, when a force acts on a body perpendicular to its direction of motion, it causes an acceleration in the same direction ○ Since there is no component of acceleration in the direction of motion, the body’s direction of motion continuously changes but its speed does not change ○ In the case of uniform motion in a circle, centripetal acceleration is the acceleration towards the centre of the circle and perpendicular to the linear velocity of the body Centripetal acceleration a = rω2 and a = v2 / r can be used to solve problems. Centripetal force Centripetal force F = mrω2 and F = mv2 / r can be used to solve problems. Gravitational force between point masses Newton’s Law of Gravitation states that every particle of matter in the universe attracts every other particle with a gravitational force F that is directly proportional to the product of the masses of the particles m1m2 and inversely proportional to the square of the distance r between them, i.e. F = Gm1m2 / r2, where G is the gravitational constant which has the value 6.67 × 10−11 N m2 kg−2. Circular orbits For a mass m orbiting at a certain distance r from the centre of a mass M, the gravitational force provides the required centripetal acceleration for the mass m to orbit about mass M, i.e. GMm / r2 = mv2 / r = mrω2 – this relation can be used to analyse circular orbits in inverse square law fields. Geostationary orbits and their application: ○ Geostationary satellites are satellites with orbits such that the satellites are always positioned over the same geographical spot on Earth ○ The plane of orbit of the satellite must be the same as that of the equator, as the gravitational force exerted by the Earth on the satellite is always directed towards the centre of the Earth ○ All geostationary satellites have the same orbital radius, period and velocity 9  ○ Geostationary satellites are useful because they allow a fixed antenna on Earth to maintain a constant line of communication with the satellite Section III: Electricity and Magnetism Topic 7: Current of Electricity Electric current Electric current is the net rate of flow of electric charge. The equation Q = It can be used to solve problems by relating the current to the rate of flow of charge. Potential difference The equation V = W / Q can be used to solve problems by relating the potential difference across a conductor to the work done to drive a unit charge through it. The equations P = VI, P = I2R and P = V2 / R, where R is resistance, can be used to solve problems involving the power dissipated in a resistor. Resistance and resistivity The resistance of a circuit component is the ratio of the potential difference across the component to the current passing through it – the equation V = IR can be used to solve problems involving the resistance of a circuit component. I-V characteristics of various electrical components: ○ For an ohmic resistor, its steady-state temperature remains constant as the potential difference across it varies ○ Since the mobility of charge carriers remains constant, the resistance of the ohmic conductor remains constant ○ For a semiconductor diode, resistance is very high in the reverse-bias direction but insignificant in the forward-bias direction ○ At a certain threshold potential in the reverse-bias direction, a Zener breakdown occurs, allowing the diode to conduct an infinitely large current ○ For a filament lamp, the steady-state temperature of the filament increases as the potential difference across it increases ○ This causes conducting electrons to collide more frequently with the lattice ions in the wire, decreasing the mobility of the charge carriers and increasing the resistance of the filament ○ For a negative temperature coefficient (NTC) thermistor, its temperature increases as the potential difference across it increases, resulting in more mobile charge carriers being liberated in it ○ As there is an increase in the amount of mobile charge carriers, the resistance of the thermistor decreases 10  Resistance-temperature characteristic of an NTC thermistor: The equation R = ρl / A , where ρ, l and A are the resistivity, length and cross-sectional area of the conductor respectively, can be used to solve problems. Electromotive force Distinction between electromotive force (e.m.f.) and potential difference (p.d.): ○ The potential difference between two points is the electrical energy converted to other forms of energy per unit charge passing from one point to another ○ The electromotive force of a source is the energy converted from other forms to electrical energy per unit charge passing through the source Effects of the internal resistance of a source of e.m.f. on the terminal potential difference and output power: ○ The terminal potential difference across the cell is lower than the e.m.f. of the cell because some power is dissipated in the internal resistance, causing a potential drop ○ The output power will be lower than the theoretical power output as some energy is dissipated as heat in the internal resistance 11 Topic 8: D.C. Circuits Circuit symbols and diagrams Circuit symbols: Using these symbols, circuit diagrams can be drawn to represent circuits, which contain one or more source(s) together with switches, resistors, ammeters, voltmeters or other components. Series and parallel arrangements The formula for the combined resistance of two or more resistors in series, RT = R1 + R2 + … + Rn, can be used when there is a common current through the resistors.. The formula for the combined resistance of two or more resistors in parallel, 1 / RT = 1 / R1 + 1 / R2 + … + 1 / Rn, can be used if there is a common potential difference across each resistor. Problems involving series or parallel circuits for one source of e.m.f. can be solved by rearranging or simplifying the circuit diagram in one of the following two ways: ○ Redraw the circuit so that it is convenient to see resistors arranged in parallel or in series ○ Progressively reduce the number of resistors until the circuit can be simplified to a single resistor Potential divider Use of a potential divider circuit as a source of variable p.d.: ○ When two resistors are arranged in series, they have a common current through them, thus the potential difference across each resistor will be directly proportional to its resistance ○ By allowing one of the resistances to vary, the output voltage in a potential divider circuit could be varied Use of thermistors and light-dependent resistors in potential divider circuits: ○ The resistance of most thermistors decreases when temperature increases ○ The resistance of a light-dependent resistor decreases when the incident light intensity increases 12  ○ A thermistor can be connected in a potential divider circuit to provide a potential difference which is temperature dependent, such as in a fire detection system or an air-conditioner ○ A light-dependent resistor can be used in a potential divider circuit to provide a potential difference which is illumination dependent, such as in lighting circuits Topic 9: Electromagnetism Concept of an electric field Concept of an electric field and definition of electric field strength at a point: ○ An electric field is a region of space where a charge experiences a force, and is an example of a field of force ○ Electric field strength at a point is defined as the electric force per unit positive charge on a small test charge placed at that point, i.e. E = F / Q or F = QE Representation of an electric field by means of field lines: ○ A field line indicates the direction of the force a positive charge would experience if it is placed at that point in the field ○ The number of field lines per unit cross-sectional area is proportional to the electric field strength Concept of a magnetic field A magnetic field is an example of a field of force produced either by current-carrying conductors or by permanent magnets, and it is where a moving charge, current-carrying conductor or magnetic material experiences a force. Magnetic fields due to currents Flux patterns due to currents in a long straight wire, a flat circular coil and a long solenoid: long straight wire flat circular coil 13  long solenoid The magnetic field due to a solenoid may be influenced by the presence of a ferrous core – it has the ability to align its dipoles by magnetisation and concentrate the field lines, thus strengthening the magnetic field. Force on a current-carrying conductor A current-carrying conductor placed in a magnetic field will experience a force if the field is perpendicular to or has a component perpendicular to the direction of current flow. The equation F = BIl sinθ, with directions as interpreted by Fleming’s left-hand rule, where l is the length of the conductor and θ is the angle between the current and the magnetic field, can be used to solve problems involving a current-carrying conductor in a magnetic field. Magnetic flux density at a point is defined as the magnetic force per unit length exerted on a long straight conductor carrying a unit current placed perpendicular to the magnetic field, i.e. B = F / Il. How the force on a current-carrying conductor can be used to measure the flux density of a magnetic field using a current balance: ○ Part of a current-carrying rectangular coil is placed inside the magnetic field such that it experiences a downward magnetic force F ○ A rider of known mass m is hung at the opposite end of the coil ○ A pivot is placed under the coil and is shifted to a position d1 from the part of the coil experiencing a force due to the magnetic field and d2 from the rider where the coil is in rotational equilibrium ○ The magnetic flux density can be calculated using B = mgd2 / Ild1 by taking moments about the pivot Force between current-carrying conductors Forces between current-carrying conductors: ○ Since a magnetic field is set up when there is a current in a conductor, each conductor lies in the magnetic field created by the current in the other conductor ○ Each conductor thus experiences a magnetic force ○ By Fleming’s left-hand rule, when the currents flow in the same direction, there is a force of attraction between them ○ By Fleming’s left-hand rule, when the currents flow in opposite directions, there is a repulsive force between them ○ These can be used to predict the direction of the forces acting on the conductors Force on a charge The direction of the force on a charge moving in a magnetic field can be obtained by Fleming’s left-hand rule, with the thumb indicating the direction of the force, the index finger indicating the direction of the magnetic field and the middle finger indicating the direction of movement of the charge if it is positive or opposite to its direction of movement if it is negative. 14  The equation F = BQv sinθ can be used to solve problems involving moving charges in a magnetic field. The forces on charges in uniform electric fields can be calculated using the equation F = Eq where E is the electric field strength and q is the charge. Effect of a uniform electric field on the motion of charged particles: ○ A charge projected parallel to the electric field will be accelerated parallel to its direction of motion, resulting in a linear trajectory ○ A charge projected perpendicularly or at an angle to the electric field will be accelerated perpendicularly or at an angle to its direction of motion, resulting in a parabolic trajectory Section IV: Nuclear Physics Topic 10: Nuclear Physics The nucleus The existence and small size of the atomic nucleus as inferred from the results of the Rutherford α-particle scattering experiment: ○ Most of the α-particles travelled undeflected through the gold film – this shows that an atom consists of mostly empty space and the nucleus is very small compared to the atom ○ A very small number of α-particles were deflected more than 90° – this shows that the nucleus is positively charged and that a gold nucleus has a much larger mass than the α-particles to be able to repel them backwards Distinction between nucleon number (mass number) and proton number (atomic number): ○ Nucleon number (mass number) is the total number of nucleons in the nucleus ○ Proton number (atomic number) is the number of protons in the nucleus Isotopes An element can exist in various isotopic forms each with a different number of neutrons in the nucleus. Nuclear processes Usual notation for the representation of nuclides and representation of simple nuclear reactions: ○ Nuclides may be represented by AZX where A is the nucleon number (mass number) of the element, Z is the proton number (atomic number) of the element and X is the chemical symbol of the element ○ Simple nuclear reactions may be represented by nuclear equations of the form 147N + 42He → 178O + 11H where the left hand side shows the reactant nuclides and the right hand side shows the product nuclides Nucleon number, charge and mass-energy are all conserved in nuclear processes – this concept can be applied to solve problems involving nuclear reactions. 15 Mass defect and nuclear binding energy Concept of mass defect: ○ Mass defect is the difference between the total mass of the nucleons of the atom taken separately and the mass of the nucleus ○ It is due to the energy supplied to separate completely the individual nucleons of the nucleus The equivalence between energy and mass, as represented by E = mc2, where c is the speed of light in free space which has the value 3.00 × 108 m s−1, can be applied to solve problems involving mass defect and nuclear binding energy. Concept of nuclear binding energy and its relation to mass defect: ○ Nuclear binding energy is the energy required to separate the nucleons in the nucleus to infinity ○ It is also the energy released when a nucleus is formed from separated nucleons ○ Binding energy is directly proportional to mass defect and can be calculated using the equivalence between energy and mass Variation of binding energy per nucleon with nucleon number: Relevance of binding energy per nucleon to nuclear fusion and to nuclear fission: ○ For A < 56, if nuclei are fused together in a nuclear fusion reaction, the product nucleus will have a greater binding energy per nucleon, causing a loss of mass and a release of energy ○ For A > 56, if a nucleus is split into nuclei with lower nucleon number in a nuclear fission reaction, the product nuclei will each have a greater binding energy per nucleon, causing a loss of mass and a release of energy ○ Otherwise, an energy input is required for the nuclear reaction to take place so that energy is conserved ○ The net energy released in a nuclear fusion or nuclear fission process is equal to the difference between the total binding energies of the reactant and product nuclei, plus the input energy Radioactive decay The spontaneous and random nature of nuclear decay and the term activity: 16  ○ Nuclear decay is spontaneous – it is not affected by external factors such as temperature or pressure ○ Nuclear decay is random – each nucleus has a constant probability of decay per unit time ○ Activity is the rate at which radioactive nuclei decay The random nature of radioactive decay can be inferred from fluctuations in count rate. Origin and significance of background radiation: ○ Background radiation originates from a variety of sources emitting small quantities of radiation such as food and water, building materials, soil and outer space (in the form of cosmic rays) ○ Background radiation gives rise to a systematic error in the measurement of count rate which has to be eliminated by recording it first and then subtracting it from the count rate obtained in the experiment Nature of α, β and γ: ○ α-particles are helium nuclei, β-particles are electrons and γ-rays consist of high-energy photons ○ α-particles are heavy (4u) , β-particles are light (1/1840 u) and γ-ray photons have no rest mass ○ α-particles have a charge of +2e, β-particles have a charge of −e and γ-ray photons have no charge ○ α-particles produce the strongest ionisation, followed by β-particles and subsequently γ-ray photons ○ α-particles typically move the slowest (0.1c) followed by β-particles (up to 0.9c) and subsequently γ-ray photons (c) Half-life is defined as the time taken for a quantity x, where x could represent activity, number of undecayed particles or received count rate, to reduce to half its original value – this term may be used to solve problems involving half-life which might involve information in tables or decay curves which require the half-life to be determined by reading off the table or graph. Biological effects of radiation Effects of ionising radiation on living tissues and cells: ○ α- and β-particles are able to ionise atoms by removing electrons from the atom, while γ-rays are able to ionise atoms by means of the photoelectric effect ○ Direct effects include the interaction of radiation with atoms in the DNA molecule or any other critical component of the cell resulting in damage to these components and subsequently cell death or mutation ○ Cell mutation could lead to the rapid and uncontrolled production of defective cells resulting in cancer ○ Indirect effects include the interaction of radiation with water molecules in the cell which may lead to its radiolytic decomposition and the subsequent formation of toxic substances, contributing to the cell’s destruction ○ Radiation can also be used to treat cancer since rapidly growing cancer cells are especially susceptible to destruction by radiation 17