One handout per topic, in plain English. Read the handout before the textbook, not after it — each one takes about five minutes and is designed to make the idea land first, so the formal version has somewhere to stick.
25 handoutsCambridge AS & A LevelPrintableFree to copy and share
Every measurement is a number and a unit, and the unit is doing half the work.
Picture itIf a friend says “I'll be there in 20”, you immediately ask: twenty what? Minutes? Hours? Days? The number alone is useless. Physics is the same, except nobody comes to rescue you when you get it wrong.
Six units build everything
There are six basic measurements everything else is made from: the kilogram (mass), metre (length), second (time), ampere (current), kelvin (temperature) and mole (amount of stuff). Every other unit is these six multiplied and divided together. A newton is just kg·m/s². A joule is a newton times a metre. Nothing is magic — it is all built from the same six bricks.
This gives you a free way to check your work
If you rearrange an equation and end up with metres on one side and metres-per-second on the other, you have made a mistake. You do not need to know any physics to spot it — the units disagree, so the equation is wrong. Physicists use this constantly. It is the cheapest error-check that exists.
No measurement is exact
Measure your desk with a ruler and you get, say, 74.3 cm. Measure again and you might get 74.4 cm. Neither is “the” answer. Every measurement has a range it could really be, and that range is called the uncertainty. Real scientists always quote it: 74.3 ± 0.1 cm. Pretending a number is exact is the mark of someone who does not understand measurement.
Two ways to be wrong
Suppose your ruler is missing its first centimetre and you never noticed. Every single measurement is 1 cm too big — always in the same direction. That is a systematic error and repeating the measurement will never fix it. Now suppose your hand wobbles slightly each time. Some readings are a bit high, some a bit low. That is a random error, and averaging lots of readings does fix it. Knowing which one you have tells you whether repeating is worth the effort.
The bit that catches people outPeople mix up accurate and precise. Imagine three darts landing in a tight cluster — but in the wrong corner of the board. That is precise (they agree with each other) and inaccurate (they are nowhere near the target). A broken ruler gives beautifully precise, consistently wrong answers.
The grown-up words
What it means
What it is called
Note
How spread out repeats are
precision
Close together = precise. Says nothing about being right.
How close to the truth
accuracy
Close to the real value = accurate.
The range a value could really be
uncertainty
Always written with ±
Has size and direction
vector
Force, velocity, momentum
Has size only
scalar
Mass, energy, temperature, time
Check you have got it
A ruler marked in millimetres measures a pencil. Why is the uncertainty ±1 mm and not ±0.5 mm?
Because you judge two ends against the scale, and each end carries its own ±0.5 mm. They add.
Your equation gives an answer in kg·m/s². Have you calculated a force or an energy?
A force. kg·m/s² is the newton. Energy would need an extra metre on top.
Edvia Free Resources · Physics 9702 · Topic 1 — free to copy and share
Topic 2
Kinematics
Describing motion with four equations — and the discovery that sideways and downwards do not talk to each other.
Picture itDrop a coin off a table at the exact moment you flick another one sideways off the same table. They hit the floor at the same time. Every time. It feels wrong, and it is one of the most useful facts in physics.
Speed and velocity are not the same word
Speed is how fast. Velocity is how fast and which way. Drive round a roundabout at a steady 30 km/h and your speed never changes — but your velocity changes constantly, because your direction does. And since acceleration means “change of velocity”, you are accelerating the whole way round, even at constant speed. This trips up almost everyone the first time.
Four equations, one condition
There are four equations of motion and they are genuinely useful — but only when the acceleration is constant. If something is speeding up unevenly, they are simply wrong. Check that condition before you write anything down.
Graphs are equations you can see
On a displacement–time graph, the steepness tells you velocity. On a velocity–time graph, the steepness tells you acceleration and the area underneath tells you how far you went. That area trick saves enormous amounts of algebra, and examiners love asking for it.
Projectiles: two problems, not one
A ball thrown sideways is doing two independent things at once. Sideways: nothing pushes it, so it travels at a steady speed. Downwards: gravity pulls, so it accelerates exactly as if you had dropped it. The trick is to split the problem in two, solve each separately, and only combine at the end. The link between them is time — the same clock runs for both.
The bit that catches people outStudents find the time from the vertical motion, then forget to use it in the horizontal motion — or try to use the sideways speed in a gravity equation. Keep two columns on your page, one headed “across” and one “down”, and never let a number jump between them except time.
The grown-up words
What it means
What it is called
Note
How far and in which direction from the start
displacement
Not the same as distance travelled
How fast, with direction
velocity
Vector
Rate of change of velocity
acceleration
Changing direction counts
The curved path of a thrown object
projectile motion
Solve across and down separately
Speeding up unevenly
non-uniform acceleration
The four equations do NOT apply
Check you have got it
A ball is thrown horizontally off a cliff. Does its sideways speed change as it falls (ignore air resistance)?
No. Nothing pushes it sideways, so the horizontal velocity stays constant the whole way down.
A car drives round a circular track at a steady 20 m/s. Is it accelerating?
Yes. The direction of its velocity keeps changing, and that is an acceleration even though the speed is constant.
Edvia Free Resources · Physics 9702 · Topic 2 — free to copy and share
Topic 3
Dynamics
Forces do not make things move. They make things change how they are moving.
Picture itYou are on a bus that brakes hard and you lurch forward. Nothing pushed you forward. You were already moving, and you simply kept going while the bus slowed underneath you. That lurch is Newton's first law happening to your body.
Things keep doing what they are doing
Left alone, a moving object keeps moving in a straight line at a steady speed, and a stationary object stays put. This felt absurd for two thousand years because on Earth friction is always secretly slowing things down. Remove the friction — a puck on ice, a probe in space — and objects really do just keep going forever.
Force is about change, not motion
A car cruising at a constant 100 km/h has a huge engine force pushing it — and an equally huge drag force pushing back. The two cancel, the resultant force is zero, and it does not accelerate. Motion does not need force. Changing motion needs force.
Momentum: how hard something is to stop
Momentum is mass × velocity. A shopping trolley at walking pace and a bullet have wildly different masses and speeds, but momentum captures the thing that matters: how much effort it takes to stop them. The real version of Newton's second law is that force equals the rate at which momentum changes.
The total momentum never changes
When two things collide, add up all the momentum before and all the momentum after — you get the same number. Always. Energy might be lost to heat and noise, but momentum is never lost, only shuffled between objects. This one rule solves an enormous number of collision problems.
The bit that catches people outNewton's third law says forces come in pairs — but the two forces act on different objects. A book on a table: its weight and the table's push are not a third-law pair, because both act on the book. The real partner to the book's weight is the book pulling the Earth upwards. Yes, really — the book pulls the whole Earth.
The grown-up words
What it means
What it is called
Note
Force left over after all forces are added
resultant force
Zero resultant = no acceleration
Mass × velocity
momentum
Vector — direction and sign matter
Bounces with no energy lost
elastic collision
Kinetic energy conserved
Sticks together or deforms
inelastic collision
Momentum still conserved
The steady speed of a falling object
terminal velocity
Drag has grown to equal weight
Check you have got it
A skydiver reaches terminal velocity. What is the resultant force on them?
Zero. Drag has grown until it exactly balances weight, so there is no acceleration — but they are still falling fast.
Two trolleys collide and stick together. Is momentum conserved? Is kinetic energy?
Momentum: yes, always. Kinetic energy: no — some becomes heat and sound. That is what makes it inelastic.
Edvia Free Resources · Physics 9702 · Topic 3 — free to copy and share
Topic 4
Forces, density and pressure
Where a force acts matters as much as how big it is — and fluids push on everything they touch.
Picture itTry opening a heavy door by pushing right next to the hinge. It barely moves. Push at the far edge and it swings easily. Same force, completely different result, because turning effect depends on distance from the pivot.
Turning effect = force × distance
The moment of a force is the force multiplied by how far it acts from the pivot — measured perpendicular to the force. That is why spanners have long handles and why door handles are never next to the hinge. Double the distance and you halve the force you need.
Balanced means balanced twice over
For something to stay still, two separate things must be true. First, the forces must cancel, or it will fly off. Second, the turning effects must cancel, or it will spin. Both. A seesaw with equal weights at unequal distances has balanced forces but unbalanced moments, and down it goes.
Pressure: the same force, spread differently
Pressure is force divided by area. A drawing pin has a tiny point, so a gentle thumb-push becomes enormous pressure at the tip and it slides into the wood. Lie on a bed of nails and your weight spreads over hundreds of points, so the pressure at each is survivable. The force never changed — only the area.
Why things float
Push down into a bath and you feel water pushing back up. Pressure in a fluid increases with depth, so the bottom of a submerged object gets pushed up harder than the top gets pushed down. The leftover upward push is upthrust, and it equals the weight of the fluid the object shoved out of the way. If that beats the object's weight, it floats.
The bit that catches people outIn hydrostatic pressure, the depth means straight down, not the distance along a sloping tube. A tube that runs diagonally for 50 cm but only drops 30 cm vertically gives pressure for 30 cm. Water does not care how scenic the route was.
The grown-up words
What it means
What it is called
Note
Turning effect of a force
moment
Force × perpendicular distance
Two equal opposite forces that spin but do not push
couple
Produces torque, no resultant force
Not moving and not spinning
equilibrium
Forces AND moments both balance
Force per unit area
pressure
Pascals = N/m²
Upward push from a fluid
upthrust
Equals weight of fluid displaced
Check you have got it
Why is it easier to cut with a sharp knife than a blunt one?
The sharp edge has a much smaller area, so the same force produces far greater pressure on the material.
A block weighs 12 N and the upthrust on it in water is 19 N. What happens when you let go?
It accelerates upwards and floats — upthrust beats weight by 7 N.
Edvia Free Resources · Physics 9702 · Topic 4 — free to copy and share
Topic 5
Work, energy and power
Energy is the currency of physics. It gets swapped between forms but the total never changes.
Picture itThink of energy like money in a sealed room. It moves from your pocket to a friend's, gets changed from notes to coins, but nobody can print more and nobody can burn any. Physics has never once caught energy breaking this rule.
Work has a narrow meaning here
In physics, you only do work when a force moves something in the direction of the force. Hold a heavy bag perfectly still for an hour and you will be exhausted — but you have done zero work on the bag, because it has not moved. Your muscles burnt energy internally, which is a different thing. Physics is being fussy, but consistently so.
Two energies to know cold
Kinetic energy is energy of movement: ½mv². Notice the v is squared — double your speed and you get four times the kinetic energy, which is exactly why car crashes get so much worse so quickly. Gravitational potential energy is energy of height: mgh. Lift something up and you have stored energy in it; let go and it converts straight back.
Power is energy per second
Two cranes lift the same load to the same height. They do identical work. But if one takes 10 seconds and the other takes 60, the first has six times the power. Power says nothing about how much — only how fast.
Efficiency: what you wanted vs what you paid for
No machine converts all its input into what you actually want. A filament lamp turns about 5% of its electrical energy into light and the rest into heat. That is not a fault; some waste is unavoidable. Efficiency is simply useful output ÷ total input, and it can never exceed 1.
The bit that catches people outmgh only works near the ground. It quietly assumes gravity has the same strength throughout the height change, which is fine for a ladder and badly wrong for a satellite. When you get to gravitational fields you will meet a different equation for exactly this reason.
The grown-up words
What it means
What it is called
Note
Force × distance moved in the force's direction
work done
Perpendicular force does no work
Energy of movement
kinetic energy
½mv² — note the square
Energy of position in a field
potential energy
mgh near the Earth only
Rate of doing work
power
Watts = joules per second
Useful out ÷ total in
efficiency
Never more than 100%
Check you have got it
You carry a box across a flat room at a steady speed. How much work do you do on the box against gravity?
None. Gravity acts downwards, the box moves horizontally — the force and the motion are perpendicular.
A car doubles its speed. What happens to its kinetic energy and its braking distance?
Both go up by a factor of four, because KE depends on v².
Edvia Free Resources · Physics 9702 · Topic 5 — free to copy and share
Topic 6
Deformation of solids
Every solid is a bit springy — and each material has its own fixed stiffness that no amount of reshaping can change.
Picture itPull a rubber band and it stretches easily. Pull a steel wire the same thickness and almost nothing happens. That difference is not about the shape. It is baked into what the material is.
Springs share the load fairly
For small stretches, doubling the force doubles the extension. That is Hooke's law, and it holds up to a limit. Push past that limit and the neat proportional relationship breaks down.
Stretch it too far and it never comes back
Below the elastic limit, let go and the object returns to its original length. Beyond it, the object is permanently longer — plastic deformation. You have felt this: bend a paperclip a little and it springs back; bend it hard and it stays bent.
Fair comparison needs stress and strain
A thick wire holds more load than a thin one, and a long wire stretches more than a short one — but that tells you about the wires, not the metal. So we divide out the shape. Stress is force per unit area. Strain is extension as a fraction of the original length. Now we are comparing materials, not specimens.
The Young modulus is the material's fingerprint
Divide stress by strain and you get the Young modulus — a single number for how stiff a material is. Steel has the same Young modulus whether it is a wire, a beam or a bridge. Change the shape all you like; the number does not move.
The bit that catches people outWhen you find the Young modulus in the lab, the thing wrecking your result is almost always the diameter. It is tiny, you measure it with a micrometer, and then you square it to get the area — which doubles its percentage uncertainty. Measure the diameter in several places and at several angles. The length is metres long and barely matters.
The grown-up words
What it means
What it is called
Note
Force per unit area
stress
Pascals, same unit as pressure
Extension ÷ original length
strain
Just a number, no units
Stress ÷ strain
Young modulus
Property of the material
Springs back when released
elastic
Below the elastic limit
Stays deformed
plastic
Beyond the elastic limit
Check you have got it
Two wires of the same steel: one thick, one thin. Do they have the same Young modulus?
Yes — identical. Young modulus depends on the material, not the dimensions. The thick one is stronger, not stiffer per unit area.
How do you get the energy stored in a stretched wire from a force–extension graph?
Find the area underneath the line. For a straight line that is just the triangle, ½ × force × extension.
Edvia Free Resources · Physics 9702 · Topic 6 — free to copy and share
Topic 7
Waves
A wave moves energy from one place to another without moving any material along with it.
Picture itWatch a duck on a rippling pond. The ripples travel right across the water, but the duck just bobs up and down in the same spot. The wave went somewhere. The water did not.
Two flavours of wave
In a transverse wave the wobbling happens at right angles to the direction of travel — like flicking a rope, or every kind of light. In a longitudinal wave the wobbling is along the direction of travel, squashing and stretching as it goes — that is sound. Sound is a pressure wave in air, which is why it needs air, and why space really is silent.
The one equation that runs everything
Speed = frequency × wavelength. Frequency is how many waves pass per second; wavelength is how long each one is. Multiply them and you get how far the wave travels per second.
Intensity falls off fast
Double your distance from a lamp and it does not get half as bright — it gets a quarter as bright. The energy spreads over a sphere, and doubling the radius quadruples the sphere's area. Intensity also depends on amplitude squared, so doubling the wave's height gives four times the energy.
Moving sources change the pitch
When an ambulance races towards you, each successive sound wave is emitted from slightly closer, so the waves bunch up, the wavelength shortens and the pitch rises. As it passes, they stretch out and the pitch drops. You have heard this a thousand times; it is called the Doppler effect, and astronomers use the same effect on starlight to work out how fast galaxies are running away from us.
The bit that catches people outOnly transverse waves can be polarised — filtered so they wobble in one plane only. This is not a small technical detail: it is the actual proof that light is transverse and sound is not. Sunglasses work because of it.
The grown-up words
What it means
What it is called
Note
Wobbling across the direction of travel
transverse
All light; waves on a string
Wobbling along the direction of travel
longitudinal
Sound
Waves per second
frequency
Hertz
Length of one whole wave
wavelength
Metres
Power per unit area
intensity
Proportional to amplitude²
Pitch change from a moving source
Doppler effect
Approaching = higher pitch
Check you have got it
Why can sound travel through a wall but light cannot?
Sound is a vibration of the material itself, so it passes through solids. Light is an electromagnetic wave that the opaque material absorbs.
A wave's amplitude is tripled. What happens to its intensity?
It becomes nine times larger, because intensity is proportional to amplitude squared.
Edvia Free Resources · Physics 9702 · Topic 7 — free to copy and share
Topic 8
Superposition
When two waves meet, they simply add up — and that produces effects that look like magic.
Picture itTwo people drop stones into a still pond. Where the ripples cross, some places churn violently and others go oddly flat. Nothing was destroyed. The waves just added, and in the flat places one wave's peak landed exactly on the other's trough.
Adding waves gives loud and silent spots
Peak meets peak: you get a bigger peak — constructive interference. Peak meets trough: they cancel — destructive interference. With light this produces bright and dark stripes. With sound you can genuinely find quiet spots in a room by walking around between two speakers playing the same tone.
It only works if the sources are in step
For a stable pattern you need coherent sources: the same frequency and a constant phase relationship. Two ordinary lamps will not do it — their light flickers randomly out of step billions of times a second, so the pattern smears into uniform brightness. That is why Young's famous experiment sends light from a single source through two slits.
Stationary waves: the wave that goes nowhere
Send a wave down a string and let it reflect off the end. The outgoing and returning waves superpose and produce a pattern that does not travel at all. Some points never move (nodes) and some swing wildly (antinodes). Every guitar string, organ pipe and wind instrument works on this.
Waves bend round corners
Waves spread out when they squeeze through a gap — diffraction — and they spread most when the gap is about the same size as the wavelength. Sound has wavelengths of roughly a metre, so it diffracts easily through a doorway and you hear round corners. Light's wavelength is under a millionth of a metre, so it barely spreads at all and you cannot see round them.
The bit that catches people outFor a diffraction grating, students learn the equation and then forget to convert. “600 lines per millimetre” means 600 000 lines per metre, so the spacing is 1/600000 m. Getting this wrong makes your answer a thousand times off, and it happens every single exam session.
The grown-up words
What it means
What it is called
Note
Waves adding together
superposition
Just addition, nothing exotic
Same frequency, constant phase link
coherent
Required for a stable pattern
A point that never moves
node
Adjacent nodes are half a wavelength apart
A point of maximum swing
antinode
Halfway between nodes
Spreading through a gap
diffraction
Greatest when gap ≈ wavelength
Extra distance one wave travels
path difference
Whole wavelengths = bright
Check you have got it
Why do you use a single light source and two slits, rather than two separate lamps?
Two lamps are not coherent — their phase relationship changes randomly, so no stable interference pattern forms.
You are 2 m from two speakers playing the same note and you find a quiet spot. What is happening?
Destructive interference: the path difference is half a wavelength (or an odd multiple), so a peak from one arrives with a trough from the other.
Edvia Free Resources · Physics 9702 · Topic 8 — free to copy and share
Topic 9
Electricity
Current is charge flowing. Voltage is the energy each bit of charge carries. Resistance is how hard the journey is.
Picture itThink of a water park. Current is how many people go down the slide per second. Voltage is how high the slide starts — how much energy each person has to spend. Resistance is how narrow and twisty the slide is. The analogy is not perfect, but it gets you a long way.
Current is a rate
Current is the amount of charge passing a point each second. Charge comes in fixed lumps: every electron carries the same tiny charge, 1.6 × 10⁻¹⁹ coulombs. You cannot have half an electron's worth.
Voltage is energy per unit charge
A potential difference of 1 volt means each coulomb of charge gives up 1 joule of energy as it passes through. So voltage is not a force and it is not a flow — it is energy per charge. E.m.f. is the same idea in reverse: energy the battery gives each coulomb.
Electrons crawl; the signal sprints
Here is something genuinely surprising. Work out how fast electrons actually drift along a wire and you get roughly 0.1 mm per second — slower than a snail. Yet the light comes on instantly when you flip the switch. The resolution: the electric field spreads through the whole circuit at nearly the speed of light, so every electron everywhere starts shuffling at once. The bulb does not wait for electrons to travel from the switch.
Resistance vs resistivity
Resistance depends on the object: a long thin wire has more than a short fat one. Resistivity divides out the shape, so it describes the material itself. Copper's resistivity is the same in a cable or a coin.
The bit that catches people outStretching a wire to double its length does not double its resistance — it quadruples it. The metal cannot appear from nowhere, so as the wire gets twice as long it also gets half as thick. Longer ×2 and thinner ×2 multiply together.
The grown-up words
What it means
What it is called
Note
Rate of flow of charge
current
Amperes = coulombs per second
Energy given up per unit charge
potential difference
Volts = joules per coulomb
Energy supplied per unit charge
e.m.f.
What the battery provides
Opposition to current
resistance
Ohms = volts per amp
Material's own opposition
resistivity
Independent of shape
Average speed of charge carriers
drift velocity
Astonishingly slow
Check you have got it
A lamp is 3 m from the switch. Why does it light instantly if electrons drift at 0.1 mm/s?
The electric field propagates almost at light speed, so electrons everywhere in the circuit — including inside the lamp — start moving essentially at once.
Does a filament lamp obey Ohm's law?
No. As it heats up, its resistance rises, so the I–V graph curves instead of staying straight. Ohm's law needs constant temperature.
Edvia Free Resources · Physics 9702 · Topic 9 — free to copy and share
Topic 10
D.C. circuits
Two conservation rules — charge and energy — solve every circuit you will ever be asked about.
Picture itA busy junction: however many cars drive in per minute, exactly that many drive out. Nobody vanishes. That is the first circuit rule, and it is really just “charge cannot be created or destroyed” wearing a hat.
What goes in comes out
At any junction, the current arriving equals the current leaving. Charge does not pile up or disappear. This is Kirchhoff's first law and it is pure common sense once you see it.
Round any loop, energy balances
Follow any complete loop around a circuit and the energy supplied by the sources equals the energy used by the components. Kirchhoff's second law. Together these two rules let you solve circuits far more complicated than anything an exam will show you.
Batteries are not perfect
A real battery has its own internal resistance, so some energy is wasted heating the battery itself before anything reaches your circuit. That is why the voltage at the terminals sags when you draw a big current, and why a dying battery still reads a decent voltage until you actually load it.
Potential dividers give you any voltage you want
Two resistors in series split the supply voltage in proportion to their resistances. Swap one for a thermistor (resistance drops when hot) or an LDR (resistance drops in light) and the output voltage now responds to temperature or brightness. That is the heart of most simple sensor circuits.
The bit that catches people outParallel resistors: students calculate 1/R and then write that down as the answer. You must flip it at the end. A useful sanity check — the combined resistance of parallel resistors is always smaller than the smallest one. If your answer is bigger, you forgot to invert.
The grown-up words
What it means
What it is called
Note
Current in = current out at a junction
Kirchhoff's first law
Conservation of charge
E.m.f.s = p.d.s round a loop
Kirchhoff's second law
Conservation of energy
Resistance inside the battery
internal resistance
Causes 'lost volts'
Voltage actually delivered
terminal p.d.
E.m.f. minus lost volts
Two resistors splitting a voltage
potential divider
Basis of sensor circuits
Check you have got it
Two resistors, 6 Ω and 3 Ω, in parallel. What is the combined resistance?
1/R = 1/6 + 1/3 = 1/2, so R = 2 Ω. Note it is smaller than 3 Ω, as it must be.
Why does a car's headlights dim when you start the engine?
The starter motor draws a huge current, so the lost volts across the battery's internal resistance become large and the terminal p.d. drops.
Edvia Free Resources · Physics 9702 · Topic 10 — free to copy and share
Topic 11
Particle physics
Everything you have ever touched is built from a handful of particles — and two of them are not fundamental at all.
Picture itFor a long time 'atom' meant 'uncuttable'. Then we cut it. Inside were protons, neutrons and electrons. Then we cut the protons too. What we have not managed to cut are quarks and electrons — so far.
The experiment that found the nucleus
Fire alpha particles at gold foil so thin it is nearly transparent. Almost all of them sail through as if nothing is there. A few deflect. A very few bounce almost straight back — which, as Rutherford said, was about as surprising as a shell bouncing off tissue paper. The only explanation: the atom is mostly empty space with a tiny, dense, positively charged nucleus.
Three kinds of radiation
Alpha is a helium nucleus — heavy, strongly ionising, stopped by paper. Beta is a fast electron — stopped by a few millimetres of aluminium. Gamma is a high-energy photon with no mass or charge — you can reduce it with thick lead but never quite stop it. The more strongly something ionises, the faster it runs out of energy and the less it penetrates.
The missing energy that predicted a new particle
Beta particles came out with a range of energies rather than one fixed value, which looked like energy was disappearing. Rather than abandon conservation of energy, physicists proposed an invisible particle carrying the rest away. Decades later the neutrino was found, exactly as predicted. That is the scientific method working at its best.
Protons and neutrons are made of quarks
A proton is two up quarks and a down quark; a neutron is one up and two downs. Quarks have odd fractional charges — up is +⅔ and down is −⅓ — which sounds bizarre until you add them up and get exactly +1 for a proton and exactly 0 for a neutron. Electrons and neutrinos are leptons and appear to be genuinely fundamental.
The bit that catches people outIn beta-minus decay, the electron that shoots out does not come from the electron shells. It is created at the moment a neutron turns into a proton inside the nucleus. Nothing was orbiting and got knocked loose.
The grown-up words
What it means
What it is called
Note
Helium nucleus
alpha particle
Stopped by paper
Fast electron from the nucleus
beta particle
Stopped by aluminium
High-energy electromagnetic photon
gamma ray
Reduced by lead, never fully stopped
Three quarks
baryon
Proton, neutron
Quark + antiquark
meson
Fundamental, no quarks inside
lepton
Electron, neutrino
Check you have got it
Add up the quark charges in a neutron (up, down, down).
+⅔ − ⅓ − ⅓ = 0. Exactly neutral, as required.
Why is gamma radiation the least ionising but the most penetrating?
It interacts weakly with matter, so it loses energy slowly — which means it ionises little but travels far.
Edvia Free Resources · Physics 9702 · Topic 11 — free to copy and share
Topic 12
Motion in a circle
To go round in a circle you must be pulled towards the centre, constantly, forever.
Picture itWhirl a ball on a string round your head. You can feel the string pulling the ball inwards. Let go and the ball does not fly outwards — it flies off in a straight line, along the tangent. There was never an outward force. There was only ever an inward one, and the moment it stops, so does the circle.
Constant speed is not constant velocity
Going round at a steady speed, your direction changes every instant, so your velocity changes every instant, so you are accelerating. And accelerating requires a resultant force. This is why circular motion needs constant pulling even when nothing speeds up.
Radians make the maths behave
Instead of degrees we use radians: one radian is the angle where the arc length equals the radius. A full circle is 2π radians. It looks like an inconvenience and turns out to make every circular-motion and oscillation equation dramatically simpler.
The centre-seeking force is never a new force
'Centripetal force' is not an extra force you draw on the diagram. It is the name for whatever real force happens to be pointing at the centre. For a whirled ball it is tension. For a car on a bend it is friction. For the Moon it is gravity. Always identify which real force is doing the job.
Why the pull has to grow with speed
The required force is mv²/r. Go twice as fast round the same bend and you need four times the friction. That is why speed limits tighten on sharp corners, and why a car that takes a bend too fast slides straight on — the road simply cannot supply enough friction.
The bit that catches people outThere is no such thing as centrifugal force in your answers. That outward feeling in a spinning car is your body trying to go straight while the car curves underneath you. Draw only real forces, and set their resultant equal to mv²/r.
The grown-up words
What it means
What it is called
Note
Angle where arc = radius
radian
2π radians in a full circle
Angle turned per second
angular velocity
ω, in rad/s
Acceleration towards the centre
centripetal acceleration
v²/r or rω²
The resultant force pointing inwards
centripetal force
A job, not a new force
Straight-line path if released
tangential
Where the object actually goes
Check you have got it
A conker on a string is whirled in a vertical circle. Where is the string tension greatest?
At the bottom. There, tension must both support the weight and provide the centripetal force, so they add.
A car takes a bend twice as fast. How much more friction is needed?
Four times as much, because the required force depends on v².
Edvia Free Resources · Physics 9702 · Topic 12 — free to copy and share
Topic 13
Gravitational fields
Every mass pulls every other mass, everywhere, forever — and the pull weakens with the square of the distance.
Picture itThe Moon is falling. It has been falling towards Earth for four and a half billion years. It never lands because it is also moving sideways fast enough that the Earth's surface curves away beneath it just as quickly. An orbit is just falling and missing.
Everything attracts everything
Newton's law of gravitation says any two masses attract with a force proportional to both masses and inversely proportional to the square of their separation. You and this page attract each other right now. The force is roughly a billionth of a newton, which is why you have not noticed.
Inverse square: distance punishes you fast
Go twice as far from a planet's centre and gravity is not half — it is a quarter. Three times as far, a ninth. This is because the pull spreads over the surface of a sphere, and sphere area grows as radius squared.
The mass in orbit cancels out
Set gravity equal to the centripetal force and the orbiting object's mass appears on both sides and cancels. The consequence is remarkable: at a given orbital radius, a paperclip and a space station orbit at exactly the same speed with exactly the same period. This is also why astronauts float — they are not beyond gravity, they are in free fall along with their spacecraft.
Why potential is negative
We define potential energy as zero at infinite distance. As a mass falls inwards, gravity does work on it, so its potential energy drops below zero. Hence the minus sign in every gravitational potential equation. It is not a mistake and it is not arbitrary — it follows directly from choosing infinity as the zero.
The bit that catches people outThe r in these equations is measured from the centre of the planet, not the surface. A satellite '400 km up' is at r = 6 400 km + 400 km = 6 800 km from the centre. Forgetting to add the planetary radius is the single most common error in this topic.
The grown-up words
What it means
What it is called
Note
Force per unit mass
gravitational field strength
g, in N/kg
Work done per unit mass from infinity
gravitational potential
Always negative
Orbit with a 24-hour period over the equator
geostationary
Radius ≈ 42 000 km
Speed needed to escape completely
escape velocity
≈ 11 km/s from Earth
Falling freely with your surroundings
weightlessness
Not the absence of gravity
Check you have got it
Astronauts on the space station appear weightless. Has gravity switched off?
No — gravity there is about 90% of its surface value. They are in continuous free fall together with the station, so nothing pushes up on them.
Why does escape velocity not depend on the mass of the escaping object?
The object's mass appears in both its kinetic energy and its potential energy, so it cancels out of the equation.
Edvia Free Resources · Physics 9702 · Topic 13 — free to copy and share
Topic 14
Temperature
Temperature is not how much energy something has. It is how energetic its particles are on average.
Picture itA sparkler burns at over a thousand degrees and you can hold it safely. A bath at forty degrees would scald you if you sat in it too long. The bath is far cooler and contains vastly more energy. Temperature and energy are different questions.
Temperature decides which way energy flows
Put two objects in contact and energy always flows from the hotter to the cooler — regardless of how much total energy each contains. When the flow stops, they are at the same temperature and in thermal equilibrium. That is really what a thermometer measures: it comes into equilibrium with the thing and reports its own state.
Absolute zero is a real floor
Cool something down and its particles slow. Keep cooling and you eventually reach −273.15 °C, where the particles have the minimum energy possible. You cannot go lower, because there is no less than minimum. That is why the kelvin scale starts there, and why every gas and thermodynamics equation demands kelvin.
Heating and temperature rise are linked by a material property
Some substances need a lot of energy to warm up and some very little. Specific heat capacity is the energy needed to raise one kilogram by one kelvin. Water's is unusually high, which is why the sea takes all summer to warm up and all winter to cool down, and why coastal places have milder weather.
Changing state costs energy but no temperature
Heat ice at 0 °C and the temperature stubbornly refuses to rise until every last bit has melted. The energy is going into breaking the bonds holding the solid together, not into speeding the particles up. That is latent heat, and it is why ice keeps a drink cold so effectively.
The bit that catches people outEvery gas-law and thermodynamics calculation needs kelvin. Using Celsius does not just shift the answer slightly — ratios go completely wrong. Doubling 20 °C to 40 °C is not doubling the temperature; in kelvin that is 293 K to 313 K, a rise of under 7%.
The grown-up words
What it means
What it is called
Note
Same temperature, no net energy flow
thermal equilibrium
What a thermometer relies on
Scale starting at absolute zero
thermodynamic (kelvin) scale
T/K = θ/°C + 273.15
Energy to raise 1 kg by 1 K
specific heat capacity
Water's is very high
Energy to change state, no temperature change
specific latent heat
Breaks bonds instead
Lowest possible temperature
absolute zero
0 K = −273.15 °C
Check you have got it
Why does a bag of frozen peas keep a picnic cooler than the same mass of water at 0 °C?
The peas must absorb latent heat to melt before they can warm at all, so they soak up far more energy at the same temperature.
Convert 27 °C to kelvin.
27 + 273 = 300 K.
Edvia Free Resources · Physics 9702 · Topic 14 — free to copy and share
Topic 15
Ideal gases
Gas pressure is billions of tiny collisions per second, and temperature is just how fast those particles are moving.
Picture itBlow up a balloon and it holds its shape. Nothing solid is holding it out — it is air molecules hammering the inside surface constantly, billions of times a second, each one a tiny push. Add them all up and you get steady pressure.
One equation ties everything together
pV = nRT connects pressure, volume, amount of gas and temperature. Squash a gas (V down) and pressure rises. Heat it (T up) and pressure rises. It is one relationship covering every gas question you will meet.
The model behind it is deliberately simple
We pretend the molecules are points with no size, that they never attract each other, and that all collisions are perfectly bouncy. Real molecules do have size and do attract — but at everyday pressures and temperatures they are so far apart that the simple model works beautifully. It fails when you squeeze a gas hard or cool it near liquefying, which is exactly when the molecules are close enough to notice each other.
Temperature is molecular kinetic energy
The single most important result here: the average kinetic energy of a gas molecule is directly proportional to the absolute temperature. Temperature is not a separate thing that happens to gases. It is the energy of their motion, measured in different units.
Molecules are much faster than you would guess
Nitrogen molecules in this room are averaging roughly 500 metres per second — faster than a rifle bullet. They do not get anywhere fast because they collide constantly and ricochet, which is also why smells take seconds rather than microseconds to cross a room.
The bit that catches people outThe kinetic theory equation uses ⟨c²⟩ — the mean of the squares of the speeds. Take the square root right at the end to get the root-mean-square speed. Squaring first and rooting last is not the same as averaging the speeds, and the difference is examined.
The grown-up words
What it means
What it is called
Note
Point particles, no forces, elastic collisions
ideal gas
Model, not reality
pV = nRT
equation of state
Temperature must be in kelvin
6.02 × 10²³ particles
one mole
Avogadro constant
Square root of the mean squared speed
r.m.s. speed
Not the average speed
Deviates at high p, low T
real gas
Molecules are close enough to interact
Check you have got it
Why do real gases behave least like ideal gases at high pressure and low temperature?
The molecules are close together, so their own volume and their mutual attractions stop being negligible.
A sealed container of gas is heated. Its volume cannot change. What happens to the pressure and why?
Pressure rises. The molecules move faster, so they hit the walls harder and more often.
Edvia Free Resources · Physics 9702 · Topic 15 — free to copy and share
Topic 16
Thermodynamics
You can heat a gas or you can squash it. Both put energy in, and the first law keeps the books.
Picture itPump up a bicycle tyre and feel the pump barrel get hot. You did not heat it with a flame. You did work on the air by compressing it, and that work turned into internal energy. Energy accounting, live in your hands.
Internal energy is the total of everything inside
It is the sum of the kinetic energies of all the particles plus the potential energies of their interactions. For an ideal gas we assume no intermolecular forces at all, so there is no potential part — its internal energy is purely kinetic and therefore depends only on temperature.
Two ways to change it
Heating the system, or doing work on it. That is the whole of the first law: ΔU = q + W. The increase in internal energy equals the energy you added by heating plus the work you did on it. It is conservation of energy written for gases.
Signs are the whole battle
Compress a gas and you do work on it, so W is positive. Let it expand and it does work on the surroundings, so W is negative. Get the sign wrong and your answer is wrong by twice the work done. Decide which way the energy is going before you write a single number.
Two special cases worth knowing
Isothermal: temperature constant, so for an ideal gas ΔU = 0 and any heating is exactly matched by work done. Adiabatic: no heating at all, so ΔU = W — which is why compressing a gas quickly heats it and why a spray can goes cold as it empties.
The bit that catches people out'ΔU = 0' does not mean nothing is happening. In an isothermal expansion the gas is absorbing energy and doing work at the same rate — plenty is happening, it just balances.
The grown-up words
What it means
What it is called
Note
Total energy of all particles inside
internal energy
Kinetic + potential
Increase in U = heating + work done on
first law of thermodynamics
ΔU = q + W
Temperature constant
isothermal
ΔU = 0 for an ideal gas
No energy transferred by heating
adiabatic
q = 0, so ΔU = W
Work when volume changes at constant p
pΔV
Sign depends on direction
Check you have got it
A gas expands and pushes a piston out. Is W positive or negative in ΔU = q + W?
Negative. The gas does work on the surroundings, so energy leaves it.
Why does a can of deodorant feel cold after a long spray?
The gas expands rapidly with almost no time to absorb heat — an adiabatic expansion — so it does work at the expense of its own internal energy and cools.
Edvia Free Resources · Physics 9702 · Topic 16 — free to copy and share
Topic 17
Oscillations
Anything pulled back towards a resting point, harder the further it strays, will wobble in the same universal way.
Picture itA swing, a guitar string, a mass on a spring, the balance wheel in a watch, atoms in a crystal. Wildly different objects, one identical piece of maths. That is not a coincidence — it comes from the same simple condition being met in every case.
The condition that creates the pattern
If the pull back towards the middle is proportional to how far you have strayed, you get simple harmonic motion. Pull it twice as far and the restoring force doubles. That single relationship produces the smooth sine-wave motion you see everywhere in nature.
Where the speed and the force live
At the extremes, the object is momentarily stationary but the restoring force is at its maximum — so acceleration is greatest exactly where speed is zero. At the centre it is flying fastest but there is no force at all. Speed and acceleration are completely out of step, and understanding that resolves most confusion in this topic.
Energy sloshes back and forth
At the extremes everything is potential energy. At the centre everything is kinetic. In between it is a mix, and the total stays constant if nothing is damping it. Because both energies depend on displacement squared, they cycle at twice the frequency of the motion itself.
Damping and resonance
Real oscillators lose energy to friction and air — damping — and gradually die away. But push an oscillator at exactly its own natural frequency and the energy you add accumulates instead of fighting itself. The amplitude grows dramatically. That is resonance: how you tune a radio, how a microwave heats food, and how a wine glass shatters at the right note.
The bit that catches people outMore damping does not just make the resonance peak lower. It also makes it broader and shifts it to a slightly lower frequency. Examiners want all three effects, and most students remember only the first.
The grown-up words
What it means
What it is called
Note
Restoring force proportional to displacement
simple harmonic motion
The defining condition
Furthest distance from the middle
amplitude
Energy depends on amplitude²
Time for one complete cycle
period
T = 1/f
Energy lost to friction
damping
Light, critical or heavy
Driving at the natural frequency
resonance
Maximum amplitude, maximum energy transfer
Returns to rest fastest without wobbling
critical damping
Used in car suspension and door closers
Check you have got it
Where in the swing of a pendulum is the acceleration greatest?
At the extreme ends, where the displacement is largest — even though the bob is momentarily stationary there.
Soldiers break step when crossing a bridge. Why?
To avoid driving the bridge at its natural frequency and causing resonance, which could build a dangerously large amplitude.
Edvia Free Resources · Physics 9702 · Topic 17 — free to copy and share
Topic 18
Electric fields
Charges push and pull each other across empty space, following almost exactly the same maths as gravity.
Picture itRub a balloon on your hair and stick it to a wall. There is nothing between the balloon and the wall, yet a force holds it there. That invisible region of influence around a charge is what we call a field.
Field strength is force per unit charge
A field tells you what force a charge would feel at any point. Divide the force by the charge and you get a property of the field itself, independent of whatever test charge you used to measure it.
Almost gravity, but with a twist
Coulomb's law for charges looks nearly identical to Newton's law for masses — both inverse square, both proportional to the product of the two quantities. Two differences matter. Electric forces can repel as well as attract, and they are vastly stronger. The electrical repulsion between two protons is about 10³⁶ times their gravitational attraction.
Between parallel plates the field is uniform
Two flat charged plates produce a field of the same strength everywhere between them, given by voltage divided by separation. A charged particle fired sideways into that region traces a perfect parabola — mathematically identical to a thrown ball, with the electric force playing the role of gravity.
Potential runs as 1/r, field runs as 1/r²
This catches people out constantly. The field weakens as the inverse square of distance; the potential weakens only as the inverse of distance. The reason is that field is the gradient of potential, and differentiating 1/r gives you 1/r². Learn them as a pair.
The bit that catches people outFor confidentiality of sign: gravitational potential is always negative because gravity only attracts. Electric potential can be positive or negative, because charges come in two kinds. Do not carry the gravity habit across.
The grown-up words
What it means
What it is called
Note
Force per unit positive charge
electric field strength
N/C or V/m
Inverse square law for charges
Coulomb's law
Can repel as well as attract
Same strength everywhere
uniform field
Between parallel plates
Work per unit charge from infinity
electric potential
Can be + or −
Crossed fields selecting one speed
velocity selector
v = E/B
Check you have got it
An electron is fired horizontally between two charged plates. What shape is its path?
A parabola — constant sideways speed, constant vertical acceleration. Exactly like a projectile.
Why is gravity irrelevant when calculating the path of an electron between charged plates?
The electric force on it is many orders of magnitude larger than its weight.
Edvia Free Resources · Physics 9702 · Topic 18 — free to copy and share
Topic 19
Capacitance
A capacitor is a bucket for charge — and it fills and empties on a predictable exponential curve.
Picture itA camera flash needs a huge burst of energy in a thousandth of a second. A small battery cannot deliver that. So the battery slowly fills a capacitor over a few seconds, and the capacitor dumps the lot instantly. Slow in, fast out.
Capacitance is charge per volt
Push charge onto a capacitor and the voltage across it climbs. Capacitance measures how much charge it takes to raise the voltage by one volt. Big capacitance means it holds a lot of charge without the voltage rising much.
Stored charge means stored energy
The energy is ½QV, and that ½ has a real reason behind it. The first charges arrive when the capacitor is empty and the voltage is zero, so they cost nothing to push on. The last arrive against the full voltage. Average out the whole process and you get half. It is the area under a charge–voltage graph — a triangle.
The rules are backwards from resistors
Capacitors in parallel simply add. Capacitors in series combine as reciprocals. That is the opposite way round from resistors, and it is worth pausing on: in parallel you are effectively making the plates bigger, so capacitance grows.
Discharge is exponential
Connect a charged capacitor across a resistor and the voltage does not fall steadily — it drops fast at first, then ever more slowly, approaching zero without quite reaching it. After one time constant (R × C seconds) it has fallen to about 37% of where it started. Every time constant, another 63% of what remains disappears.
The bit that catches people outTo find RC from an experiment, do not try to read a curve. Plot ln V against t and you get a straight line with gradient −1/RC. Turning a curve into a straight line by taking logarithms is one of the most useful moves in all of practical physics.
The grown-up words
What it means
What it is called
Note
Charge stored per volt
capacitance
Farads = coulombs per volt
½QV or ½CV²
energy stored
Area under a Q–V graph
R × C, in seconds
time constant
Falls to 37% after one
Add directly
capacitors in parallel
Opposite rule to resistors
Falls by a constant fraction each interval
exponential decay
Straightened by a log graph
Check you have got it
A 100 µF capacitor discharges through a 10 kΩ resistor. What is the time constant?
RC = 10 000 × 100 × 10⁻⁶ = 1.0 second.
Why is the energy stored ½QV and not QV?
The voltage rises from zero as it charges, so the average voltage the charge is pushed through is half the final value.
Edvia Free Resources · Physics 9702 · Topic 19 — free to copy and share
Topic 20
Magnetic fields
Moving charges make magnetic fields, and magnetic fields push moving charges sideways.
Picture itHold a wire near a compass and switch on a current. The needle swings. Nobody touched it, there is no magnet — the moving charge itself created a magnetic field. Every electric motor in the world is a consequence of that one observation.
The force is sideways to everything
A current-carrying wire in a magnetic field feels a force that is perpendicular to both the current and the field. Not along either of them — at right angles to both. Fleming's left-hand rule gets you the direction: First finger Field, seCond finger Current, thuMb Motion.
Magnetic forces never do work
Because the force is always perpendicular to the velocity, it can change a charged particle's direction but never its speed. That is why a charged particle entering a magnetic field travels in a perfect circle rather than speeding up or slowing down. This fact runs particle accelerators and mass spectrometers.
Changing flux creates voltage
Move a magnet through a coil and a voltage appears. Hold it still and nothing happens, no matter how strong the magnet. It is change that matters — specifically the rate of change of magnetic flux linkage. That is Faraday's law, and it is where essentially all the world's electricity comes from.
Nature always opposes the change
The induced current always flows in whichever direction opposes what caused it. Push a magnet into a coil and the coil pushes back. This is Lenz's law, and it is not arbitrary — if the induced current helped instead of opposed, you would get free energy forever. Conservation of energy demands it.
The bit that catches people out'Flux' and 'flux linkage' are not the same. Flux is B × A for one loop. Flux linkage is that multiplied by the number of turns, N. A 500-turn coil has 500 times the flux linkage of a single loop in the same field, which is exactly why generators have many turns.
The grown-up words
What it means
What it is called
Note
Force per unit current per unit length
magnetic flux density
B, in tesla
B × area
magnetic flux
Webers
Flux × number of turns
flux linkage
What actually matters for induction
E.m.f. ∝ rate of change of flux linkage
Faraday's law
Change is essential
Induced effects oppose their cause
Lenz's law
Conservation of energy
Voltage across a current-carrying slab in a field
Hall voltage
Measures B
Check you have got it
You hold a strong magnet perfectly still inside a coil. What voltage is induced?
Zero. There is flux but no change of flux, and only change induces an e.m.f.
Why does a magnet dropped down a copper pipe fall unusually slowly?
Its motion induces currents in the pipe, and by Lenz's law those currents oppose the motion that created them.
Edvia Free Resources · Physics 9702 · Topic 20 — free to copy and share
Topic 21
Alternating currents
Mains electricity reverses direction a hundred times a second, so 'how many volts' needs a careful answer.
Picture itYour socket is labelled 230 V, but the voltage there is changing constantly — it is zero twice every cycle and peaks at about 325 V. So what does 230 mean? It is a fair average, defined by the heating it produces.
Why the ordinary average is useless
An alternating current spends as much time negative as positive, so its plain average over a cycle is exactly zero. Yet it clearly heats a kettle. The plain average is the wrong tool.
Root mean square: the honest average
Square the current first (which makes everything positive), take the mean of that, then square-root at the end. The result — the r.m.s. value — is the steady direct current that would heat a resistor at the same rate. That is why it is the number worth quoting.
The √2 relationship
For a sine wave, the peak value is √2 times the r.m.s. value. So 230 V r.m.s. mains actually peaks at 325 V — which matters enormously when you are choosing components that must survive the peak, not the average.
Turning a.c. into d.c.
A single diode blocks the reverse half of every cycle (half-wave rectification). Four diodes in a bridge flip the reverse half instead of discarding it (full-wave), giving twice as many pulses. Then a capacitor across the output charges at each peak and discharges gently between them, smoothing the bumps. Bigger capacitance means less ripple.
The bit that catches people outThe √2 relationship only holds for a sine wave. For a square or triangular waveform the relationship between peak and r.m.s. is different. Exam questions occasionally show a non-sinusoidal trace to check whether you noticed.
The grown-up words
What it means
What it is called
Note
Steady current with the same heating effect
r.m.s. current
I₀/√2 for a sine wave
Maximum value reached
peak value
√2 × r.m.s.
Removing the reverse half-cycles
rectification
Diodes do this
Capacitor reducing the bumps
smoothing
Larger RC = less ripple
Leftover variation in the output
ripple
Never quite eliminated
Check you have got it
Mains is 230 V r.m.s. What peak voltage must a component survive?
230 × √2 ≈ 325 V.
Why is the mean power in an a.c. circuit half the peak power?
Power depends on the square of the current, and the mean of sin² over a cycle is exactly ½.
Edvia Free Resources · Physics 9702 · Topic 21 — free to copy and share
Topic 22
Quantum physics
Light arrives in indivisible lumps, and particles have wavelengths. Both statements are true and both feel wrong.
Picture itShine a very dim red light on a metal and no electrons come off, however long you wait. Shine a very faint blue light and electrons come off immediately. If light were a wave, this makes no sense at all — enough energy should eventually accumulate. It does not.
Light comes in packets
Energy arrives in discrete lumps called photons, and each photon's energy depends only on the frequency. A red photon carries less energy than a blue one, full stop. Making the red light brighter sends more photons but does not make any individual photon more energetic.
Which explains the photoelectric effect exactly
One photon interacts with one electron. If that single photon has less energy than the metal's work function, the electron cannot escape — and a billion such photons will not help, because their energy is not pooled. Above the threshold frequency, electrons come off instantly. Brighter light then means more electrons, not faster ones. Every observation the wave model failed on, the photon model explains.
Then particles turned out to be waves too
De Broglie proposed that if waves can behave as particles, particles might behave as waves — with a wavelength equal to Planck's constant divided by momentum. It sounded like numerology. Then someone fired electrons at a crystal and got a diffraction pattern, which is something only waves do.
Why you do not diffract through doorways
The de Broglie wavelength of a walking human is around 10⁻³⁵ metres — unimaginably smaller than any gap you could pass through, so no diffraction is observable. An electron's is about 10⁻¹⁰ m, comparable to atomic spacing, which is precisely why crystals diffract electrons.
The bit that catches people outAn electron cannot save up energy from several photons. This is not a technical caveat — it is the entire reason a threshold frequency exists. If energy could accumulate, dim red light would eventually work, and it never does.
The grown-up words
What it means
What it is called
Note
A single packet of light energy
photon
E = hf
Minimum energy to free an electron
work function
Property of the metal
Frequency below which nothing happens
threshold frequency
hf₀ = work function
Wavelength of a moving particle
de Broglie wavelength
λ = h/mv
Electrons producing a diffraction pattern
electron diffraction
Evidence particles are waves
Fixed allowed energies inside an atom
energy levels
Why spectra are lines
Check you have got it
Doubling the intensity of light above the threshold frequency — what changes?
More electrons are emitted per second, but their maximum kinetic energy is unchanged. Energy per electron depends on frequency alone.
Why are atomic spectra made of sharp lines rather than a continuous rainbow?
Electrons can only occupy specific energy levels, so emitted photons can only have the specific energies of the gaps between them.
Edvia Free Resources · Physics 9702 · Topic 22 — free to copy and share
Topic 23
Nuclear physics
A nucleus weighs less than its parts, and that missing mass is the energy holding it together.
Picture itWeigh a helium nucleus. Now weigh two protons and two neutrons separately and add them up. The separate parts weigh more. Mass has genuinely gone missing — and Einstein's E = mc² tells you exactly where it went.
Mass and energy are the same thing
The missing mass is the mass defect, and multiplying it by c² gives the binding energy — the energy you would have to supply to pull the nucleus apart. Because c² is such an enormous number, a tiny mass difference corresponds to a huge energy. That is why nuclear processes release millions of times more energy per reaction than chemical ones.
Compare per nucleon, not in total
Uranium has a far bigger total binding energy than iron simply because it has more nucleons. To judge stability you must divide by the number of nucleons. Do that and iron-56 sits at the very top of the curve — the most stable nucleus there is.
Which explains both fission and fusion
Both release energy by moving towards iron on that curve. Split a heavy nucleus and the fragments are more tightly bound. Join two light nuclei and the product is more tightly bound. Either way, binding energy per nucleon rises and the surplus is released. The Sun does the second; power stations do the first.
Decay is random but reliable
You cannot predict when any individual nucleus will decay — it is genuinely random, not merely unpredictable. But with billions of nuclei, the statistics are rock solid, which is why half-life is such a dependable quantity. And it is unaffected by temperature, pressure or chemistry: you cannot speed radioactive decay up or slow it down.
The bit that catches people outKeep the decay constant and the time in the same units. If λ is per second, t must be in seconds. Working in whole half-lives sidesteps this entirely — after n half-lives, just halve n times.
The grown-up words
What it means
What it is called
Note
Missing mass of a nucleus
mass defect
Multiply by c² for the energy
Energy to split into separate nucleons
binding energy
Compare per nucleon
Splitting a heavy nucleus
fission
Used in power stations
Joining light nuclei
fusion
Powers the Sun
Probability of decay per second
decay constant
λ = 0.693/t½
Decays per second
activity
Becquerels
Check you have got it
Iron-56 has a smaller total binding energy than uranium-235. Why is iron more stable?
Stability depends on binding energy per nucleon, and iron-56 has the highest value of any nucleus.
A sample has a half-life of 6 hours. What fraction remains after 24 hours?
24 hours is 4 half-lives, so ½ × ½ × ½ × ½ = 1/16 remains.
Edvia Free Resources · Physics 9702 · Topic 23 — free to copy and share
Topic 24
Medical physics
Ultrasound, X-rays and PET scans — three ways of seeing inside a person without opening them.
Picture itBefore 1895, the only way to see inside a living body was to cut it open. Then Röntgen photographed his wife's hand and she reportedly said “I have seen my death.” Everything in this topic descends from that moment.
Ultrasound: listening for echoes
Send a very high-frequency sound pulse into the body and time the echoes coming back from each boundary. A crystal that vibrates when you apply a voltage — a piezo-electric transducer — both sends the pulse and detects the return. It is sonar, pointed at a person.
Why the gel is not optional
How much sound reflects at a boundary depends on the mismatch in acoustic impedance between the two materials. Air and skin are so mismatched that over 99.9% of the ultrasound would bounce straight off the surface and never enter the body. The gel has an impedance close to skin, so the pulse gets in. Without it the scan is simply blank.
X-rays: shadows, not echoes
X-rays pass through the body and are absorbed more by dense material. Bone absorbs strongly and casts a shadow; soft tissue barely does. What you see is a shadow-gram. A CT scanner takes many such shadows from different angles and reconstructs a three-dimensional picture by computer.
PET: the body lights itself up
Inject a tracer that emits positrons — antimatter electrons. Each positron meets an electron almost immediately and both annihilate, converting entirely into two gamma photons that fly off in exactly opposite directions. Detectors around the patient catch both and draw a line between them. Millions of such lines build an image of where the tracer collected, which shows metabolic activity rather than just structure.
The bit that catches people outThe two gamma photons in PET fly apart at 180° because the electron–positron pair had almost no momentum to begin with, and momentum must be conserved. A single photon could not conserve both energy and momentum, which is why there are always exactly two.
The grown-up words
What it means
What it is called
Note
Crystal that converts voltage to vibration
piezo-electric transducer
Sends and receives
ρ × c, deciding reflection at boundaries
acoustic impedance
Air–skin mismatch is huge
Gel between probe and skin
coupling medium
Lets the ultrasound in
How much a material absorbs X-rays
attenuation coefficient
I = I₀e⁻ᵘˣ
Thickness that halves the intensity
half-value thickness
ln2 / µ
Matter and antimatter converting to photons
annihilation
0.511 MeV each
Check you have got it
Why is ultrasound preferred over X-rays for scanning a foetus?
Ultrasound is non-ionising, so it carries far less risk of damaging rapidly dividing cells.
Why can ultrasound not image the brain through an adult skull easily?
Bone has a very different acoustic impedance from soft tissue, so most of the pulse reflects at the skull rather than passing through.
Edvia Free Resources · Physics 9702 · Topic 24 — free to copy and share
Topic 25
Astronomy and cosmology
You can measure the size, temperature and distance of a star you will never visit — using only its light.
Picture itEverything we know about the universe beyond the solar system arrived as light. No samples, no visits, no instruments out there. Just light, decoded very carefully.
Brightness plus known power gives distance
If you know how much light a star actually emits (its luminosity) and you measure how much reaches you, the inverse square law gives you the distance. The catch is knowing the true luminosity — which is where standard candles come in. Certain objects, notably type Ia supernovae, always explode with very nearly the same brightness. Spot one, measure how dim it looks, and you know how far away its galaxy is.
Colour reveals temperature
Hot things glow blue, cooler things glow red — a poker in a fire runs through the sequence as it heats. Wien's law makes this quantitative: the peak wavelength is inversely proportional to temperature. Measure where a star's spectrum peaks and you have its surface temperature without leaving Earth.
Temperature plus luminosity gives size
The Stefan–Boltzmann law says total power depends on surface area and on temperature to the fourth power. You already have the luminosity and the temperature, so rearrange and out comes the radius. A star that is cool but extremely luminous must be enormous — that is precisely how we know red giants are giant.
Redshift and an expanding universe
Light from distant galaxies is stretched towards longer wavelengths, and the further away a galaxy is, the more stretched it is. Hubble found recession speed is proportional to distance. Run that expansion backwards and everything converges — which is the observational foundation of the Big Bang.
The bit that catches people outRedshift is not really galaxies flying through space away from us, and we are not at the centre of anything. Space itself is expanding, stretching the light while it travels. Every observer in every galaxy sees exactly the same thing. At A Level you may use the Doppler equation, but describe it as recession rather than as motion through a fixed space.
The grown-up words
What it means
What it is called
Note
Total power radiated by a star
luminosity
Watts
Power per unit area reaching us
radiant flux intensity
Falls as 1/d²
Object of known luminosity
standard candle
Type Ia supernovae
Peak wavelength ∝ 1/T
Wien's displacement law
Colour gives temperature
L = 4πσr²T⁴
Stefan–Boltzmann law
Gives the radius
Stretching of light from receding sources
redshift
Δλ/λ ≈ v/c
Check you have got it
A star is cool and red but extremely luminous. What can you conclude about its size?
It must be very large. Low temperature means little power per unit area, so a huge surface area is needed to reach that luminosity.
Why does every galaxy appear to be receding from us, without us being at the centre?
Space itself is expanding everywhere, so every observer in every galaxy sees all the others receding. There is no centre.
Edvia Free Resources · Physics 9702 · Topic 25 — free to copy and share
Like how this is taught?
Every handout starts with the idea in plain English and only then the formal version. That is how every class at Edvia College works — for two full years of Cambridge A Levels.