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v = fλ R = ρL/A E = hf F = ma

Particles

Core foundations of matter, charge, isotopes, antiparticles and particle classification.

Atomic structure

  • The nucleus contains protons and neutrons and holds almost all the mass of the atom.
  • Electrons exist outside the nucleus and have very small mass compared with nucleons.
  • A neutral atom has equal numbers of protons and electrons.
  • Proton number defines the element.
neutrons = nucleon number − proton number

Isotopes and ions

  • Isotopes are atoms of the same element with the same proton number but different neutron number.
  • Ions form when atoms gain or lose electrons.
  • Changing electrons changes charge. Changing neutrons does not.

Specific charge

  • Specific charge means charge per unit mass.
  • Electrons have a much larger magnitude of specific charge than protons because their mass is far smaller.
  • This matters when comparing how particles behave in fields.
specific charge = Q / m

Antiparticles

  • Every particle has a corresponding antiparticle with the same mass but opposite charge or quantum number.
  • When a particle meets its antiparticle, annihilation can occur.
  • Energy is released as photons.

Particle families

  • Hadrons experience the strong interaction; leptons do not.
  • Baryons are hadrons made of three quarks.
  • Mesons are hadrons made from a quark and an antiquark.
  • Leptons include electrons and neutrinos.

Quark structure

  • Proton = uud.
  • Neutron = udd.
  • Quarks have fractional charge.
  • They are not observed freely in normal conditions.

Quick test

What changes between isotopes: protons, neutrons or electrons?

Neutrons change. The proton number stays the same, so it remains the same element.

Why is the electron’s specific charge much larger in magnitude than the proton’s?

Because the charge magnitude is the same, but the electron has far smaller mass, so Q / m is much larger.

Key terms

proton number nucleon number specific charge isotope antiparticle baryon

Exam traps

  • Same proton number = same element.
  • Do not confuse ions with isotopes.
  • Antiparticles have same mass, not opposite mass.
Common mark-loser Saying isotopes are different elements. They are not. If proton number stays the same, it is the same element.

Quantum

Photon model, photoelectric effect, work function, threshold frequency and line spectra.

Photon model

  • Electromagnetic radiation can be described as packets of energy called photons.
  • Photon energy depends on frequency, not intensity.
  • Higher frequency means higher photon energy.
E = hf

Photoelectric effect

  • Electrons are emitted from a metal surface only if incoming photons have enough energy.
  • Emission is effectively immediate once the threshold condition is met.
  • This supports the particle model of light.

Work function

  • The work function is the minimum energy needed to remove an electron from a metal surface.
  • If photon energy is below this value, no emission occurs.
hf = Φ + Ek,max

Threshold frequency

  • The threshold frequency is the lowest frequency that can cause photoelectron emission.
  • Below threshold, no electrons are emitted even if the light is very intense.
f₀ = Φ / h

Intensity vs frequency

  • Increasing intensity increases the number of photons each second.
  • If above threshold, that increases the number of emitted electrons.
  • Increasing frequency increases the maximum kinetic energy of the electrons.

Energy levels and spectra

  • Electrons in atoms occupy discrete energy levels.
  • Excitation moves an electron to a higher level.
  • De-excitation emits a photon with energy equal to the energy gap.
  • This produces line spectra, not continuous spectra.
ΔE = hf = hc / λ

Quick test

What changes when intensity rises but frequency stays the same above threshold?

The number of emitted electrons per second increases. The maximum kinetic energy does not change.

Why does a line spectrum support quantised energy levels?

Because only specific photon energies are emitted, showing that electrons can only move between fixed energy levels with fixed energy gaps.

Key terms

photon photoelectric effect work function threshold frequency excitation line spectrum

Exam traps

  • Brighter light does not mean more energetic electrons.
  • Frequency affects energy. Intensity affects number.
  • Below threshold frequency, no photoelectrons are emitted.
Common mark-loser Students often mix up intensity and frequency. Keep it strict: intensity changes how many photons arrive; frequency changes the energy per photon.

Electricity

Current, potential difference, resistance, resistivity, potential dividers and internal resistance.

Current and p.d.

  • Current is the rate of flow of charge.
  • Potential difference is energy transferred per unit charge.
  • Current tells you how much charge moves; p.d. tells you how much energy each coulomb transfers.
I = Q / t   |   V = W / Q

Resistance

  • Resistance measures how much a component opposes current.
  • Ohmic conductors have constant resistance at constant temperature.
  • Filament lamps are non-ohmic because their temperature changes.
R = V / I

Resistivity

  • Resistivity is a property of the material.
  • Longer wires have greater resistance.
  • Thicker wires have smaller resistance because cross-sectional area is larger.
R = ρL / A

Potential dividers

  • A potential divider shares the supply voltage across components in series.
  • The output depends on the ratio of resistances.
  • Useful in sensors and variable voltage circuits.
Vout = Vin × Rselected / Rtotal

Thermistors and LDRs

  • For an NTC thermistor, resistance falls as temperature rises.
  • For an LDR, resistance falls as light intensity rises.
  • That changes the output voltage in a potential divider.

EMF and internal resistance

  • EMF is the total energy supplied per unit charge by a source.
  • Internal resistance causes some energy to be dissipated inside the cell.
  • Terminal p.d. falls when current increases.
ε = V + Ir

Quick test

Why does doubling wire length double resistance if everything else is constant?

Because resistance is directly proportional to length in R = ρL / A, so charge carriers undergo more collisions overall.

Why does terminal p.d. decrease when the current increases?

Because the lost volts across the internal resistance increase as Ir increases, so less of the emf appears across the external circuit.

Key terms

current potential difference resistance resistivity potential divider internal resistance

Exam traps

  • Resistivity is not the same as resistance.
  • Potential divider output depends on a ratio, not one resistor alone.
  • EMF is not just “voltage”; it is energy per unit charge from the source.
Common mark-loser Resistance depends on dimensions and material. Resistivity belongs to the material only.

Mechanics

Motion graphs, equations of motion, projectile motion, forces, moments, work, power and energy.

Motion graphs

  • Gradient of displacement–time gives velocity.
  • Gradient of velocity–time gives acceleration.
  • Area under velocity–time gives displacement.
  • Area under acceleration–time gives change in velocity.

Equations of motion

  • Use SUVAT only when acceleration is constant.
  • Choose the equation that avoids unnecessary unknowns.
  • Always define a positive direction first.
v = u + at   |   s = ut + ½at²

Projectile motion

  • Horizontal and vertical motion are analysed separately.
  • Horizontal velocity stays constant if air resistance is ignored.
  • Vertical motion has constant downward acceleration g.
  • The two directions are linked only by time.

Forces and Newton’s laws

  • Zero resultant force means constant velocity, not necessarily zero velocity.
  • A resultant force causes acceleration.
  • Interaction pairs act on different objects.
F = ma

Moments and equilibrium

  • A moment is the turning effect of a force about a pivot.
  • Use the perpendicular distance from pivot to line of action.
  • For equilibrium, resultant force = 0 and resultant moment = 0.
moment = force × perpendicular distance

Work, power and energy

  • Work done is energy transferred by a force.
  • Power is the rate of energy transfer.
  • Efficiency compares useful output with total input.
W = Fs cosθ   |   P = W / t   |   Ek = ½mv²

Quick test

At the highest point of a projectile, what is zero and what is not zero?

The vertical component of velocity is zero. The acceleration is not zero; it is still g downward. The horizontal velocity is usually still non-zero.

Why is the path of a projectile curved even though there is no horizontal acceleration?

Because the object keeps moving horizontally while also accelerating downward vertically, so the combined motion produces a curved path.

What does the area under a velocity–time graph represent?

Displacement. If the graph goes below the time axis, signed area matters.

Key terms

gradient area under graph SUVAT projectile resultant force moment

Exam traps

  • At maximum height, acceleration is not zero.
  • SUVAT only works for constant acceleration.
  • Moment uses perpendicular distance, not just any distance.
Common mark-loser Students often write “acceleration is zero at the top of the projectile”. It is not. Only the vertical velocity is zero at that instant.

Waves

Wave quantities, superposition, interference, stationary waves and diffraction.

Core quantities

  • Amplitude is maximum displacement from equilibrium.
  • Frequency is oscillations per second.
  • Wavelength is the distance between two adjacent points in phase.
  • Wave speed links them together.
v = fλ

Transverse and longitudinal

  • Transverse waves oscillate perpendicular to the direction of energy transfer.
  • Longitudinal waves oscillate parallel to the direction of energy transfer.
  • Only transverse waves can be polarised.

Superposition

  • When waves overlap, the resultant displacement is the sum of the individual displacements.
  • Constructive interference occurs in phase.
  • Destructive interference occurs out of phase.

Interference conditions

  • Stable interference patterns need coherent sources.
  • Bright fringes form when path difference is a whole number of wavelengths.
  • Dark fringes form when path difference is a half-integer number of wavelengths.

Stationary waves

  • Formed by two waves of the same frequency travelling in opposite directions.
  • Nodes have zero amplitude.
  • Antinodes have maximum amplitude.
  • There is no net energy transfer along a stationary wave.

Diffraction

  • Diffraction is spreading when waves pass through a gap or around an obstacle.
  • It is greatest when gap size is similar to wavelength.
  • Longer wavelengths diffract more for the same gap size.

Quick test

Why is there no net energy transfer in a stationary wave?

Because it is formed by two equal waves travelling in opposite directions, so energy transfer one way is balanced by energy transfer the other way.

When is diffraction most noticeable?

When the gap size is about the same as the wavelength.

Key terms

wavelength frequency coherent superposition node antinode

Exam traps

  • Progressive waves transfer energy; stationary waves do not.
  • Node means zero amplitude, not zero displacement at every instant elsewhere.
  • Coherent means same frequency and constant phase difference.
Common mark-loser Students often say stationary waves “move less energy”. They do not transfer net energy along the wave at all.