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Electrons, Waves and Photons

4. Electrons, Waves and Photons

5 min read 9 parts Lesson 1 of 62 Unit quiz Virtual lab

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Lesson summary

Electrons, Waves and Photons — OCR A LEVEL PHYSICS A H556 notes: Explain electric current, resistance and resistivity, describe waves and superposition, and use the photon model of light and electron diffraction.Current — Current is the rate of flow of charge, I = Q / t, measured…

  • Charge carriers
  • Kirchhoff's first law
  • Drift velocity
  • Which options give 8 mA
  • Direction in an electrolyte
  • Series and parallel

Part 1 of 7Charge and current

1
Current
  • Current is the rate of flow of charge, I = Q / t, measured in amperes.
  • Conventional current is taken from positive to negative, while electrons in a metal flow from negative to positive.
2
Charge
  • The coulomb is the charge passing a point when a current of 1 A flows for 1 s.
  • Charge is quantised in multiples of the elementary charge e = 1.60 x 10-19 C.
3
Charge carriers
  • In metals the carriers are electrons; in electrolytes they are positive and negative ions.
4
Ammeter
  • It is connected in series with the part of the circuit being measured.
5
Kirchhoff's first law
  • The sum of currents entering a junction equals the sum leaving, which follows from conservation of charge.
6
Drift velocity
  • I = n A v e, where n is the number density of charge carriers, A is the cross-sectional area and v the mean drift velocity.
  • Conductors have a large n, semiconductors have a small n, and insulators have almost no free carriers.
7
Example
  • A charge of 4 C passes in 500 s, so I = 8 mA.
Charge and current
Which options give 8 mA
  • 4 C in 500 s gives 8 mA, 8 C in 100 s gives 80 mA and 1 C in 8 s gives 125 mA.
Direction in an electrolyte
  • Direction in an electrolyte anions go to the anode and cations go to the cathode.
Series and parallel
  • Series and parallel current is the same everywhere in series, and divides at junctions in parallel.

Part 2 of 7Resistance and I-V characteristics

Resistance and I-V characteristics
Resistance
  • R = V / I, in ohms (1 ohm = 1 V A-1).
Ohm's law
  • For a conductor at constant temperature, current is proportional to the potential difference.
Ohmic conductor
  • A resistor at constant temperature gives a straight I-V line through the origin.
Filament lamp
  • The I-V curve flattens as the filament heats up and resistance increases.
Diode
  • It conducts in one direction only after a threshold voltage of about 0.6 V for silicon.
Thermistor
  • An NTC thermistor has resistance that falls as temperature rises.
Light-dependent resistor
  • The resistance falls as light intensity rises.
Plotting
  • Use a potential divider circuit to vary the voltage from zero, with the ammeter in series and the voltmeter in parallel.
Resistance and I-V characteristics
Example
  • Example a 10 ohm resistor carrying 0.30 A has V = IR = 3.0 V.
LED
  • LED a light-emitting diode conducts and emits light only in forward bias.

Part 3 of 7Resistivity

1Definition
  • Resistivity rho is given by R = rho L / A, with unit ohm metre.
2Dependence
  • Resistance increases with length and decreases with cross-sectional area.
3Measuring resistivity of a wire
  • Measure the diameter with a micrometer and find resistance at different lengths.
  • Plot R against L; the gradient is rho / A, so rho = gradient x A.
4Temperature
  • The resistivity of metals increases with temperature, while that of semiconductors decreases.
5Power and heating
  • P = VI = I2R = V2/R.
    What the symbols mean: P = power (W) · I = current (A) · V = potential difference (V)
6Example
  • A wire 2.0 m long with a cross-sectional area of 1.0 x 10-7 m2 and resistivity 5.0 x 10-7 ohm m has R = 10 ohm.

Part 4 of 7Waves and superposition

1Wave quantities
  • Wave speed v = f lambda; frequency f = 1 / T.
2Transverse and longitudinal
  • Transverse waves vibrate at right angles to the direction of travel and can be polarised;
    • longitudinal waves vibrate parallel to it.
3Intensity
  • Intensity = power / area and is proportional to amplitude squared.
4Electromagnetic spectrum
  • Radio, microwave, infrared, visible, ultraviolet, X-ray and gamma ray, all travelling at 3.0 x 108 m s-1 in a vacuum.
5Superposition
  • Displacements add;
    • constructive interference occurs at a path difference of n lambda, destructive at (n + 1/2) lambda.
6Young's double slit
  • Fringe spacing w = lambda D / a for slit separation a and screen distance D.
7Diffraction grating
  • Diffraction grating d sin theta = n lambda.
8Stationary waves
  • They form from the superposition of two waves travelling in opposite directions, with nodes and antinodes.
1Phase and path difference
  • Phase and path difference path difference of n lambda gives constructive interference.
2Polarisation
  • Polarisation only transverse waves can be polarised, which shows that light is transverse.
3Stationary wave on a string
  • Stationary wave on a string the fundamental frequency is f = v / 2L.

Part 5 of 7Photons and the photoelectric effect

Photon energy
  • E = h f = h c / lambda, where h = 6.63 x 10-34 J s.
Electronvolt
  • 1 eV = 1.60 x 10-19 J.
Photoelectric effect
  • Electrons are emitted from a metal surface when light above a threshold frequency strikes it.
  • Each electron absorbs one photon, so the wave model cannot explain why intensity does not affect the energy of emitted electrons.
Einstein equation
  • Einstein equation h f = phi + KEmax, where phi is the work function.
Threshold frequency
  • Threshold frequency f0 = phi / h.
Line spectra
  • Photons are emitted when electrons fall between energy levels: h f = E1 - E2.

Part 6 of 7Wave-particle duality

Wave-particle duality
de Broglie wavelength
  • de Broglie wavelength lambda = h / p = h / mv.
Electron diffraction
  • Electrons passing through a thin graphite film produce a ring pattern, which shows that particles can behave as waves.
Effect of speed
  • Faster electrons have a larger momentum, so a shorter wavelength and smaller diffraction rings.
Duality
  • Light shows wave behaviour and particle behaviour (photoelectric effect).
    • (interference and diffraction)
Use of results
  • Electron microscopes can resolve smaller detail than light microscopes because electron wavelengths are much shorter.

Part 7 of 7Worked examples

  1. A wire has a charge of 120 C passing through it in 4.0 minutes. Calculate the current. [2]2 marks

  2. A copper wire of diameter 0.50 mm and length 3.0 m has resistivity 1.7 x 10-8 ohm m. Calculate its resistance. [3]3 marks

  3. Light of wavelength 400 nm falls on a metal of work function 2.0 eV. Calculate the maximum kinetic energy of the electrons. [4]4 marks

  4. Explain why increasing the temperature of a filament lamp reduces the gradient of its I-V curve. [3]3 marks

Key terms

TermMeaning
CurrentThe rate of flow of charge.
ResistivityA property of a material giving resistance for unit length and area.
Work functionThe minimum energy needed to remove an electron from a metal surface.
PhotonA quantum of electromagnetic energy.
SuperpositionThe addition of displacements when waves meet.
de Broglie wavelengthThe wavelength associated with a moving particle, h / p.
Drift velocityThe mean velocity of charge carriers in a conductor.
Threshold frequencyThe minimum frequency of light to cause photoemission.

Avoid these mistakes

1
Saying that electrons flow in the same direction as conventional current — they flow in the opposite direction.
2
Saying the resistance of a lamp is constant because it obeys Ohm's law — it does not at changing temperature.
3
Confusing intensity (affects the number of photons) with frequency (affects the photon energy).
4
Using diameter in place of radius when calculating cross-sectional area.
5
Forgetting to convert wavelength from nm and energy from eV to SI units.
Try it in the virtual labPhotoelectric effect and the Planck constant \n