Quantum Physics
22. Quantum Physics
5 min read 8 parts Lesson 1 of 1
Lesson summary
22. Quantum Physics — Cambridge AS & A Level Physics 9702 — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Use the photon model, the photoelectric equation, de Broglie wavelength and atomic energy levels to explain light–matter interactions.Evidence — electromagnetic…
- Photon energy
- Photon momentum
- Photon rate
- Radiation pressure
- Electronvolt (eV)
- Accelerated charge
Part 1 of 8The photon: energy and momentum
- Evidence — electromagnetic radiation shows diffraction and interference (wave behaviour), while the photoelectric effect and line spectra need a particle model.
- Photon = a massless packet (quantum) of electromagnetic energy, transferring its energy all at once rather than continuously.
- Photon energy — E = hf, or E = hc/λ using c = fλ, where h = 6.63 × 10−34 J s is Planck's constant.
- Higher frequency means a more energetic photon.
- Energy is inversely proportional to wavelength, so long-wavelength photons have less energy.
- Photon momentum — a photon has momentum even though it has no mass, p = E/c = hf/c = h/λ.
- Photon rate — photons per second = power ÷ energy of one photon.
- Radiation pressure — force = photons per second × momentum of each photon (if all are absorbed), and pressure = force ÷ area.
Part 2 of 8The electronvolt
- Electronvolt (eV) = the energy gained by an electron moving through a potential difference of one volt, 1 eV = 1.60 × 10−19 J.
- eV to joules: multiply by 1.60 × 10−19; joules to eV: divide by 1.60 × 10−19.
- It is convenient because quantum energies are far smaller than a joule.
- Accelerated charge — a charge accelerated from rest through V gains eV = ½mv2, so v = √(2eV/m).
Part 3 of 8The photoelectric effect
- Photoelectric effect = electrons (photoelectrons) are emitted from a metal surface when radiation of sufficient frequency is absorbed.
- It shows that light is quantised, since each electron absorbs a single photon.
- The electrons were already in the metal and are not created by the light.
- Threshold frequency f0 = the minimum frequency of radiation that can release a photoelectron from the surface.
- Threshold wavelength λ0 = the longest wavelength that can release a photoelectron.
- Work function φ = the minimum energy needed to release an electron from the surface, φ = hf0.
- A high work function means electrons are bound more tightly.
- Alkali metals (sodium, potassium) have thresholds in the visible region because surface electrons are weakly attracted.
- Transition metals such as iron have thresholds in the ultraviolet because binding is stronger.
- Analogy — many low-frequency quanta (table-tennis balls) cannot dislodge a coconut, but one high-frequency quantum (a bullet) can.
| Metal | f0 / Hz | λ0 / nm |
|---|---|---|
| Sodium | 4.40 × 1014 | 682 |
| Potassium | 5.56 × 1014 | 540 |
| Zinc | 1.02 × 1015 | 294 |
| Iron | 1.04 × 1015 | 289 |
| Copper | 1.13 × 1015 | 266 |
| Gold | 1.23 × 1015 | 244 |
Part 4 of 8The photoelectric equation and stopping potential
1Energy conservation3 points
— hf = φ + Ek max, where Ek max = ½mvmax2.
- If hf is less than φ, no electrons are emitted.
- The maximum kinetic energy depends only on frequency and work function, not on intensity.
- Most photoelectrons have less than the maximum, because deeper electrons lose energy reaching the surface.
2Graph of Ek max against f3 points
— a straight line Ek max = hf − φ.
- The x-intercept is the threshold frequency f0.
- The gradient is Planck's constant h.
- The magnitude of the y-intercept is the work function φ.
3Stopping potential Vs2 points
= the potential difference that just stops photoelectrons crossing from the emitter to the collector.
- A variable supply makes the emitter positive so electrons are attracted back, and V is raised until the photocurrent is zero.
- At Vs, eVs = Ek max, and only the magnitude of Vs matters.
Part 5 of 8Intensity, frequency and the failure of wave theory
- Intensityit is the energy per unit time per unit area, proportional to the number of photons hitting the surface per second.
- Photocurrentit is proportional to the intensity, because each photoelectron comes from one photon.
- Kinetic energyit is unaffected by intensity, so the stopping potential is the same for any intensity.
- Higher frequencyat constant intensity fewer photons arrive per second, so the photocurrent falls; at constant photon number the current stays constant but the kinetic energy rises.
| Wave theory predicts | Observation |
|---|---|
| Any frequency gives emission if the exposure is long enough | No emission below the threshold frequency, however long or intense the light |
| Energy builds up gradually in each electron | Emission is instantaneous above the threshold |
| Kinetic energy rises with intensity | Kinetic energy depends only on frequency; greater intensity gives more electrons per second |
- Wave–particle duality — light travels as a wave but interacts with matter as particles, and the photon model explains the observations.
Part 6 of 8Electron diffraction and the de Broglie wavelength
1De Broglie's idea
— matter such as electrons also shows wave behaviour.
2Evidence2 points
— a beam of electrons through a thin graphite film produces concentric rings on a fluorescent screen.
- The gaps between neighbouring planes of carbon atoms act as slits of a size similar to the electron wavelength.
- Particles would be spread uniformly across the screen instead of forming rings.
3Electron gun1 point
— electrons are accelerated through a p.d. V to gain Ek = ½mv2 = eV.
- A higher voltage gives faster electrons, a shorter wavelength and smaller rings.
4De Broglie wavelength2 points
= the wavelength associated with a moving particle, λ = h/p = h/mv.
What the symbols mean: λ = de Broglie wavelength (m) · h = 6.63 × 10−34 J s · p = momentum (kg m s−1) · m = mass (kg) · v = speed (m s−1)
- In terms of kinetic energy p = √(2mE), so λ = h/√(2mE).
- For the same kinetic energy λ ∝ 1/√m, so heavier particles have shorter wavelengths.
5Size
— for everyday objects the wavelength is far too small to notice, and quantum effects appear only for samples of about that size.
Part 7 of 8Atomic energy levels and line spectra
- Discrete levels — electrons in atoms can only have certain energies, drawn as horizontal lines.
- Ground state — the lowest level that an electron normally occupies.
- Excitation — an electron moves up by absorbing a photon, through collisions or by heating.
- Ionisation — the electron gains enough energy to leave the atom.
- De-excitation — an electron falling to a lower level emits a photon.
- Emission spectrum — coloured lines on a dark background, each from a particular downward transition.
- Absorption spectrum — a continuous spectrum with dark lines where photons were absorbed by atoms of a cool, low-pressure gas.
- The re-emitted photons go in all directions, so those wavelengths seem missing from the original beam.
- The dark lines match the bright lines in the emission spectrum of the same element.
- Unique — each element has its own set of lines, so a spectrum identifies the element.
- Evidence — discrete lines show that electrons occupy discrete energy levels.
Part 8 of 8Calculating transition wavelengths
- Photon energyhf = E2 − E1, so λ = hc/(E2 − E1).
- Energy gapa larger gap gives a shorter wavelength and a smaller gap a longer wavelength.
- Unitsconvert eV to J (× 1.60 × 10−19) before using h and c.
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