Quantum physics

• Intensity is the number of photons per second; frequency is the energy of each one. Every result in this chapter that surprises a wave model follows from that one sentence.
• One photon, one electron. Intensity is photons per second; frequency is energy per photon. λ = h/p, so faster means shorter and smaller rings. Big gap, short wavelength.

• 22.1.1 I can understand — understand that electromagnetic radiation has a particulate nature
• 22.1.2 I can understand — understand that a photon is a quantum of electromagnetic energy
• 22.1.3 I can recall — recall and use E = hf
• 22.1.4 I can use — use the electronvolt (eV) as a unit of energy
• 22.1.5 I can understand — understand that a photon has momentum and that the momentum is given by p = E / c
• 22.2.1 I can understand — understand that photoelectrons may be emitted from a metal surface when it is illuminated by electromagnetic radiation
• 22.2.2 I can understand — understand and use the terms threshold frequency and threshold wavelength
• 22.2.3 I can explain — explain photoelectric emission in terms of photon energy and work function energy
• 22.2.4 I can recall — recall and use hf = Φ + ½mv_max²
• 22.2.5 I can explain — explain why the maximum kinetic energy of photoelectrons is independent of intensity, whereas the photoelectric current is proportional to intensity
• 22.3.1 I can understand — understand that the photoelectric effect provides evidence for a particulate nature of electromagnetic radiation while phenomena such as interference and diffraction provide evidence for a wave nature
• 22.3.2 I can describe — describe and interpret qualitatively the evidence provided by electron diffraction for the wave nature of particles
• 22.3.3 I can understand — understand the de Broglie wavelength as the wavelength associated with a moving particle
• 22.3.4 I can recall — recall and use λ = h / p
• 22.4.1 I can understand — understand that there are discrete electron energy levels in isolated atoms (e.g. atomic hydrogen)
• 22.4.2 I can understand — understand the appearance and formation of emission and absorption line spectra
• 22.4.3 I can recall — recall and use hf = E₁ − E₂

Why “isolated” matters. In a solid, each atom's levels are disturbed by its close neighbours, and the allowed energies are no longer a short list of sharp values. That is why a hot solid (a lamp filament) gives a continuous spectrum, while a hot gas of separate atoms gives lines (card P). Discreteness is the second place in the course where a quantity takes only certain values; the first was the fixed energies of the α-particles from one source in Topic 11.

• “Brighter light has more energetic photons.” Correct Brighter light of the same frequency has more photons per second, not bigger ones. Each photon still carries hf. So a brighter beam releases more photoelectrons per second (a larger current) with the same maximum kinetic energy.
• “Below the threshold frequency, electrons come out if you shine the light for long enough.” Correct One photon gives its energy to one electron, at once. Below f0 no photon has enough, and an electron cannot collect energy from several photons, so there is no emission however long or intense the illumination.
• “Every photoelectron has kinetic energy hf − Φ.” Correct That is the maximum. Φ is the minimum energy to remove an electron, so only electrons at the surface leave with hf − Φ; electrons from deeper lose more on the way out.
• “The threshold wavelength is the shortest wavelength that causes emission.” Correct It is the longest. Shorter wavelength means higher frequency and more energetic photons, so every wavelength shorter than λ0 = hc/Φ causes emission.
• “Put the energy in eV straight into E = hf.” Correct h = 6.63 × 10−34 J s. Multiply electronvolts by 1.60 × 10−19 to get joules first, or the frequency comes out about 1019 times too large.
• “A higher accelerating voltage makes the electron diffraction rings bigger.” Correct Higher V gives faster electrons with more momentum, so a shorter de Broglie wavelength, smaller diffraction angles and smaller rings.
• “The biggest energy gap gives the longest wavelength.” Correct The biggest gap gives the most energetic photon, so the highest frequency and the shortest wavelength: λ = hc/ΔE.
• “A more intense beam has more energetic photons.” Repair Intensity at a fixed frequency is the number of photons per second per unit area. Each photon still has hf.
• “Brighter light gives faster photoelectrons.” Repair EK,max = hf − Φ contains no intensity. Brighter light gives more photoelectrons per second, a larger current, with the same maximum kinetic energy.
• “Below the threshold frequency, electrons come out if you wait long enough.” Repair One photon gives its energy to one electron. Below f0 no photon has enough, and an electron cannot store energy from several photons.
• “All the photoelectrons have kinetic energy hf − Φ.” Repair That is the maximum. Electrons from below the surface lose more energy getting out and leave slower.
• “The work function is the energy of the photon needed for emission, so it depends on the light.” Repair Φ is a property of the metal (and its surface): the minimum energy to remove an electron from it. The light decides only whether hf reaches Φ.
• “The threshold wavelength is the minimum wavelength for emission.” Repair It is the maximum. Shorter wavelengths have more energetic photons, so they all cause emission.
• “f0 = 2.28 / 6.63 × 10−34 = 3.44 × 1033 Hz.” Repair The work function was left in eV. Convert first: 2.28 × 1.60 × 10−19 = 3.648 × 10−19 J, giving 5.50 × 1014 Hz. A frequency of 1033 Hz should stop you at once.
• “Photons have no mass, so they have no momentum.” Repair p = E/c = h/λ. Momentum is not only mv.
• “For an electron accelerated through V, λ = h/(eV).” Repair eV is the kinetic energy, not the momentum. Use p = √(2mEK) = √(2meeV), then λ = h/p.
• “Increasing the accelerating voltage makes the rings bigger.” Repair Higher V → larger p → shorter λ → smaller diffraction angles → smaller rings.
• “Energy levels are positive, with the ground state at zero.” Repair Levels are negative, with zero at ionisation; the ground state is the most negative.
• “An absorption spectrum is dark because the gas absorbs all the light.” Repair Only photons that match a transition are absorbed. The dark lines sit on a continuous spectrum, at the wavelengths of the emission lines that involve the level the atoms are in.
• “The biggest energy gap gives the longest wavelength.” Repair The biggest gap gives the highest frequency and the shortest wavelength.

• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.
• Two dials, two meanings. Frequency sets the energy of each photon. Intensity (at fixed frequency) sets the number of photons per second. Card 22.2.5 builds its whole explanation on keeping these apart.
• Joules in, joules out. h is in J s, me in kg and c in m s−1, so every equation in this chapter needs the energy in joules before you use it. Keep eV for stating answers and for comparing energies with each other (“2.11 eV is less than 2.28 eV”), where no constant is involved.
• Two separate points in “describe and interpret”. A description names the parts (electron gun, thin graphite, fluorescent screen) and the observation (concentric rings). An interpretation says what the rings mean (diffraction, so wave behaviour) and why they change with V (momentum, wavelength, angle). Say both.
• Two families, one constant. Most equations above contain h, and h is in joule seconds. The habit that protects every answer is to write every energy in joules before it meets h, and to convert back to eV only for the final statement or a comparison.
• Say what limits the precision, and why. The calipers are not the problem; the ring is. A source of uncertainty is always a feature of the apparatus or the method, stated with its reason, and an improvement must change something about the apparatus or the method. An uncertainty blamed on the person reading it does not count.
• Interleave with the chapters that use this one. Topic 23 measures nuclear energies in MeV: re-convert 1 MeV to joules when you start it. Topic 24 makes X-ray photons: re-answer drill item 6 there. Topic 25 reads stellar line spectra: re-answer energy-level studio item 6 there. Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Physics 9702 has five components. Topic 22 is A Level content, so it is examined in Papers 4 and 5. A Level content: examined in Paper 4 (A Level structured, which also requires the AS content) and, as practical context, Paper 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E. The Data and formulas sheet is printed as page 2 of Papers 1 and 2 and as pages 2 and 3 of Paper 4: it gives the constants and a short list of formulas. Every other equation in this chapter is one the syllabus says you must recall, and this chapter says which is which.
• Structured questions ask you to state what a photon, the work function or the threshold frequency is, to explain photoelectric emission, the effect of intensity, or why a gas gives lines rather than a continuous spectrum, and to describe electron diffraction and what it shows. The explanations are marked on the physics named in them: one photon, one electron; photons per second versus energy per photon; discrete levels.
• E = hf, p = E/c, hf = Φ + ½mvmax2, λ = h/p and hf = E1 − E2 are all recall; none is on the Data and formulas sheet. The sheet gives h, c, e and me. The graph is EK,max against f: gradient h, intercepts f0 and −Φ. Convert electronvolts to joules before any use of h.
• Paper 5 can set its context outside the syllabus, but this topic supplies a natural one: the diameter D of a diffraction ring measured against the accelerating p.d. V. A plan names the variables, the vernier calipers and the kilovolt safety precautions; an analysis tests D = kVn with a graph of lg D against lg V, error bars and a worst acceptable line. The ring edge, not the instrument, limits the precision.
• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.