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Theme E — Nuclear and Quantum Physics

E.2 Quantum Physics — IB Physics HL Revision Notes & Topical Questions

5 min read 12 parts Lesson 10 of 45 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

E.2 Quantum Physics — IB PHYSICS HL notes: Explain the photoelectric effect and equation, the particle nature of light, de Broglie waves, wave-particle duality and Compton scattering.Definition — emission of photoelectrons from a metal surface when it absorbs electromagnetic radi…

  • Threshold frequency f0
  • Work function Φ
  • Below threshold
  • Above threshold
  • Maximum kinetic energy
  • Photocurrent

Part 1 of 10The photoelectric effect

The photoelectric effect
Definition
  • Definition emission of photoelectrons from a metal surface when it absorbs electromagnetic radiation of sufficient frequency
Evidence
  • Evidence it shows that light is quantised, because each electron absorbs a single photon
Threshold frequency f0
  • Threshold frequency f0 the minimum frequency needed to remove a photoelectron from the surface
  • It is a property of the metal
Work function Φ
  • Work function Φ the minimum energy needed to release a photoelectron
  • hf0 = Φ
Metals
  • Metals alkali metals have thresholds in the visible region and transition metals in the ultraviolet

Part 2 of 10Observations

Below threshold
  • Below threshold no electrons are emitted whatever the intensity or time of exposure
Above threshold
  • Above threshold emission is immediate
Maximum kinetic energy
  • Maximum kinetic energy it depends on frequency and not on intensity
Photocurrent
  • Photocurrent for a given frequency it is proportional to intensity, the number of electrons per second

Part 3 of 10Photoelectric equation

1Equation
  • Equation hf = Φ + Ek,max
2Meaning
  • Meaning one photon is absorbed by one electron, with Φ used to escape and the rest becoming kinetic energy
3Surface and deeper electrons
  • Surface and deeper electrons surface electrons have the maximum kinetic energy and deeper ones less
4Graph
  • Ek,max against f is a straight line with gradient h, x-intercept f0 and y-intercept −Φ
5Units
  • Units hf, Φ and Ek,max must be in the same units, all in eV or all in J
6Maximum speed
  • Ek,max = ½mevmax2

Part 4 of 10Intensity, frequency and current

Intensity
  • Intensity it is proportional to the number of photons per second, so a higher intensity gives more photoelectrons and a larger current
Constant intensity
  • Constant intensity raising the frequency makes each photon more energetic, so fewer photons are needed and the photocurrent falls
Constant photon rate
  • Constant photon rate changing frequency does not change the photocurrent
Relation
  • I = nhf/(tA) for n photons in time t on area A

Part 5 of 10Stopping potential

Definition
  • Definition the potential difference that just stops photoelectron emission across the gap
Equation
  • Ek,max = eVs
Intensity
  • Intensity a higher intensity increases the current but leaves Vs unchanged
Frequency
  • Frequency a higher frequency raises Vs
Sign
  • Sign the stopping potential is negative, but only its magnitude is used

Part 6 of 10Failure of the wave model

Wave prediction 1
  • Wave prediction 1 any frequency should eventually eject electrons as energy accumulates, so there would be no threshold
Wave prediction 2
  • Wave prediction 2 a time delay at low intensity
Wave prediction 3
  • Wave prediction 3 kinetic energy would increase with intensity
Observation
  • Observation none of these occurs, so the photon model is needed
Gold-leaf electroscope
  • UV light on a negatively charged zinc plate makes the leaf fall at once
  • The leaf falls slower at low intensity and not at all at low frequency however bright

Part 7 of 10Matter waves

de Broglie wavelength
  • de Broglie wavelength 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)
Kinetic energy form
  • λ = h/√(2mEk)
Electron diffraction
  • Electron diffraction electrons through graphite form concentric rings
  • A larger accelerating voltage gives shorter wavelength and smaller rings
Size condition
  • Size condition diffraction needs gaps similar to the de Broglie wavelength such as atomic spacing
Maximum
  • Maximum for spacing d the first maximum is at sin θ = λ/d
Evidence
  • Evidence electron diffraction was the first clear evidence for wave properties of matter

Part 8 of 10Wave–particle duality

1Light as a particle
  • Light as a particle it interacts with matter as photons, shown by the photoelectric effect
2Light as a wave
  • Light as a wave it propagates as a wave, shown by diffraction and interference in Young's experiment
3Wave theory
  • Wave theory it fails to explain the photoelectric effect
4Single electrons
  • Single electrons in a double-slit experiment the pattern builds up from single detections
5History
  • History the debate about light lasted about 300 years until the early 20th century

Part 9 of 10Compton scattering

Definition
  • Definition a high-energy photon interacts with an orbital electron, ejecting it and increasing the photon's wavelength
Energy transfer
  • Energy transfer the photon loses energy, its wavelength increases and it is deflected
Compton formula
  • Δλ = (h/mec)(1 − cos θ)
Compton wavelength
  • Compton wavelength h/mec = 2.43 × 10−12 m
Angle dependence
  • Angle dependence no shift at 0° and a maximum shift of 2h/mec at 180°
Assumption
  • Assumption the electron is initially at rest
Significance
  • Significance further evidence for the particle nature of light

Part 10 of 10More from the specification

Photoelectric effect
  • Electrons are emitted from a metal surface when incident radiation exceeds a threshold frequency.
Einstein's equation
  • Einstein's equation hf = Φ + Ekmax, where Φ is the work function needed to release an electron.
Intensity
  • Increasing intensity of incident radiation raises the number of photoelectrons but not their maximum kinetic energy.
Stopping potential
  • Stopping potential eVs = Ekmax, found whilst keeping frequency constant and varying the potential.
Photon model
  • Light is quantised in photons with energy E = hf, supporting the particle nature.

Key terms

TermMeaning
Photoelectric effectThe emission of electrons from a metal surface when radiation of high enough frequency falls on it.
Work functionThe minimum energy needed to remove an electron from the surface of a metal.
Threshold frequencyThe minimum frequency of radiation that causes photoemission from a given metal.
Stopping potentialThe potential difference that just stops the most energetic photoelectrons, eVs = Ek,max.
de Broglie wavelengthThe wavelength of a moving particle, λ = h/p.
Compton scatteringThe scattering of a photon by an electron with an increase in the photon's wavelength.

Avoid these mistakes

1
Saying a brighter light gives electrons more energy — it gives more electrons.
2
Thinking an electron can store energy from several photons — each electron absorbs one photon.
3
Using photon energy as the kinetic energy — subtract the work function.
4
Taking the gradient of Ek,max against f as Φ — it is h.
5
Saying the Compton shift depends on the incident wavelength — it depends only on the angle.

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