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Theme E — Nuclear and Quantum Physics

E.2.2 The Photoelectric Equation — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 12 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.2.2 The Photoelectric Equation — IB PHYSICS HL notes: Use hf = Φ + Ek,max, the threshold condition and the Ek,max against f graph.Photon energy — E = hf, so energy is directly proportional to frequencyWhat the symbols mean: E = energy of one photon (J) · h = Planck constant (6.…

  • Energy division
  • Below threshold
  • At threshold
  • Above threshold
  • Alternative form
  • Maximum speed

Part 1 of 7Einstein's equation

Photon energy
  • E = hf,
  • so energy is directly proportional to frequency
    What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
Energy division
  • Energy division an energy Φ liberates the electron and the rest becomes kinetic energy
Equation
  • Equation hf = Φ + Ek,max so Ek,max = hf − Φ
Symbols
  • Symbols h Planck constant in J s, f frequency in Hz, Φ work function in J or eV, Ek,max in J

Part 2 of 7Consequences

1Below threshold
  • Below threshold photons with hf less than Φ liberate no electrons
2At threshold
  • At threshold hf0 = Φ, the electrons just escape with zero kinetic energy
3Above threshold
  • Above threshold the majority of electrons have kinetic energy below Ek,max
4Intensity
  • Ek,max depends only on the frequency and the work function, not the intensity
5Alternative form
  • Ek,max = h(f − f0)
6Maximum speed
  • Ek,max = ½mevmax2

Part 3 of 7Threshold values

Frequency
  • Frequency f0 = Φ/h
Wavelength
  • λ0 = hc/Φ
Visible photons
  • 1.8 to 3.1 eV, so they eject electrons only from metals with low work function

Part 4 of 7Graph of maximum kinetic energy against frequency

Form
  • Ek,max = hf − Φ compares with y = mx + c
Gradient
  • Planck's constant h, the same for every metal
x-intercept
  • x-intercept the threshold frequency f0
y-intercept
  • −Φ when extended back
Below f0
  • Below f0 no electrons are emitted
Different metals
  • Different metals parallel lines shifted along the frequency axis
Stopping potential graph
  • Stopping potential graph eVs against f has the same features

Part 5 of 7Working in electronvolts

Photon energy
  • Photon energy in eV it is 1240/λ(nm)
Same units
  • Same units hf, Φ and Ek,max must all be in eV or all in J
Conversion
  • 1 eV = 1.60 × 10−19 J, divide joules by this to get eV
Stopping potential
  • Stopping potential its value in volts equals Ek,max in eV

Part 6 of 7Changing the conditions

1Double the intensity
  • Double the intensity doubles the number of photons per second and the photocurrent, but Ek,max is unchanged
2Raise the frequency
  • Raise the frequency raises Ek,max and Vs linearly
3Different metal
  • Different metal changes the threshold but not the gradient
4Two wavelengths on one metal
  • Two wavelengths on one metal e(V2 − V1) = hc(1/λ2 − 1/λ1)

Part 7 of 7More from the specification

More from the specification
Radiation
  • Transfer by electromagnetic waves, requiring no medium
Diffraction
  • Spreading of waves through a gap or around an edge
Scattering
  • Deflection of particles from their original path.
Photoelectric effect
  • The emission of electrons from a metal surface when electromagnetic radiation of high enough frequency is absorbed.
Scattering angle
  • The angle θ through which the photon is deflected.
Wave-particle duality
  • The property that radiation and matter show both wave and particle behaviour.
Compton scattering
  • Scattering of a photon by an outer electron, with transfer of part of the photon's energy.
Wave theory prediction
  • Wave theory prediction energy would build up gradually, so any frequency should eventually eject electrons and brighter light should give faster ones.
Constant intensity
  • Constant intensity a higher frequency means each photon carries more energy, so fewer photons per second give the same intensity.

Key terms

TermMeaning
Photoelectric equationhf = Φ + Ek,max.
Work functionThe minimum energy needed to remove an electron from the surface.
Threshold frequencyf0 = Φ/h, the lowest frequency that causes emission.
Maximum kinetic energyThe kinetic energy of the most energetic photoelectrons, hf − Φ.
Planck constanth = 6.63 × 10−34 J s, the gradient of the Ek,max–f graph.

Avoid these mistakes

1
Using the photon energy as the kinetic energy — always subtract the work function.
2
Using wavelength where frequency is required, or leaving nm unconverted.
3
Thinking Ek,max depends on intensity or that all electrons have Ek,max.
4
Taking the gradient to be Φ — it is h.
5
Mixing eV and J in the same equation.

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