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Lesson 11.2 • Competency 11.2Interactive Simulation
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Photoelectric Effect and the Photon

Master Planck’s quantum hypothesis E = hf, the failure of classical wave theory, Einstein’s photoelectric equation hf = Φ + ½mv_max², threshold frequency f₀, work function Φ, stopping potential V_s, and photocurrent-voltage characteristics.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • Explain why classical wave theory fails to explain threshold frequency, instantaneous emission, and intensity independence of electron kinetic energy.
  • Apply Einstein’s photoelectric equation hf = Φ + eV_s to calculate photon energies, work functions, and stopping potentials.
  • Interpret stopping potential vs frequency graphs (gradient h/e, x-intercept f₀) and photocurrent vs collector voltage curves.

Core Theory & Concepts

When electromagnetic radiation illuminates a clean metal surface, electrons can be instantaneously ejected. Heinrich Hertz discovered this phenomenon in 1887, but classical wave physics predicted that electrons would require hours to accumulate enough energy, and that their kinetic energy should increase with light intensity. In 1905, Albert Einstein resolved this crisis by proposing that light behaves as localized packets of energy called photons.

Photon Energy & Momentum

Each photon carries a quantized discrete energy E = hf = hc/λ, and momentum p = h/λ = E/c, where h = 6.626 × 10⁻³⁴ J s and c = 3.0 × 10⁸ m/s.

E = h f = \frac{h c}{\lambda}, \quad p = \frac{h}{\lambda} = \frac{E}{c}

Work Function & Threshold Frequency

The work function Φ is the minimum energy required to liberate an electron from the metal surface: Φ = h f₀ = hc / λ₀. If the incident photon frequency f < f₀, no electrons can be emitted regardless of intensity.

\Phi = h f_0 = \frac{h c}{\lambda_0}

Einstein’s Photoelectric Equation

By conservation of energy in a single 1-to-1 photon-electron interaction: hf = Φ + K_max = Φ + ½ m_e v_max² = Φ + e V_s. The stopping potential is V_s = (h/e) f - (Φ/e).

h f = \Phi + e V_s \implies V_s = \left(\frac{h}{e}\right) f - \frac{\Phi}{e}

Common Misconceptions

Misconception

Increasing light intensity increases the maximum kinetic energy of emitted photoelectrons.

Physical Clarification:Intensity only determines the rate of photons arriving per second (and hence saturation photocurrent). Maximum kinetic energy depends strictly on the individual photon frequency f and the metal work function Φ.

Syllabus Topic Outline

Competency 11.2
  • 1Experimental observations of photoelectric emission
  • 2Limitations of classical electromagnetic wave theory
  • 3Photon concept: energy E = hf and momentum p = h/λ
  • 4Work function Φ, threshold frequency f₀, and threshold wavelength λ₀
  • 5Einstein’s equation: hf = Φ + K_max = hf₀ + eV_s
  • 6Stopping potential (V_s) vs frequency graph: gradient h/e
  • 7Interactive Photoelectric Lab: wavelength, intensity & stopping potential
Matter and Radiation Interactive Simulation Lab

Explore the photoelectric effect, Bohr hydrogen orbital transitions, line emission spectra, and radioactive half-life decays in real time.

Photon Energy (hf)3.26 eV
Work Function (Φ)2.14 eV
Max Kinetic Energy (K_max)1.12 eV
Stopping Potential (V_s)-1.12 V
Threshold Wavelength (λ₀)579 nm
Photocurrent (I)33.43 µA
Wavelength (λ):380 nm
Light Intensity:75%
Collector Potential (V):1.50 V