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E.2.2 (HL)—Threshold frequency

Syllabus
First assessment 2025
Objective
—
Level
HL

Apply Threshold Frequency

HL only

Define the threshold

The threshold frequency f0f_0 is the minimum photon frequency that can eject an electron from a particular metal. At threshold, the photon has just enough energy to equal that metal's work function Φ\Phi, leaving zero maximum kinetic energy.

hf_0=\Phi\qquad\Rightarrow\qquad f_0=\frac{\Phi}{h}

Worked example — threshold frequency

For Φ=2.70 eV=(2.70)(1.60×10−19)=4.32×10−19 J\Phi=2.70\,\mathrm{eV}=(2.70)(1.60\times10^{-19})=4.32\times10^{-19}\,\mathrm{J}, f0=Φ/h=(4.32×10−19)/(6.63×10−34)=6.52×1014 Hzf_0=\Phi/h=(4.32\times10^{-19})/(6.63\times10^{-34})=6.52\times10^{14}\,\mathrm{Hz}. Brighter light below this frequency still ejects no electrons.

Explain the intensity result

Below f0f_0, each photon has too little energy to overcome the work function. Increasing intensity supplies more low-energy photons, but it does not make any one photon energetic enough, so no electrons are emitted.

Keep the metal fixed

Threshold frequency depends on the metal’s work function. Two metals illuminated by the same radiation can behave differently because their electron-binding energies differ.

Common trap

Do not explain the threshold in terms of total light energy accumulated over time. The interaction is photon-by-photon.

E.2.2 (HL) Exam Analysis

HL only

Assessment in practice

2 marks
How it is assessed

Questions ask why increasing intensity cannot eject electrons below threshold frequency.

Command terms

Explain / Why

What earns marks

Use photon energy, not total beam energy: state that hf is below the work function and intensity only increases photon number.

Watch for

Saying electrons need more time to absorb energy or failing to mention insufficient photon energy.

Retrieve the Quantum Model

HL only

Retrieve the light model

The photoelectric effect and Compton scattering show photon-like energy and momentum transfer. Threshold frequency and Ek,max=hf−ΦE_{k,max}=hf-\Phi make the photon energy budget explicit.

Retrieve the matter model

Particle diffraction and λ=h/p\lambda=h/p show wave-like matter. For Compton scattering, track energy loss, increased wavelength, and Δλ=hmec(1−cos⁡θ)\Delta\lambda=\frac{h}{m_ec}(1-\cos\theta).