KinexiaLEARN PHYSICS

Photoelectric Effect — Threshold Wavelength (Worked Example)

Hard
Problem

What is the longest wavelength of light that can still eject electrons from zinc with work function 4.3 eV?

Given

  • Φ = 4.3 eV

Find

The threshold wavelength λ₀.

Principle

At threshold, KE = 0, so hc/λ₀ = Φ — rearrange to λ₀ = hc/Φ. Longer wavelengths lack the energy.

Formula

Solution

  1. Set KE=0KE = 0: hc/λ0=Φhc/\lambda_0 = \Phi

  2. Rearrange: λ0=hc/Φ\lambda_0 = hc/\Phi

  3. Convert Φ: 4.3×1.602×10−19=6.889×10−19 J4.3 \times 1.602 \times 10^{-19} = 6.889 \times 10^{-19}\ \mathrm{J}

  4. Divide: λ0=1.986×10−25/6.889×10−19=2.88×10−7 m=288 nm\lambda_0 = 1.986 \times 10^{-25}/6.889 \times 10^{-19} = 2.88 \times 10^{-7}\ \mathrm{m} = 288\ \mathrm{nm}

288 nm

Unit check

J·m ÷ J = m — a wavelength, correct.

What this means physically

288 nm — deep ultraviolet. Any wavelength longer than this (visible light included) cannot eject zinc electrons at any intensity — the classic proof that light energy comes in photon packets.

Common mistake

Inverting the fraction (Φ/hc). Check units: hc/Φ gives metres; Φ/hc gives 1/metres — units catch the error.