KinexiaLEARN PHYSICS

Photoelectric Effect — Sodium Under Violet Light (Worked Example)

Hard
Problem

Violet light of wavelength 400 nm shines on a sodium surface whose work function is 2.75 eV. What is the maximum kinetic energy of the ejected photoelectrons?

Given

  • λ = 400 nm

  • Φ = 2.75 eV

  • hc = 1240 eV·nm

Find

Maximum kinetic energy KE_max of photoelectrons.

Principle

Einstein's photoelectric equation: each photon gives its energy to one electron; whatever exceeds the work function becomes kinetic energy.

Formula

Solution

  1. Photon energy: E=hc/λ=1240/400=3.10 eVE = hc/\lambda = 1240/400 = 3.10\ \mathrm{eV}

  2. Subtract the work function: KEmax=3.10−2.75KE_{max} = 3.10 - 2.75

  3. Calculate: KEmax=0.35 eVKE_{max} = 0.35\ \mathrm{eV}

  4. In joules: 0.35×1.602×10−19=5.61×10−20 J0.35 \times 1.602 \times 10^{-19} = 5.61 \times 10^{-20}\ \mathrm{J}

KE_max ≈ 0.35 eV (≈ 5.6 × 10⁻²⁰ J)

Unit check

eV − eV = eV; the joule conversion uses the defined 1 eV = 1.602×10⁻¹⁹ J. Consistent.

What this means physically

Each freed electron carries just 0.35 eV — barely above the escape threshold. Slightly redder light (longer wavelength) would eject nothing at all, no matter how bright: intensity raises the electron count, never their energy.

Common mistake

Thinking brighter light ejects faster electrons. Brightness adds photons (more electrons); only shorter wavelength adds energy per electron.