Photoelectric Effect

Concept overview

The photoelectric effect is the emission of electrons from a metal surface when light is shone on it. Classical wave theory predicted that any light frequency should eventually kick electrons out if the intensity is high enough. Experiment showed the opposite: electrons are emitted only above a threshold frequency ν₀, and the maximum kinetic energy of ejected electrons depends on frequency, not intensity.

Einstein's 1905 explanation: light comes in discrete quanta (photons) of energy E = hν. An electron absorbs a single photon; if hν exceeds the metal's work function φ, the electron escapes with kinetic energy KE_max = hν − φ. This is Einstein's photoelectric equation, and it earned him the 1921 Nobel Prize.

The stopping potential V_s is the retarding voltage needed to just stop the fastest emitted electrons: eV_s = KE_max = hν − φ. Plotting V_s against ν gives a straight line with slope h/e — this is how h was first measured experimentally.

The intensity of the light affects the number of electrons emitted per second (photoelectric current), but not their maximum kinetic energy. This intensity-vs-frequency independence is the signature test of the photon picture.

Key formulas & concepts

• Photon energy: E = hν = hc/λ (h = 6.626 × 10⁻³⁴ J·s)
• Einstein's equation: KE_max = hν − φ = h(ν − ν₀)
• Threshold frequency: ν₀ = φ/h (below this, no emission)
• Threshold wavelength: λ₀ = hc/φ
• Stopping potential: eV_s = KE_max = hν − φ
• Photon momentum: p = h/λ = hν/c

Common mistakes to avoid

• Assuming intensity affects maximum KE — it doesn't; only the number of emitted electrons scales with intensity.
• Forgetting to convert photon energy from J to eV when comparing to work function.
• Using ν₀ = φ where φ is in eV — φ must be in Joules or you must use hc = 1240 eV·nm.
• Applying photoelectric equation below the threshold — no emission occurs, so V_s is not defined.

JEE Main relevance

JEE Main asks 1–2 photoelectric problems every paper — usually one direct Einstein-equation calculation and often one stopping potential or threshold problem.

JEE Advanced relevance

Advanced problems combine photoelectric effect with EM waves (intensity → photon flux calculation) or with the de Broglie wavelength of the emitted electron. Photoelectric current versus intensity or frequency plots also appear.

Previous-year questions (PYQ)

Filter the PYQ bank by 'Photoelectric Effect'. The archetype is highly stable — Einstein's equation applied to specific numeric setups.