Photoelectric Effect Calculator — Photon Energy & Work Function

Photoelectric Effect Guide

What do I need to know about The Photoelectric Equation?

Einstein's photoelectric equation: hf = φ + Ek_max. Where h = Planck's constant (6.626×10⁻³⁴ J·s), f = frequency of incident light (Hz), φ = work function of the metal (J or eV), Ek_max = maximum kinetic energy of emitted electrons. Rewritten: Ek_max = hf − φ. If hf < φ: no photoelectric emission (photon energy insufficient to release an electron). Threshold frequency: f₀ = φ/h. Threshold wavelength: λ₀ = hc/φ. 1 eV = 1.6×10⁻¹⁹ J.

What do I need to know about Key Experimental Observations?

Classical physics predicted: bright light of any frequency should eventually eject electrons (given enough energy). Longer exposure should produce electrons. Higher intensity should give higher electron kinetic energy. What is actually observed: light below threshold frequency ejects NO electrons regardless of intensity. Light above threshold: electrons are emitted instantly (no delay). Higher intensity: more electrons, NOT more energetic electrons. Higher frequency: more energetic electrons — higher kinetic energy — regardless of the light's intensity, a result classical wave theory could not explain at all.

What should I know about Stopping Potential?

To measure Ek_max: apply a decelerating voltage (stopping potential V_s). When V_s reduces electron current to zero: eV_s = Ek_max. V_s = Ek_max / e = (hf − φ) / e. Plotting V_s against frequency: straight line. Gradient = h/e (Planck's constant divided by electron charge). x-intercept = threshold frequency f₀. y-intercept = −φ/e (negative of work function in electron volts). This method was used by Millikan to accurately measure h — giving strong experimental confirmation of Einstein's quantum

What do I need to know about Historical Significance?

The photoelectric effect was explained by Einstein in 1905 — his Nobel Prize-winning paper (not Special Relativity). This was a foundational paper in the development of quantum mechanics. Before this, the wave theory of light (Maxwell's equations, 1865) successfully explained all known optical phenomena. The photoelectric effect required quantised photons — particles of light. This dual nature (wave and particle) of light is central to quantum mechanics. de Broglie later extended this duality to matter itself, proposing that particles like electrons also have an associated wavelength — an idea later confirmed experimentally and underpinning electron microscopy.