Photoelectric Effect Calculator — Photon Energy & Work Function
Calculate photon energy, work function, stopping potential, and maximum kinetic energy for the photoelectric effect using E=hf.
Photoelectric Effect Guide
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.
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 (hi
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
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
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