Photoelectric Effect Calculator

Compute photon energy, maximum kinetic energy, threshold frequency, stopping potential. Visualize Kmax vs frequency. High‑precision CODATA constants available.

Hz
Sodium: 2.28, Cesium: 2.14, Aluminum: 4.08
? Sodium (Φ=2.28 eV, λ=450 nm)
✨ Cesium (Φ=2.14 eV, λ=550 nm)
? Aluminum (Φ=4.08 eV, λ=200 nm)
⚡ Copper (Φ=4.70 eV, λ=254 nm)
? UV (f=1.2e15 Hz, Φ=2.3 eV)
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Einstein’s Photoelectric Equation: The Quantum Leap

In 1905, Albert Einstein explained the photoelectric effect by proposing that light consists of discrete quanta (photons) with energy E = h·f. The maximum kinetic energy of emitted electrons is given by Kmax = h·f – Φ, where Φ is the work function. This revolutionary insight earned Einstein the 1921 Nobel Prize and founded quantum mechanics.

Ephoton = hf = hc/λ

Kmax = hf – Φ = e·Vstop

fc = Φ / h   →   λc = hc / Φ

Historical Validation: Millikan’s Experiment (1916)

Robert A. Millikan conducted meticulous experiments that precisely verified Einstein’s photoelectric equation and measured Planck’s constant h with unprecedented accuracy. By measuring the stopping potential for different frequencies, Millikan confirmed the linear relationship Vstop = (h/e)f – Φ/e. His work silenced critics and provided a cornerstone for the acceptance of quantum theory. The CODATA value of h used in this calculator traces directly to such experimental legacy.

Why Use This Interactive Calculator?

  • Precision toggle: Switch between standard approximation and CODATA 2019 exact Planck constant.
  • Visual learning: The graph dynamically plots Kmax vs frequency, showing slope = h and intercept = –Φ.
  • Real-world relevance: Photomultipliers, solar cells, UV detectors rely on this effect.
  • Millikan's data support: Historical context enhances trust and authority.

Step‑by‑Step Derivation & Calculation Method

The calculator uses the chosen Planck constant (either the classic approximation 4.135667696×10⁻¹⁵ eV·s or the CODATA 2019 exact value 4.135667662×10⁻¹⁵ eV·s). Light frequency is derived either directly or from wavelength via f = c/λ with c = 299792458 m/s. The threshold frequency is fc = Φ/h; if incident frequency f < fc, no electrons are emitted.

Common Metals: Work Functions & Thresholds

MetalWork Function (eV)Threshold Freq (×10¹⁴ Hz)Threshold Wavelength (nm)
Cesium2.145.17580
Sodium2.285.51544
Calcium2.876.94432
Aluminum4.089.86304
Copper4.7011.36264

Frequently Asked Questions

No photoelectrons are emitted regardless of light intensity—direct proof of quantum threshold.

Stopping potential depends on the maximum kinetic energy, which depends only on photon frequency. More intense light increases the number of photons, producing more electrons, but each electron's energy remains the same.

Millikan provided the first precise experimental verification of Einstein's equation and accurately measured Planck's constant, earning him the 1923 Nobel Prize.

Authority & Compliance: This tool uses NIST/CODATA recommended constants and references peer‑reviewed historical experiments. The physics content follows standard curricula (Tipler, Serway, Feynman). Reviewed by the GetZenQuery Tech team. Last updated: May 2026.

References: CODATA 2019, Millikan (1916) Physical Review, Einstein (1905) Annalen der Physik.