⚛️ Photoelectric Effect Calculator
Calculate photon energy, maximum kinetic energy, work function, threshold frequency, and stopping potential using Einstein's photoelectric equation. Choose what to solve for and get step-by-step results.
What Is the Photoelectric Effect?
The photoelectric effect is the emission of electrons from a material (usually a metal) when light of sufficiently high frequency shines on its surface. It was discovered by Heinrich Hertz in 1887 and explained by Albert Einstein in 1905 — work that earned him the Nobel Prize in Physics in 1921.
The photoelectric effect was one of the first experimental proofs that light behaves as particles (photons) rather than purely as waves. Key observations include:
- Electrons are emitted only if the light frequency exceeds a threshold frequency (f₀), regardless of light intensity.
- The maximum kinetic energy of emitted electrons depends on the light frequency, not intensity.
- The number of emitted electrons (photocurrent) is proportional to light intensity.
- Emission is instantaneous — there is no time delay.
Einstein's Photoelectric Equation
Einstein proposed that light consists of discrete packets of energy called photons, each with energy:
E = hf = hc/λ
When a photon hits a metal surface, its energy is transferred to an electron. A minimum amount of energy — the work function (φ) — is required to free the electron from the metal. Any excess energy becomes the electron's kinetic energy:
Kmax = hf − φ = hc/λ − φ
where Kmax = maximum kinetic energy (J or eV), h = Planck's constant (6.626 × 10⁻³⁴ J·s), f = frequency (Hz), c = speed of light, λ = wavelength (m), φ = work function (J or eV)
Threshold Frequency and Wavelength
The threshold frequency (f₀) is the minimum frequency of light required to emit electrons. At this frequency, Kmax = 0, so:
f₀ = φ / h
and the corresponding threshold wavelength is λ₀ = hc / φ
Light with frequency below f₀ cannot eject electrons, no matter how intense it is. This is one of the key observations that classical wave theory could not explain.
Stopping Potential
The stopping potential (Vs) is the reverse voltage required to stop the most energetic emitted electrons. It is related to Kmax by:
eVs = Kmax
so Vs = Kmax / e
Why Use This Calculator?
- Solve for any variable: Calculate Kmax, work function, or stopping potential.
- Metal presets: Auto-fill work function for common metals.
- Step-by-step solution: See exactly how the calculation is performed.
- Energy visualization: See how photon energy is distributed.
- Free & private: No registration, no data storage — all calculations are done in your browser.
❓ Photoelectric Effect Calculator FAQ
What is the photoelectric effect?
The photoelectric effect is the emission of electrons from a material when light of sufficient frequency shines on it. It provided key evidence that light behaves as particles (photons).
What is Einstein's photoelectric equation?
Einstein's equation is Kmax = hf − φ, where Kmax is the maximum kinetic energy of emitted electrons, h is Planck's constant, f is the light frequency, and φ is the work function of the metal.
What is work function?
The work function (φ) is the minimum energy required to remove an electron from the surface of a material. It is typically measured in electron-volts (eV).
What is threshold frequency?
The threshold frequency (f₀) is the minimum frequency of light required to emit electrons from a metal surface. It is related to the work function by f₀ = φ/h.
What is stopping potential?
The stopping potential (Vs) is the reverse voltage needed to stop the most energetic emitted electrons. It is related to Kmax by eVs = Kmax.
Why does increasing light intensity not increase Kmax?
Increasing intensity increases the number of photons (and thus the photocurrent), but each photon still has the same energy E = hf. The maximum kinetic energy depends only on the frequency, not intensity.
What is the value of Planck's constant?
Planck's constant is h = 6.626 × 10⁻³⁴ J·s (or 4.136 × 10⁻¹⁵ eV·s).
What are some practical applications?
The photoelectric effect is used in solar panels, digital cameras, photomultiplier tubes, automatic door sensors, light meters, and imaging technology.
How accurate is this calculator?
This calculator uses the exact Einstein photoelectric equation with standard physical constants (CODATA 2022). Accuracy depends on the precision of input values.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required.