Photoelectric Effect Calculator | Work Function, Threshold Frequency & Stopping Voltage
Apply Einstein's photoelectric equation E = hf − φ to compute work function (φ), threshold frequency (f₀), threshold wavelength (λ₀), stopping voltage (Vs), and photoelectron kinetic energy. Includes a table of work functions for 15 common metals.
Frequency f (Hz)
1.5000e+15
Photon energy E (eV)
6.2041
Photon energy E (J)
9.9390e-19
KE max (eV)
1.9441
KE max (J)
3.1145e-19
Stopping voltage Vs (V)
1.9441
Ejection occurs?
Yes
Light region
Ultraviolet (UV)
METAL WORK FUNCTIONS
| Metal | φ (eV) | λ₀ threshold (nm) | Region |
|---|---|---|---|
| Cesium (Cs) | 2.1 | 591 | Visible |
| Potassium (K) | 2.3 | 539 | Visible |
| Sodium (Na) | 2.36 | 526 | Visible |
| Calcium (Ca) | 2.87 | 432 | Visible |
| Magnesium (Mg) | 3.66 | 339 | Ultraviolet (UV) |
| Aluminum (Al) | 4.08 | 304 | Ultraviolet (UV) |
| Lead (Pb) | 4.25 | 292 | Ultraviolet (UV) |
| Silver (Ag) | 4.26 | 291 | Ultraviolet (UV) |
| Tungsten (W) | 4.55 | 273 | Ultraviolet (UV) |
| Molybdenum (Mo) | 4.6 | 270 | Ultraviolet (UV) |
| Copper (Cu) | 4.65 | 267 | Ultraviolet (UV) |
| Iron (Fe) | 4.81 | 258 | Ultraviolet (UV) |
| Nickel (Ni) | 5.01 | 248 | Ultraviolet (UV) |
| Gold (Au) | 5.1 | 243 | Ultraviolet (UV) |
| Platinum (Pt) | 5.65 | 220 | Ultraviolet (UV) |
What Is the Photoelectric Effect Calculator | Work Function, Threshold Frequency & Stopping Voltage?
The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency strikes it. Albert Einstein explained this in 1905 using the concept of light quanta (photons), earning him the 1921 Nobel Prize in Physics. The observation that there is a threshold frequency below which no electrons are emitted — regardless of light intensity — could not be explained by classical wave theory.
When a photon of energy E = hf is absorbed by a surface electron, it uses φ (the work function) to escape the metal. Any remaining energy becomes kinetic energy of the ejected electron. If hf < φ, no electron is ejected no matter how bright the light. The stopping voltage Vs is the retarding potential required to bring the fastest electrons to rest: eVs = KE_max.
Work functions vary by metal and surface preparation. Alkali metals (Cs, K, Na) have low work functions and respond to visible light, while most metals require UV. Understanding the photoelectric effect is essential for designing photomultiplier tubes, CCD sensors, photodiodes, and solar cells.
Formula
Einstein's Photoelectric Equation: E_photon = h·f = h·c/λ KE_max = h·f − φ (kinetic energy of ejected photoelectron) e·Vs = KE_max (stopping voltage Vs) Threshold conditions (no ejection): f₀ = φ / h (threshold frequency) λ₀ = h·c / φ (threshold wavelength) Constants: h = 6.626×10⁻³⁴ J·s (Planck's constant) c = 3×10⁸ m/s (speed of light) e = 1.602×10⁻¹⁹ C (electron charge) 1 eV = 1.602×10⁻¹⁹ J
How to Use
- 1
Select a mode: From Wavelength, From Frequency, Find Threshold, or Find Work Function.
- 2
For From Wavelength: enter the wavelength λ in nm and the metal work function φ in eV.
- 3
For From Frequency: enter the frequency f in Hz or THz and the work function φ in eV.
- 4
For Find Threshold: enter the work function φ to find f₀ (Hz) and λ₀ (nm) and identify the light region.
- 5
For Find Work Function: enter incident frequency f (Hz) and measured stopping voltage Vs (V); the calculator identifies the nearest metal.
- 6
Compare your result against the metal work function table to identify the material.
Select a mode, enter the required values, and read photon energy, KE_max, stopping voltage, and ejection status. The metal work function table helps identify unknowns.
Example Calculation
Problem: UV light of wavelength 200 nm strikes a silver surface (φ = 4.26 eV). Find E_photon, KE_max, and Vs.
Solution:
f = c/λ = 3×10⁸ / 200×10⁻⁹ = 1.50×10¹⁵ Hz
E = hf = 6.626×10⁻³⁴ × 1.50×10¹⁵ = 9.94×10⁻¹⁹ J = 6.21 eV
KE_max = 6.21 − 4.26 = 1.95 eV = 3.12×10⁻¹⁹ J
Vs = KE_max / e = 1.95 V
The photon energy exceeds φ so ejection occurs. A stopping voltage of 1.95 V would halt the fastest electrons.
Understanding Photoelectric Effect | Work Function, Threshold Frequency & Stopping Voltage
Key Observations and Classical vs. Quantum Explanation
| Observation | Classical Wave Prediction | Quantum (Einstein) Explanation |
|---|---|---|
| Threshold frequency | None — any frequency should work given enough intensity | Photon energy must exceed φ; hf < φ means no ejection ever |
| Instantaneous emission | Delay expected for energy accumulation | Single photon absorbed instantly, no accumulation needed |
| KE independent of intensity | Brighter light → more energy → higher KE | KE_max = hf − φ depends only on frequency, not intensity |
| Emission rate ∝ intensity | Not predicted for threshold behaviour | More photons → more ejections, but same KE per electron |
Modern Applications of the Photoelectric Effect
- ›Solar cells (photovoltaics): photons with E > bandgap eject electrons across a p-n junction, generating current.
- ›CCD and CMOS image sensors: photons eject electrons trapped in potential wells; charge is read out to form an image.
- ›Photomultiplier tubes: single photon ejects electron via photoelectric effect; amplified 10⁶× by secondary emission.
- ›X-ray photoelectron spectroscopy (XPS): measures binding energies of core electrons using the photoelectric effect.
- ›Night-vision devices and photocathode electron sources in particle accelerators.
- ›Automatic door sensors and smoke detectors use light beam interruption based on photoelectric principles.
Frequently Asked Questions
Why does increasing light intensity not increase the kinetic energy of ejected electrons?
In the quantum picture, intensity determines the number of photons per second, but each photon carries a fixed energy hf. Each ejected electron absorbs exactly one photon. KE_max = hf − φ depends only on frequency. More intensity means more electrons ejected per second, but each has the same maximum kinetic energy. Classical wave theory incorrectly predicts that higher intensity should give higher KE.
What is the stopping voltage and how is it measured?
The stopping voltage Vs is the minimum reverse potential applied to the collector electrode that prevents even the fastest ejected electrons from reaching it. When the collector is at −Vs relative to the emitter, all electrons with KE ≤ eVs are stopped. Measuring Vs for different frequencies gives a linear plot (Vs vs f) with slope h/e, allowing Planck's constant to be determined experimentally.
Why do alkali metals respond to visible light?
Alkali metals (Cs, K, Na) have only one valence electron loosely held by the nucleus, giving them low work functions (2–3 eV). Visible photons have energies 1.8–3.1 eV. For Cs (φ = 2.1 eV), photons with λ < 591 nm (green) are sufficient for ejection. Most other metals have work functions 4–6 eV and require UV light.
What is the relationship between the photoelectric effect and quantum mechanics?
Einstein's 1905 explanation of the photoelectric effect was the first application of energy quantisation to light (photons). It established that electromagnetic radiation has particle-like properties with discrete energy quanta E = hf. This particle-wave duality is a cornerstone of quantum mechanics, complemented by de Broglie's matter waves and formalised in Schrödinger's equation.
How does work function depend on surface preparation?
Work function is sensitive to surface contamination, oxide layers, crystal face, and adsorbed gases. A clean (110) face of tungsten has φ ≈ 5.25 eV while a (100) face gives φ ≈ 4.63 eV. Cesium monolayer coatings on metals dramatically reduce φ to ~1.4 eV, used in night-vision photocathodes. Tabulated values assume clean, well-defined surfaces under vacuum.
You Might Also Like
Explore 360+ Free Calculators
From math and science to finance and everyday life — all free, no account needed.