E_k(max) = hν − φ with preset metal work functions or custom φ: threshold frequency, cutoff wavelength, emission verdict, stopping voltage, and photoelectron speed.
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Tool usage guide
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Key facts
Category
Science & Education
Input types
select, number
Output type
text
Sample coverage
4
API ready
Yes
Overview
The Photoelectric Effect Calculator evaluates Einstein's photoelectric equation (E_k(max) = hν − φ) to analyze electron emission from metal surfaces. Input photon parameters via wavelength or frequency along with preset cathode materials or custom work functions to compute photon energy, threshold frequency, cutoff wavelength, maximum kinetic energy, stopping voltage, and photoelectron speed.
When to use
Determining whether incident light at a given wavelength or frequency has enough energy to eject electrons from a specific metal cathode.
Calculating stopping voltage and maximum photoelectron kinetic energy for physics lab verification and homework problems.
Finding cutoff wavelengths and threshold frequencies for metals like cesium, sodium, zinc, copper, or custom materials.
How it works
1Select whether to specify the incident photon by wavelength (with units in µm, nm, or pm) or frequency in Hz.
2Choose a preset cathode metal (cesium, sodium, potassium, calcium, zinc, copper, or platinum) or select custom to enter a work function φ in eV.
3The tool computes total photon energy, material threshold values (ν₀ and λ₀), and determines the emission verdict.
4If photon energy exceeds the work function, it calculates the maximum kinetic energy (E_k(max)), required stopping voltage (V_s), and photoelectron speed.
Use cases
Physics students solving quantum mechanics problems involving photon energy and work function thresholds.
Laboratory researchers verifying experimental stopping potentials against theoretical metal work functions.
Educators demonstrating why light below cutoff frequency fails to eject electrons regardless of intensity.
Examples
1. Violet Light on Cesium Cathode
Physics Undergrad
Background
An undergraduate physics student is analyzing a modern physics lab experiment using a 400 nm light source on a cesium target.
Problem
Calculate whether electron emission occurs, the cutoff wavelength, and the required stopping voltage.
How to use
Set photonSpec to 'wavelength', enter 400 in wavelength with unit 'nm', and select 'cesium' as the metal cathode.
Outcome
Calculates photon energy of 3.10 eV against cesium's φ = 2.14 eV, yielding an emission verdict with E_k(max) = 0.96 eV, stopping voltage of 0.96 V, and a cutoff wavelength of 579.4 nm.
2. Testing Below-Threshold Light on Zinc
High School Physics Teacher
Background
A teacher is preparing a class demonstration explaining why red light cannot eject photoelectrons from high work function metals.
Problem
Demonstrate that 4.3 × 10¹⁴ Hz red light cannot overcome zinc's work function.
How to use
Set photonSpec to 'frequency', enter 430000000000000 in frequency, and select 'zinc' as the metal cathode.
Outcome
FAQ
What equation does this calculator use?
It uses Einstein's photoelectric equation: E_k(max) = hν − φ, where h is Planck's constant, ν is frequency, and φ is the material work function.
What happens if the photon energy is less than the work function?
No electrons are emitted, kinetic energy and stopping voltage are zero, and increasing light intensity will not cause emission.
Which preset cathode metals are available?
You can select cesium, sodium, potassium, calcium, zinc, copper, platinum, or provide a custom work function in eV.
What is the relationship between stopping voltage and maximum kinetic energy?
Stopping voltage (V_s) equals maximum kinetic energy divided by elementary charge (e), so an E_k(max) of 1.5 eV requires a stopping voltage of 1.5 V.
Which wavelength units are supported?
The calculator accepts wavelength inputs in micrometers (µm), nanometers (nm), and picometers (pm).
Displays photon energy of 1.78 eV against zinc's φ = 4.33 eV, confirming no electron emission and showing a threshold frequency of 1.05 × 10¹⁵ Hz (UV cutoff at 286.3 nm).