# Photoelectric Effect Calculator

E_k(max) = hν − φ with preset metal work functions or custom φ: threshold frequency, cutoff wavelength, emission verdict, stopping voltage, and photoelectron speed.

> Canonical page: https://elysiatools.com/en/tools/photoelectric-effect-calculator

- **Category:** Science & Education

- **Keywords:** photoelectric effect, work function, photon energy, stopping voltage, threshold frequency, einstein, quantum mechanics

## 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.

## Inputs

- **Photon specified by** (select)
- **Photon wavelength λ** (number): e.g. 400
- **λ unit** (select)
- **Photon frequency ν (Hz)** (number): e.g. 5.5e14
- **Cathode material** (select)
- **Custom work function φ (eV)** (number): e.g. 4.5

## 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

- Select whether to specify the incident photon by wavelength (with units in µm, nm, or pm) or frequency in Hz.
- Choose a preset cathode metal (cesium, sodium, potassium, calcium, zinc, copper, or platinum) or select custom to enter a work function φ in eV.
- The tool computes total photon energy, material threshold values (ν₀ and λ₀), and determines the emission verdict.
- If 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.

## Frequently asked questions

### 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).

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