Photoelectric Threshold Wavelength Calculator
Type a work function such as 2.28 eV and see the longest wavelength that still knocks electrons out of the surface, in nanometres and metres, with the matching frequency. Longer waves fail however bright the light. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Work function ev
- 2.28
- Work function j
- 0
- Threshold wavelength m
- 0.0000005438
- Threshold wavelength nm
- 543.7903440053
- Threshold frequency hz
- 551,301,547,195,361
The photoelectric threshold wavelength calculator finds the longest wavelength of light that can eject electrons from a metal surface. Enter the metal's work function in electronvolts, and the calculator applies the relation between photon energy, Planck's constant, and the speed of light. It reports the threshold in metres and nanometres, along with the matching frequency and the converted work function in joules. The calculation is deterministic and is useful for physics exercises, laboratory planning, and quick checks of photoelectric-effect data.
What the threshold wavelength means
In the photoelectric effect, a surface releases an electron only when an incoming photon supplies at least the material's work function. The threshold wavelength is the longest wavelength whose photons still carry that minimum energy. Light with a longer wavelength has less energy per photon and cannot eject electrons from the idealized surface, regardless of how intense the beam becomes.
Light at the threshold provides exactly enough energy for emission, leaving zero maximum kinetic energy in the simplified model. Shorter wavelengths provide more energy, so the excess may appear as electron kinetic energy. This calculator treats the supplied work function as the effective energy barrier and returns the boundary defined by that value.
Real surfaces can differ because of contamination, crystal orientation, coatings, temperature, or measurement conditions. For that reason, use a work function appropriate to the actual sample when interpreting laboratory results, rather than assuming every specimen of a named metal has one universal value.
How the calculation is performed
The calculation begins with the photon relation E = hc divided by wavelength. At the emission threshold, photon energy E equals the metal work function. Rearranging gives threshold wavelength = hc divided by the work function.
The entered work function is expressed in electronvolts, so it is first multiplied by the exact joules-per-electronvolt conversion. The algorithm then multiplies the exact defined value of Planck's constant by the exact speed of light and divides that product by the energy in joules. The result in metres is also multiplied by one billion to give nanometres.
The corresponding threshold frequency is calculated by dividing the work function in joules by Planck's constant. All reported values come from the same input and constants, which keeps the wavelength and frequency mutually consistent. The calculator rejects zero, negative, missing, nonnumeric, infinite, and unrepresentable inputs instead of returning a physically meaningless result.
It rounds only the displayed numeric results to stable significant precision.
How to use and interpret the result
Enter the work function as a positive number in electronvolts. Values are commonly found in reference tables or measured from a particular surface. Read the nanometre result when comparing the threshold with ultraviolet, visible, or infrared wavelength ranges; use the metre value when substituting into SI equations.
The threshold frequency gives the same boundary in frequency form. A source can cause photoemission in the basic one-photon model when its wavelength is at or below the returned threshold, or equivalently when its frequency is at or above the returned frequency. The result does not predict photocurrent, quantum efficiency, electron yield, stopping potential, or the kinetic-energy distribution.
Those quantities require more information, such as incident wavelength, optical power, surface condition, and experimental geometry. Also distinguish vacuum wavelength from wavelength inside a medium: standard photon-energy tables and this calculation use the vacuum relation with the defined speed of light.
What you can do with it
Check a physics exercise
Convert a stated work function into the limiting wavelength and verify the units before continuing with photoelectron energy calculations.
Select an illumination source
Compare a lamp or laser wavelength with a surface's theoretical photoemission threshold during early experiment planning.
Validate reference data
Cross-check whether published work-function, threshold-frequency, and threshold-wavelength values are mutually consistent.
FAQ
What input does the calculator require?
It requires the metal's work function as a positive finite number in electronvolts (eV).
Why is this the longest wavelength that ejects electrons?
Photon energy decreases as wavelength increases. At the threshold, one photon has exactly the work-function energy; any longer wavelength provides too little energy in the basic model.
Does brighter light with a wavelength above the threshold eject electrons?
Not in the basic one-photon photoelectric model. Greater intensity supplies more photons, but each photon still has insufficient energy.
Are the physical constants exact?
The calculation uses the defined SI values of Planck's constant, the speed of light, and the electronvolt-to-joule conversion.
Does the result include electron kinetic energy?
No. At the threshold, the ideal maximum kinetic energy is zero. Calculating kinetic energy requires the actual incident photon wavelength or frequency.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/optics/photoelectric-threshold-wavelength \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"work_function_ev":2.28}'const res = await fetch("https://api.kit.forhosting.com/optics/photoelectric-threshold-wavelength", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"work_function_ev": 2.28
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/optics/photoelectric-threshold-wavelength",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"work_function_ev": 2.28
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/photoelectric-threshold-wavelength", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"work_function_ev":2.28}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"work_function_ev":2.28}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/photoelectric-threshold-wavelength", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"work_function_ev": 2.28
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "optics.photoelectric_threshold_wavelength",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How to use and interpret the result
For automated calls, the base request price is $0.002; the same deterministic formula is used for every valid request.
Technical questions
What does an API calculation cost?
Each API request uses the base price $0.002.