Photoelectric Effect Calculator
Choose a metal, describe the light by wavelength, frequency or photon energy, and get the maximum kinetic energy of the ejected electrons, the stopping potential, their top speed and the metal's threshold frequency and wavelength. The energy bar and the Einstein graph show where the photon's energy goes, and a second mode finds Planck's constant from stopping-potential data. It uses the exact SI values of h and e. Free, no sign-up.
Results
0.8096 eV
Maximum kinetic energy (KEmax)
0.8096 V
Stopping potential
1.297 × 10⁻¹⁹ J
KEmax in joules
533700 m/s
Fastest electron speed
553.7 THz
Threshold frequency
541.4 nm
Threshold wavelength
The working
- Photon: f = 749.5 THz, so E = h × f = 3.1 eV
- KEmax = E − φ = 3.1 eV − 2.29 eV = 0.8096 eV
- Threshold: f₀ = φ ÷ h = 553.7 THz, and λ₀ = hc ÷ φ = 541.4 nm
Work functions of common metals
| Metal | φ (eV) | Handbook range (eV) | Threshold wavelength (nm) |
|---|---|---|---|
| Cesium (Cs) | 1.95 | — | 635.8 |
| Rubidium (Rb) | 2.261 | — | 548.4 |
| Potassium (K) | 2.29 | — | 541.4 |
| Sodium (Na) | 2.75 | — | 450.9 |
| Calcium (Ca) | 2.87 | — | 432 |
| Lithium (Li) | 2.90 | — | 427.5 |
| Zinc (Zn) | 3.63 | 3.63–4.90 | 341.6 |
| Magnesium (Mg) | 3.66 | — | 338.8 |
| Aluminium (Al) | 4.06 | 4.06–4.26 | 305.4 |
| Lead (Pb) | 4.25 | — | 291.7 |
| Silver (Ag) | 4.26 | 4.26–4.74 | 291 |
| Tungsten (W) | 4.32 | 4.32–4.55 | 287 |
| Titanium (Ti) | 4.33 | — | 286.3 |
| Copper (Cu) | 4.53 | 4.53–5.10 | 273.7 |
| Iron (Fe) | 4.67 | 4.67–4.81 | 265.5 |
| Beryllium (Be) | 4.98 | — | 249 |
| Nickel (Ni) | 5.04 | 5.04–5.35 | 246 |
| Gold (Au) | 5.10 | 5.10–5.47 | 243.1 |
| Platinum (Pt) | 5.12 | 5.12–5.93 | 242.2 |
Values from the CRC Handbook of Chemistry and Physics (2008), as tabulated in Wikipedia's Work function article. Where the handbook gives a range, which depends on the crystal face and surface condition, the lowest value is used in the calculator.
How to Use the Photoelectric Effect Calculator
- 1. Describe the light. Enter a wavelength, a frequency or a photon energy, with the unit that suits it (nm, THz, eV and so on).
- 2. Choose the metal. The menu lists nineteen metals with their work functions in eV, ordered from cesium (the easiest to free electrons from) to platinum. Pick Enter my own for a value from your textbook.
- 3. Read the result. You get the maximum kinetic energy and the stopping potential, the fastest electron's speed, and the threshold frequency and wavelength. If the light is below threshold, the calculator says so instead of showing a negative energy.
- 4. For a lab report, use the second mode. Enter pairs of frequency and stopping potential and the calculator fits the straight line, giving h from the slope and the work function from the intercept.
Einstein's Photoelectric Equation
Light of frequency f arrives in quanta, photons, each with energy E = hf, where h = 6.626 070 15 × 10⁻³⁴ J·s is the Planck constant. A photon that strikes a metal can free one electron, but the electron must first pay the work function φ, the minimum energy needed to escape the surface. What is left over is kinetic energy: KEmax = hf − φ. The most energetic electrons come from the surface; those from deeper in lose more on the way out, so only a maximum is predicted.
| Quantity | Formula | Notes |
|---|---|---|
| Photon energy | E = hf = hc ÷ λ | E(eV) = 1239.84 ÷ λ(nm) |
| Maximum kinetic energy | KEmax = hf − φ | Zero or less means no emission |
| Stopping potential | Vₛ = KEmax ÷ e | Numerically equal to KEmax in eV |
| Threshold frequency | f₀ = φ ÷ h | Below it, no electrons at any intensity |
| Threshold wavelength | λ₀ = hc ÷ φ | Longest wavelength that works |
| Maximum speed | v = √(2 KEmax ÷ mₑ) | Non-relativistic; mₑ = 9.109 × 10⁻³¹ kg |
Worked Example: 400 nm Light on Potassium
- Photon energy: E = 1239.84 ÷ 400 = 3.100 eV, which is a frequency of 749.5 THz.
- Work function of potassium: φ = 2.29 eV.
- KEmax = 3.100 − 2.29 = 0.8096 eV, which is 1.297 × 10⁻¹⁹ J, so the stopping potential is 0.8096 V.
- The fastest electrons move at v = √(2 × 1.297 × 10⁻¹⁹ ÷ 9.109 × 10⁻³¹) = 5.337 × 10⁵ m/s.
- Threshold: f₀ = 2.29 eV ÷ h = 553.7 THz, so λ₀ = 541.4 nm. Green light of 532 nm still works for potassium; orange light of 600 nm (2.07 eV) does not.
What the Photoelectric Effect Showed
- A threshold frequency. Below f₀ no electrons are emitted, however bright the light. Classical wave theory predicted that enough intensity should always eventually eject electrons.
- Intensity changes the number, not the energy. Brighter light of the same frequency gives more photons and so more electrons (a larger photocurrent), but KEmax is unchanged. KEmax rises only with frequency.
- Emission is immediate. Electrons appear within about a nanosecond of the light arriving, with no build-up delay, because each is freed by a single photon.
- A straight line of slope h. KEmax against frequency is a straight line whose slope is always h and whose intercepts are −φ and f₀, whatever the metal. Einstein explained this in 1905 and received the 1921 Nobel Prize in Physics for it; Robert Millikan's careful measurements of stopping potentials in 1914–1916 confirmed it and gave an accurate value of h.
A note on the work function values
Work functions depend on the crystal face and, strongly, on surface contamination and oxide films. The values come from the CRC Handbook of Chemistry and Physics (2008), as tabulated in Wikipedia's Work function article. Where the handbook lists a range (copper 4.53–5.10 eV, for example), the lowest value is used here, so check your own course data if your problem gives a different φ. Cesium's modern value is 1.95 eV; some older textbooks give 2.14 eV.
Frequently Asked Questions
- What is the photoelectric effect equation?
- KEmax = hf − φ, where h is Planck's constant, f the light's frequency and φ the metal's work function. It is conservation of energy: each photon gives all its energy hf to one electron, φ of it is spent escaping, and the rest is kinetic energy.
- What is the stopping potential?
- The reverse voltage that just stops the most energetic photoelectrons from reaching the collector, so that the current falls to zero. It satisfies eVₛ = KEmax, so in volts it equals KEmax in electronvolts: 0.8 eV needs 0.8 V.
- How do you find the threshold frequency?
- Divide the work function, in joules, by Planck's constant: f₀ = φ ÷ h. For a work function of 2.29 eV (3.67 × 10⁻¹⁹ J) that is 5.54 × 10¹⁴ Hz. Light below this frequency cannot eject electrons from that metal.
- Why does brighter light not give the electrons more energy?
- Because each electron is freed by one photon, and brightness only changes how many photons arrive per second. The energy of each photon depends on the frequency alone, so a brighter beam frees more electrons, not faster ones.
- How can the photoelectric effect be used to measure Planck's constant?
- Measure the stopping potential for several frequencies and plot it against frequency. The slope of the straight line is h/e and the vertical intercept is −φ/e, so h = e × slope. The second mode of the calculator fits the line for you.
- Which metals show the photoelectric effect with visible light?
- Those with a work function below about 3.1 eV: the alkali metals cesium, rubidium, potassium, sodium and lithium, and calcium. Most other metals, with work functions of 4 eV or more, need ultraviolet light, which is why they are not seen to emit in ordinary light.