Photoelectric Effect Simulator

Verified Content: All equations, formulas, and reference data in this simulation have been verified by the Simulations4All engineering team against authoritative sources including NIST physical constants database, MIT OpenCourseWare physics courses, and HyperPhysics. See verification log

Introduction

Here is what happens when you actually try this experiment: you shine a brilliant red heat lamp on a zinc plate. Nothing. Crank up the intensity until the lamp is painfully bright. Still nothing. Not a single electron budges. Now switch to a faint ultraviolet source, so dim you can barely see it. Electrons start flying off immediately.

The universe does not care about our intuition, but this result baffled the finest physicists of the early 1900s. Classical wave theory had a perfectly sensible prediction: give the electrons enough energy (brighter light, more intensity) and eventually they will escape. Just be patient. The math was clear. The experiments said otherwise [1].

What Einstein figured out was that light does not deliver energy the way waves in the ocean do. Instead, light comes in discrete packets, like tiny bullets of energy. Each packet (what we now call a photon) either has enough energy to kick out an electron or it does not. A million weak punches will never equal one strong punch. That is the photoelectric effect in one sentence, and it earned Einstein the 1921 Nobel Prize. Not relativity. This seemingly simple observation about light and metal. The elegant part is how completely it broke classical physics and forced us to accept that nature operates by rules we never anticipated [2].

What Is the Photoelectric Effect?

The photoelectric effect is electrons escaping from a metal surface when light hits it. Sounds straightforward. But the details turned a century of physics on its head.

Heinrich Hertz stumbled upon it in 1887 while doing something else entirely. He was generating electromagnetic waves (proving Maxwell's equations) when he noticed that ultraviolet light made sparks jump more easily between metal electrodes. Odd behavior, but he was busy with other things [3].

Philipp Lenard picked up the investigation around 1902. Here is what he found when he measured carefully: the kinetic energy of ejected electrons depended on the color of the light, not how bright it was. Red light at any intensity? Zero electrons from zinc. Faint violet light? Electrons with measurable speed. Brighter violet light gave more electrons, but each electron had the same speed as before [3].

Classical physics predicted three things, and all three were wrong:

Classical Prediction 1: Any frequency should work if you wait long enough or make it bright enough. Reality: Below a threshold frequency, nothing happens. Ever.

Classical Prediction 2: Brighter light should produce faster electrons. Reality: Brighter light produces more electrons, but they all have the same maximum speed.

Classical Prediction 3: There should be a time delay while energy accumulates in the electron. Reality: Emission is instantaneous. Within nanoseconds of light hitting the surface.

If you could slow this down enough to watch, you would see individual photons arriving at the metal surface. Each photon either has enough energy (based on its frequency) to knock out one electron, or it does not. Think of it like a vending machine with a minimum payment. Dropping in a hundred pennies one at a time will never buy you a soda. You need a coin worth at least the threshold amount, all at once [4].

How the Simulator Works

Using the Controls

The simulation layout mirrors how actual photoelectric experiments work. You have a light source shining on a metal cathode inside a vacuum tube, with a collector plate that catches ejected electrons.

Metal Selection: Start here. Each metal has a different work function, which sets the threshold frequency. Cesium (phi = 2.1 eV) responds to visible yellow-green light. Copper (phi = 4.7 eV) needs deep ultraviolet.

Frequency Slider: This is your main experimental variable. Watch the wavelength display and color indicator as you sweep from infrared (low frequency, red) through visible to ultraviolet (high frequency, violet and beyond).

Intensity Slider: Classical physics says this should matter for whether electrons escape. It does not. Intensity only affects how many electrons leave, not whether any leave at all.

Stopping Voltage: Apply positive voltage to repel electrons back toward the cathode. When current drops to zero, you have measured the maximum kinetic energy: eV_stop = KE_max.

Keyboard tip: Use left/right arrow keys for fine frequency adjustments. Hold Shift for larger steps. This is the fastest way to find threshold frequencies precisely.

The Physics of Photoelectric Emission

Einstein's Equation

The core relationship that earned Einstein his Nobel Prize:

KE_max = hf − φ

Here is what this equation actually says: every photon carries energy equal to hf (Planck's constant times frequency). When a photon hits an electron in the metal, the electron absorbs all of that energy in one instant. The electron then spends exactly φ of that energy escaping the metal surface. Whatever remains becomes kinetic energy [2].

The variables:

• h = 6.626 × 10⁻³⁴ J·s (or 4.136 × 10⁻¹⁵ eV·s in more convenient units)
• f = frequency of the incident light in Hz
• φ = work function, the minimum energy needed to remove an electron from that specific metal
• KE_max = maximum kinetic energy of ejected electrons

Why "maximum" kinetic energy? Because electrons sit at different depths in the metal. Surface electrons escape with the full leftover energy. Deeper electrons lose some energy to collisions before reaching the surface.

Threshold Frequency

Set KE_max = 0 in Einstein's equation and solve for f:

f₀ = φ / h

This is the cutoff. Below this frequency, the photon energy (hf) is less than the work function (φ), so KE_max would be negative. That is physically impossible, so no electrons escape. The elegant part is that this threshold is sharp. At 5.50 × 10¹⁴ Hz for sodium, zero electrons. At 5.51 × 10¹⁴ Hz, electrons start flying. Classical wave theory has no explanation for such a sharp boundary [4].

The corresponding threshold wavelength:

λ₀ = c / f₀ = hc / φ

For cesium (φ = 2.1 eV), this works out to about 590 nm, which is orange-yellow visible light. For copper (φ = 4.7 eV), it is 264 nm, firmly in the ultraviolet.

Stopping Potential

Here is what happens when you actually try to measure electron kinetic energy: apply a positive voltage to the collector relative to the cathode. This creates an electric field that opposes electron motion. Electrons lose kinetic energy climbing this potential hill.

When the voltage is just high enough to stop the fastest electrons:

eV_stop = KE_max

Combining with Einstein's equation:

V_stop = (hf − φ) / e = (h/e)f − φ/e

The stopping voltage varies linearly with frequency. Plot V_stop versus f for multiple frequencies, and the slope gives you h/e. This is exactly what Millikan did, and his precise measurements gave a value for Planck's constant that matched the value from blackbody radiation experiments [5].

Why Intensity Does Not Matter (for Energy)

This is the counterintuitive result that classical physics could not explain. Doubling the light intensity doubles the number of photons hitting the surface per second. Each photon still carries the same energy hf. Each ejected electron still has the same maximum kinetic energy.

More photons means more electrons, which means more current. But each electron-photon interaction is independent. A single photon either has enough energy or it does not. Intensity is just how many tries per second.

Think of throwing balls at a row of bottles at a carnival. Throwing faster (higher frequency) knocks bottles down. Throwing more balls (higher intensity) knocks down more bottles. But throwing 1000 soft balls will never knock down a bottle that one fast ball would.

Learning Objectives

After working through this simulation, you should be able to:

1. Explain the failure of classical physics: Describe why wave theory predicts continuous energy absorption and why experimental results contradict this
2. Apply Einstein's photoelectric equation: Calculate maximum kinetic energy, threshold frequency, or stopping potential given appropriate inputs
3. Predict threshold behavior: Determine whether a given photon frequency will cause emission from a specific metal
4. Interpret I-V curves: Extract physical meaning from photocurrent versus voltage graphs
5. Measure Planck's constant: Use stopping voltage data at multiple frequencies to determine h experimentally
6. Compare quantum and classical predictions: Articulate specific testable differences between the two frameworks

Exploration Activities

Activity 1: The Classical Physics Failure

Objective: See why classical wave theory fails to explain photoelectric observations

Setup: Select the "Classical Test" preset. This configures high intensity red light on zinc.

Steps:

1. Click Start and observe the chamber. No electrons leave despite high intensity.
2. Enable "Show Classical Prediction" checkbox. Note that classical theory expects emission.
3. Slowly increase frequency while keeping intensity at 100%.
4. Record the exact frequency when the first electrons appear.
5. Now reduce intensity to 10% at that same frequency. Electrons still emit.

What you should observe: Classical physics is wrong twice: high intensity below threshold produces nothing, while low intensity above threshold produces emission immediately. The threshold is about frequency, not intensity.

Activity 2: Finding the Threshold Frequency

Objective: Measure f₀ experimentally and compare to the theoretical value

Setup: Select sodium (work function 2.28 eV)

Steps:

1. Set frequency to 4.0 × 10¹⁴ Hz (below threshold)
2. Increase frequency in steps of 0.1 × 10¹⁴ Hz using arrow keys
3. Watch the emission status indicator carefully
4. Record the frequency when "No Emission" changes to "Emitting"
5. Calculate theoretical threshold: f₀ = φ/h = 2.28 eV / (4.136 × 10⁻¹⁵ eV·s) = 5.51 × 10¹⁴ Hz

Expected result: Your measured threshold should match the calculated value within the slider resolution. The transition is sharp because quantum effects do not compromise.

Activity 3: Measuring Planck's Constant

Objective: Determine h from the slope of V_stop versus frequency

Steps:

1. Select sodium, set frequency to 6.0 × 10¹⁴ Hz
2. Start the simulation and adjust stopping voltage until current just reaches zero
3. Record (f, V_stop) in the data recording section
4. Repeat for f = 7.0, 8.0, 9.0, 10.0 × 10¹⁴ Hz
5. Click Export to download your data
6. Plot V_stop versus f. The slope equals h/e.
7. Multiply slope by e = 1.602 × 10⁻¹⁹ C to get h

Expected result: Your calculated h should be close to 6.63 × 10⁻³⁴ J·s. Millikan got 6.57 × 10⁻³⁴ J·s with this method in 1916, within 1% of the accepted value [5].

Activity 4: Metal Work Function Comparison

Objective: Understand how φ affects photoelectric behavior

Steps:

1. Set frequency to 7.0 × 10¹⁴ Hz (photon energy = 2.90 eV)
2. For each metal in order (cesium, potassium, sodium, calcium, zinc, copper):
   • Note the emission status (emitting or not)
   • If emitting, record KE_max from the display
3. Create a table: Metal, φ, KE_max (or "no emission")

What you should observe: Metals with φ < 2.90 eV emit electrons. The lower the work function, the higher the kinetic energy. Zinc (φ = 4.3 eV) and copper (φ = 4.7 eV) show no emission at this frequency because the photon energy is insufficient.

Real-World Applications

1. Solar Photovoltaic Cells

Every solar panel on every rooftop works because of the photoelectric effect (specifically, the internal photoelectric effect in semiconductors). Photons with energy greater than the semiconductor's band gap create electron-hole pairs that generate current. The efficiency limits you read about in solar cell research papers trace directly back to Einstein's equation: photons below the band gap contribute nothing, and excess energy above the band gap becomes waste heat [6].

2. Photomultiplier Tubes (PMTs)

These are the most sensitive light detectors ever built. A single photon hitting a photocathode ejects one electron. That electron accelerates through a series of dynodes, knocking out 3-5 more electrons at each stage. After 10-14 stages, one photon has become 10^6 to 10^8 electrons, enough to measure easily. PMTs are essential for PET medical imaging, astronomical observations, and particle physics experiments at CERN [7].

3. Digital Camera Sensors

The CCD and CMOS sensors in your phone's camera use the internal photoelectric effect. Photons generate electron-hole pairs in silicon. The accumulated charge in each pixel, proportional to light intensity, is read out and digitized. Understanding photon-electron conversion efficiency is central to improving camera low-light performance [7].

4. Night Vision and Image Intensifiers

Military and scientific night vision devices use photocathode plates made of materials with very low work functions (gallium arsenide, for example). Incoming photons (including infrared) eject electrons that are accelerated toward a phosphor screen, producing a visible image. The photoelectric threshold determines what wavelengths the device can detect.

5. Photoelectron Spectroscopy (PES/XPS)

Scientists use the photoelectric effect to analyze material composition. Shine X-rays of known energy on a sample, measure the kinetic energy of ejected electrons, and you can calculate their binding energy. Each element has characteristic binding energies, giving you elemental identification and chemical state information. This is standard practice in materials science and surface chemistry [8].

Reference Data

Metal Work Functions

Fundamental Constants

Challenge Questions

1. Basic Application (Easy)

Light with frequency 8.0 x 10^14 Hz shines on sodium (phi = 2.28 eV). Calculate the maximum kinetic energy of emitted electrons.

Hint: Photon energy E = hf = (4.136 x 10^-15 eV s)(8.0 x 10^14 Hz) = 3.31 eV

2. Threshold Prediction (Easy)

Which metal from our reference table could detect red light at 700 nm wavelength using the photoelectric effect? Explain your reasoning.

Hint: Calculate the photon energy at 700 nm first

3. Work Function Determination (Medium)

A metal emits electrons with maximum kinetic energy 1.5 eV when illuminated by light of wavelength 400 nm. What is the work function of this metal?

Hint: Find photon energy, then use KE_max = hf − φ

4. Intensity versus Frequency (Medium)

Two light beams of identical frequency strike the same metal surface. Beam A has intensity 100 W/m^2. Beam B has intensity 25 W/m^2. Compare (a) the maximum kinetic energy of electrons from each beam and (b) the photocurrent from each beam. Explain your reasoning.

5. Millikan's Data Analysis (Challenging)

In Millikan's 1916 experiment, he measured stopping voltages of 0.65 V at frequency 5.5 x 10^14 Hz and 1.28 V at frequency 7.0 x 10^14 Hz for sodium. Use these data points to calculate Planck's constant. Show your work.

Hint: V_stop = (h/e)f − φ/e. Use both data points to eliminate φ and solve for h.

Common Misconceptions

Frequently Asked Questions

Why did classical wave theory fail so completely for this phenomenon?

Classical physics treats light as a continuous wave. If that were true, energy would flow continuously from the light wave into electrons at the metal surface. Given enough time (or enough intensity), any frequency should eventually deliver enough energy for electrons to escape. What Lenard observed directly contradicted this: there was a sharp frequency cutoff, emission was instantaneous, and brighter light below threshold did nothing [1]. Einstein's photon hypothesis resolved all three problems by treating energy transfer as discrete all-or-nothing events.

What happens to photons below the threshold energy?

They get absorbed and converted to heat. The electron receives the photon's energy, but since hf < phi, the electron cannot escape the metal's surface potential. Instead, the electron rattles around and shares that energy with neighboring atoms through collisions. This is why metals get warm under light of any frequency, but only emit electrons above the threshold [3].

How can a single photon eject an electron, but a trillion cannot if the frequency is wrong?

Think of it like a vending machine that requires a minimum coin denomination. You cannot insert 1000 pennies to buy a $1 item, one penny at a time. The machine requires at least a dollar coin, all at once. Similarly, each photon delivers its energy in one instant. An electron cannot accumulate energy from multiple photons (under normal light intensities). Either one photon has enough energy, or it does not [4].

Why does the stopping voltage give us Planck's constant?

The stopping voltage directly measures KE_max because eV_stop = KE_max. From Einstein's equation, V_stop = (h/e)f − φ/e. If you plot V_stop against f for multiple frequencies, you get a straight line with slope h/e. Multiply by e and you have h. Millikan spent 10 years trying to disprove Einstein's theory this way, and instead provided its most precise experimental confirmation [5].

Is the photoelectric effect related to why plants are green?

Yes, through the same underlying physics. Chlorophyll molecules absorb red and blue photons because those frequencies have sufficient energy to promote electrons to excited states needed for photosynthesis. Green photons have intermediate energy that chlorophyll does not absorb efficiently, so green light reflects back to our eyes. The absorption threshold is determined by the energy gap between molecular states, directly analogous to the work function in metals [8].

References

1. HyperPhysics - Photoelectric Effect. Georgia State University. Available at: http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html

2. MIT OpenCourseWare - 8.04 Quantum Physics I. Available at: https://ocw.mit.edu/courses/8-04-quantum-physics-i-spring-2016/

3. American Physical Society - This Month in Physics History: Einstein and the Photoelectric Effect. Available at: https://www.aps.org/publications/apsnews/200501/history.cfm

4. OpenStax - University Physics Volume 3, Chapter 6: Photons and Matter Waves. Available at: https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect

5. Millikan, R.A. - A Direct Photoelectric Determination of Planck's "h". Physical Review, 1916. Available at: https://journals.aps.org/pr/abstract/10.1103/PhysRev.7.355

6. NREL - Solar Photovoltaic Technology Basics. Available at: https://www.nrel.gov/research/re-photovoltaics.html

7. Khan Academy - Photoelectric effect. Available at: https://www.khanacademy.org/science/physics/quantum-physics/photons/v/photoelectric-effect

8. Nobel Prize Organization - Albert Einstein Nobel Prize biography. Available at: https://www.nobelprize.org/prizes/physics/1921/einstein/biographical/

9. HyperPhysics - Work Functions for Photoelectric Effect. Available at: http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/photoelec.html

10. NIST - CODATA Recommended Values of Fundamental Constants. Available at: https://physics.nist.gov/cuu/Constants/

11. Encyclopaedia Britannica - Photoelectric Effect. Available at: https://www.britannica.com/science/photoelectric-effect

12. Physics LibreTexts - The Photoelectric Effect. Available at: https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/06%3A_Photons_and_Matter_Waves/6.02%3A_Photoelectric_Effect

13. Einstein, A. - On a Heuristic Point of View Concerning the Production and Transformation of Light (1905). English translation available at: https://einsteinpapers.press.princeton.edu/

About the Data

All physical constants are taken from the NIST CODATA 2018 recommended values, which are exact definitions under the 2019 SI redefinition [10]. Work function values represent typical measurements for clean polycrystalline surfaces. Actual work functions can vary with surface preparation, crystal face orientation, temperature, and adsorbed contaminants. The values used here are the most commonly cited educational values to maintain consistency with standard physics textbooks [9].

The threshold wavelengths and frequencies in our reference table are calculated directly from work function values using λ₀ = hc/φ and f₀ = φ/h, with no independent measurement uncertainty.

How to Cite

Simulations4All. (2026). Photoelectric Effect Simulator: Exploring Einstein's Quantum Explanation of Light-Matter Interaction. Retrieved from https://simulations4all.com/simulations/photoelectric-effect

For academic citations:

Simulations4All (2026). Photoelectric Effect Simulator [Web-based interactive simulation]. Available at: https://simulations4all.com/simulations/photoelectric-effect

Verification Log