Modern Physics Sandbox

Interactive simulations of foundational quantum phenomena.

The Photoelectric Effect

Shine light on a metal plate and see if you can knock electrons off. A key experiment showing light behaves as a particle (a photon).

$K_{max} = hf - \phi$

The Concept

When light of a sufficiently high frequency shines on a metal, it can eject electrons. This phenomenon demonstrates that light energy is quantized into discrete packets called photons. The energy of one photon is $E = hf$. An electron is only ejected if the photon's energy is greater than the metal's work function ($\phi$).

How to Use the Lab

  • Use the Wavelength slider to change the energy of individual photons. Shorter wavelength = higher energy.
  • The Intensity slider changes the number of photons per second.
  • Select different Target Metals to see how the work function changes the outcome.

Controls

Calculated Values

Experiment

Energy Levels

Graph: Max Kinetic Energy vs. Frequency

What's Happening?

Matter Waves

De Broglie proposed that all matter has wave-like properties. See how a particle's wavelength changes with its mass and velocity.

$\lambda = h / p = h / (mv)$

The Concept

Any particle with momentum ($p$) also has an associated wavelength ($\lambda$), connecting the world of particles to the world of waves. This wavelength is usually only large enough to be meaningful for objects with a very small mass, like an electron. For everyday objects, the wavelength is too small to ever be observed.

How to Use the Lab

  • Select a Particle to set its mass.
  • Use the Velocity slider to change its speed. Notice the slider is logarithmic to cover a huge range of speeds.
  • Observe how the visualized wave changes. Is it even visible for a baseball?
  • The graph shows the inverse relationship between velocity and wavelength.

Controls

Calculated Values

Particle and its de Broglie Wave

Graph: Wavelength vs. Velocity

What's Happening?

Davisson-Germer Experiment

The definitive experiment proving electrons can behave like waves by diffracting off a crystal.

$n\lambda = d \sin\theta$

The Concept

Electrons are accelerated and fired at a nickel crystal. The regular atomic spacing of the crystal acts like a diffraction grating. If electrons are truly waves, they should diffract and create an interference pattern of high and low intensity at different angles, which is exactly what was observed. This confirmed de Broglie's hypothesis.

How to Use the Lab

  • Adjust the Accelerating Voltage to change the electrons' energy and de Broglie wavelength. Note how the incoming wave changes.
  • Rotate the Detector Angle to measure the intensity of scattered electrons.
  • Watch for the scattered waves to line up (constructive interference) and cause the detector to glow.
  • The graph shows the intensity pattern. The classic result is a peak at ~50° for 54V electrons.

Controls

Calculated Values

Electron Diffraction

Graph: Intensity vs. Angle

What's Happening?