Wave-Particle Duality Cheat Sheet

Key Facts

• The energy of a photon is $E = hf$, where $h$ is Planck's constant and $f$ is frequency.
• For electromagnetic waves in a vacuum, the speed relation is $c = f\lambda$, where $c = 3.00 \times 10^8\ \text{m/s}$.
• A photon's momentum is $p = \frac{h}{\lambda}$, so shorter wavelength photons have greater momentum.
• The de Broglie wavelength of a particle is $\lambda = \frac{h}{p} = \frac{h}{mv}$ for nonrelativistic motion.
• In the photoelectric effect, the maximum kinetic energy of emitted electrons is $K_{\max} = hf - \phi$.
• The threshold frequency for photoemission is $f_0 = \frac{\phi}{h}$, and no electrons are emitted if $f < f_0$.
• The uncertainty principle is $\Delta x\Delta p \, \ge \, \frac{\hbar}{2}$, where $\hbar = \frac{h}{2\pi}$.
• Wave behavior is shown by interference and diffraction, while particle behavior is shown by localized impacts and energy packets.

Vocabulary

Photon

A photon is a quantum of electromagnetic radiation with energy $E = hf$ and momentum $p = \frac{h}{\lambda}$.

Wave-particle duality

Wave-particle duality is the principle that quantum objects can display both wave-like and particle-like properties.

de Broglie wavelength

The de Broglie wavelength is the wavelength associated with a moving particle, given by $\lambda = \frac{h}{p}$.

Photoelectric effect

The photoelectric effect is the emission of electrons from a material when photons with sufficient frequency strike its surface.

Work function

The work function $\phi$ is the minimum energy needed to remove an electron from a material.

Uncertainty principle

The uncertainty principle states that position and momentum cannot both be known exactly, expressed as $\Delta x\Delta p \ge \frac{\hbar}{2}$.