The Wave Nature of Matter
In 1924, French physicist Louis de Broglie proposed a radical idea: if light waves can act like particles (photons), then perhaps particles of matter can act like waves.
He theorized that any object with mass and momentum has an associated "matter wave." The wavelength of this wave is inversely proportional to the object's momentum ($p = m \cdot v$).
The Micro vs. Macro World
- Electrons: Because an electron has such a tiny mass, its de Broglie wavelength is significant (around the size of an atom). This is why electrons behave like waves in quantum experiments.
- Baseballs: A thrown baseball also has a wavelength, but because its mass is so huge, its wavelength is unimaginably small (around $10^{-34} , \text{meters}$). This is why a baseball acts purely like a solid particle and doesn't diffract around a baseball bat.
The Formula
Where:
=
De Broglie Wavelength (meters)h=
Planck's Constant (6.626 × 10⁻³⁴ J·s)p=
Momentum (kg·m/s)m=
Mass of the particle (kg)v=
Velocity of the particle (m/s)Example Calculation
Calculate the wavelength of an electron ($m = 9.1 \times 10^{-31} , \text{kg}$) moving at $1,000,000 , \text{m/s}$.
- Calculate Momentum ($m \cdot v$): $(9.1 \times 10^{-31}) \times 1,000,000 = 9.1 \times 10^{-25} , \text{kg}\cdot\text{m/s}$.
- Divide Planck's Constant by p: $(6.626 \times 10^{-34}) / (9.1 \times 10^{-25}) \approx 7.28 \times 10^{-10} , \text{meters}$.
The wavelength is $0.728 , \text{nm}$, which is about the diameter of a large atom.