An electron is moving at 1 imes 10^6 m/s. If its speed is doubled, what happens to its de Broglie wavelength?

It is halved (1/2) Since lambda propto 1/v, doubling the velocity (2v) results in a wavelength that is half of the original value.

de Broglie Wavelength Calculator

Q: Why don't we notice the wave properties of a moving car?

Extremely small wavelength due to large mass Because lambda = h/(mv) and h is extremely small, the large mass of a car makes its wavelength many orders of magnitude smaller than an atom, making wave effects impossible to observe.

Calculate matter wave wavelength λ = h/(mv). Presets for electron, proton, baseball, and human. Shows scale comparison and wave visualization.

WHAT IS THE DE BROGLIE WAVELENGTH?

In 1924, Louis de Broglie proposed that all matter exhibits wave-like properties. This **wave-particle duality** states that an object with momentum has an associated wavelength , where is Planck's constant. While these wavelengths are far too small to detect for macroscopic objects (like a baseball), they are highly significant for subatomic particles (like electrons), explaining electron diffraction and the quantized orbits of atoms.

HOW TO USE THIS VISUALIZATION

1. **Select an Object**: Choose from the presets (Electron, Proton, Alpha Particle, or Baseball).2. **Adjust Velocity**: Change the speed of the object. Observe how the wavelength decreases as the object speeds up.3. **Compare Scales**: See how the calculated wavelength relates to the physical size of the object. Notice that for macroscopic objects, is effectively zero.

CORE FORMULAS

de Broglie Wavelength Equation

Planck's Constant

Classical momentum

AP EXAM CONNECTION

Unit: Unit 7: Quantum, Atomic, and Nuclear Physics (Topic 7.2)
Learning Objective: LO 6.F.4

COMMON MISCONCEPTIONS

Wavelength depends on the object's charge (it only depends on mass and velocity)
The wave is a physical wave of the object's surface (it is a probability wave/matter wave)

KEY TAKEAWAYS

All matter has wave properties.
Wavelength is inversely proportional to momentum.
Evidence for matter waves includes electron diffraction experiments.
Quantum effects are only noticeable when the wavelength is comparable to the scale of the environment.

PRACTICE QUESTIONS

Q1 (QUANTITATIVE): An electron is moving at m/s. If its speed is doubled, what happens to its de Broglie wavelength?

Show Answer & Explanation

Answer: It is halved (1/2)

Explanation: Since , doubling the velocity () results in a wavelength that is half of the original value.

Q2 (CONCEPTUAL): Why don't we notice the wave properties of a moving car?

Show Answer & Explanation

Answer: Extremely small wavelength due to large mass

Explanation: Because and is extremely small, the large mass of a car makes its wavelength many orders of magnitude smaller than an atom, making wave effects impossible to observe.