Calculate the de Broglie wavelength of a 143-g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?

Key Concepts

de Broglie Wavelength

The de Broglie wavelength is a concept in quantum mechanics that describes the wave-like behavior of particles. It is calculated using the formula λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. This wavelength becomes significant for microscopic particles, such as electrons, but is negligible for macroscopic objects like a baseball.

Momentum

Momentum is a physical quantity defined as the product of an object's mass and its velocity (p = mv). It is a vector quantity, meaning it has both magnitude and direction. In the context of the de Broglie wavelength, momentum is crucial because it directly influences the wavelength; larger momentum results in a shorter wavelength, making wave properties less observable in larger objects.

Wave-Particle Duality

Wave-particle duality is a fundamental principle of quantum mechanics stating that every particle exhibits both wave-like and particle-like properties. While this duality is significant for small particles, such as photons and electrons, it is not observable in larger objects like a baseball due to their relatively large mass and momentum, which result in extremely short de Broglie wavelengths that are practically unnoticeable.