How does the wavelength of a fast-pitched baseball compare...

How does the wavelength of a fast-pitched baseball compare to the wavelength of an electron traveling at $1 / 10$ the speed of light? What is the significance of this comparison? See Example $7.3$

Key Concepts

De Broglie Wavelength

The de Broglie wavelength is the fundamental concept that relates a particle’s momentum to its wavelength via the equation ? = h/p, where h is Planck’s constant and p is the momentum. This concept applies universally to matter, implying even macroscopic objects have an associated wavelength; however, for objects with large mass and momentum, such as a baseball, the wavelength becomes vanishingly small, making wave-like behavior undetectable.

Wave-Particle Duality

Wave-particle duality is the principle that every particle or quantum entity can exhibit both wave-like and particle-like properties. While electrons, with their relatively small mass and significant wavelength, clearly demonstrate wave properties in phenomena like interference, the extremely small wavelengths associated with everyday objects mean their wave-like nature is not observable on a macroscopic scale.

Quantum vs Classical Scale

The comparison between the wavelength of a fast-pitched baseball and that of an electron traveling at one-tenth the speed of light highlights the dramatic difference in scales. In quantum mechanics, the observable effects of a particle's wave nature are significant only when its de Broglie wavelength is comparable to the size of the system or experimental apparatus, a condition met by electrons but not by macroscopic objects, thereby underscoring why classical mechanics accurately describes the latter while quantum mechanics governs the former.

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