A fly with a mass of 1.0 ×10^-4 kg crawls across a table at a speed of 2 mm / s. Compute the d

Step 1: Recall the de Broglie wavelength formula. The de Broglie wavelength (Î») of a particle i

A fly with a mass of 1.0 ×10^-4 kg crawls across a table at...

A fly with a mass of $1.0 \times 10^{-4} \mathrm{~kg}$ crawls across a table at a speed of $2 \mathrm{~mm} / \mathrm{s}$. Compute the de Broglie wavelength of the fly and compare it to the size of a proton (about $1 \mathrm{fm}, 1 \mathrm{fm}=10^{-15} \mathrm{~m}$ ).

Key Concepts

de Broglie Wavelength

The de Broglie wavelength describes the wave-like behavior of matter and is given by the equation ? = h/p, where h is Planck's constant and p is the momentum of the particle. This concept is central to quantum mechanics, as it extends wave-particle duality from photons to all matter, showing that every particle has an associated wavelength.

Momentum

Momentum, defined as the product of an object's mass and velocity, is a key concept in both classical and quantum mechanics. In the context of the de Broglie wavelength, momentum determines the scale of a particle's wavelength, with larger momentum corresponding to a shorter wavelength.

Planck's Constant

Planck's constant is a fundamental physical constant that sets the scale of quantum effects. It appears in various quantum relations, including the de Broglie equation, and its extremely small value means that the wave-like properties of macroscopic objects are typically unobservable.

Wave-Particle Duality

Wave-particle duality is the principle that every particle exhibits both particle-like and wave-like properties. This duality is mathematically expressed by the de Broglie wavelength, allowing particles such as electrons to exhibit interference patterns under appropriate conditions, even though such effects are negligible for objects with large masses.

Scale Comparison in Quantum Mechanics

In quantum mechanics, comparing a particle's de Broglie wavelength to characteristic physical scales, such as the size of a proton, helps determine whether quantum effects are significant. For macroscopic objects, the de Broglie wavelength is extremely small compared to atomic or subatomic dimensions, underscoring why quantum behaviors are generally observed only at very small scales.

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