Calculate the de Broglie wavelength for each of the...

Calculate the de Broglie wavelength for each of the following.
a. an electron with a velocity 10.% of the speed of light
b. a tennis ball ( 55 g) served at 35 $\mathrm{m} / \mathrm{s}(\sim 80 \mathrm{mi} / \mathrm{h})$

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Key Concepts

Relativistic Considerations

At velocities approaching a significant fraction of the speed of light, relativistic effects become important. This means that the simple classical formula for momentum (m*v) may need corrections to account for relativistic momentum, ensuring accurate evaluation of the de Broglie wavelength for high-speed particles.

Momentum

Momentum, defined as the product of mass and velocity, is a key physical quantity in both classical and quantum physics. In the context of the de Broglie wavelength, it is the momentum that determines the wavelength associated with a moving object, with heavier or faster-moving particles exhibiting shorter wavelengths.

Wave-Particle Duality

This concept describes the fundamental nature of matter exhibiting both particle-like and wave-like properties. It is a cornerstone in quantum mechanics and is exemplified by phenomena such as interference and diffraction in particles, demonstrating that entities like electrons can behave as waves under certain conditions.

de Broglie Hypothesis

This hypothesis states that every moving particle has an associated wavelength given by ? = h/p, where h is Planck's constant and p is the momentum of the particle. It bridges classical mechanics with quantum mechanics by linking a particle's momentum to its wave properties.

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