A 2.22 -caliber handgun fires a 1.9 -g- bullet at a velocity of 765 m / s . Calculate the de Bro

step 1 So in this problem, we're told, a handgun fires a 1 .9 gram bullet at 765 meters per second. And

A 2.22 -caliber handgun fires a 1.9 -g- bullet at a velocity...

A 2.22 -caliber handgun fires a 1.9 -g- bullet at a velocity of 765 $\mathrm{m} / \mathrm{s}$ . Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?

Key Concepts

Quantum Effects in Macroscopic Objects

Quantum mechanical effects, such as the wave nature of matter, are significant at the microscopic scale but become negligible for macroscopic objects. For objects with large masses and everyday velocities, like a bullet, the associated de Broglie wavelength is extremely small, rendering quantum effects unobservable in practice.

Momentum

Momentum, defined as the product of an object's mass and its velocity, is a crucial quantity in both classical and quantum mechanics. In the context of the de Broglie relation, momentum directly determines the wavelength of a particle, linking the classical concept of motion to quantum wave behavior.

de Broglie Wavelength

The de Broglie wavelength is a fundamental concept in quantum mechanics that assigns a wavelength to any moving particle. It is given by the formula ? = h/(mv), where h is Planck’s constant, m is the mass, and v is the velocity of the particle. This concept highlights the wave-particle duality inherent in all matter.

Wave-Particle Duality

Wave-particle duality is the principle that every particle or quantum entity exhibits both wave-like and particle-like properties. This duality is a cornerstone of quantum mechanics and is most pronounced in microscopic particles, where the wave nature (e.g., interference and diffraction) can be observed experimentally.

Transcript

Please give Ace some feedback