(c) What is the velocity of an electron with a de Broglie wavelength equal to (b)?

Key Concepts

de Broglie Wavelength

The de Broglie wavelength is a fundamental concept in quantum mechanics that relates the wavelength of a particle to its momentum. It is given by the formula λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. This concept illustrates the wave-particle duality of matter, indicating that particles like electrons exhibit both wave-like and particle-like properties.

Momentum of an Electron

Momentum is a vector quantity defined as the product of an object's mass and its velocity (p = mv). For an electron, which has a very small mass, its momentum can significantly influence its behavior in quantum mechanics. Understanding how to calculate the momentum of an electron is essential for determining its velocity when given its de Broglie wavelength.

Velocity Calculation

Velocity is defined as the rate of change of an object's position with respect to time and is calculated as v = p/m, where p is momentum and m is mass. In the context of the de Broglie wavelength, once the momentum of the electron is determined using its wavelength, the velocity can be easily calculated. This relationship is crucial for solving problems involving the motion of quantum particles.