De Broglie Wavelength: Videos & Practice Problems

To calculate the de Broglie wavelength of a particle, you use the de Broglie equation, which relates a particle's wavelength to its momentum. The formula is given by:

Where:

• $\lambda$ (lambda) is the de Broglie wavelength
• $h$ is the Planck constant (approximately 6.626 x 10^-34 Js)
• $p$ is the momentum of the particle

The momentum ($p$) of a particle is the product of its mass ($m$) and velocity ($v$), so $p=mv$. Therefore, the de Broglie wavelength can also be calculated by:

If you're dealing with an electron or any other charged particle that's been accelerated by a voltage ($V$), you can relate its kinetic energy to the voltage by the equation $\mathrm{KE}=eV$, where $e$ is the elementary charge (approximately 1.602 x 10^-19 C). Since the kinetic energy ($\mathrm{KE}$) is also equal to $\frac{1}{2}m{v}^2$, you can solve for $v$ and then use that to find the momentum, which you can then plug into the de Broglie equation to find the wavelength.

The De Broglie wavelength is a fundamental concept in quantum mechanics, introduced by the French physicist Louis de Broglie in 1924. It relates to the wave-particle duality of matter, which proposes that all particles exhibit both wave-like and particle-like properties. The De Broglie wavelength is the wavelength associated with a particle and is given by the De Broglie equation:

where $\lambda$ (lambda) is the De Broglie wavelength, $h$ is the Planck constant (approximately 6.626 x 10^-34 Js), and $p$ is the momentum of the particle (the product of its mass $m$ and velocity $v$).

This concept is particularly significant when dealing with microscopic particles, such as electrons, where the wave-like behavior becomes evident. For example, electrons can exhibit diffraction patterns, which is a wave phenomenon, when passed through a double-slit apparatus. The De Broglie wavelength has been instrumental in the development of quantum mechanics and has applications in various fields such as electron microscopy and the study of atomic and subatomic systems.

The de Broglie wavelength of an electron is inversely proportional to its momentum. This relationship is given by the de Broglie equation, which states that the wavelength (λ) is equal to the Planck constant (h) divided by the momentum (p) of the particle:

Momentum is the product of the mass and velocity of a particle (p = mv). Therefore, when the momentum of an electron increases, which can happen if its velocity increases (assuming its mass remains constant), its de Broglie wavelength decreases. Conversely, if the momentum of the electron decreases, its de Broglie wavelength increases.

In a more intuitive sense, you can think of it like this: as the electron moves faster and its momentum goes up, it behaves more like a particle with a shorter wavelength. When it moves slower and its momentum goes down, it behaves more like a wave with a longer wavelength.