Calculating the De Broglie Wavelength of an Accelerated Particle

In summary, the de Broglie wavelength of a particle of mass m and charge q accelerated across a potential difference V to a non-relativistic velocity is given by ## \frac{h}{\sqrt{2mqV}} ##. This can be derived from the equation ## qV = \frac{p^2}{2m}##, or the principle of conservation of energy. The units of the proposed solution are different from the given options, providing additional confidence in the correctness of the answer.
  • #1
Safinaz
260
8

Homework Statement

A particle of mass m and charge q is accelerated across a potential dierence V to a non-relativistic velocity. What is the de Broglie wavelength of this particle?

Homework Equations



Is it

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The Attempt at a Solution



I think it's
## \frac{h}{\sqrt{2mqV}} ##, because ## qV = \frac{p^2}{2m}## , or : P.E (at rest) = K.E (after acceleration), so that ## p= \sqrt{2mqV}, \lambda= \frac{h}{p}= \frac{h}{\sqrt{2mqV}}##
 
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  • #2
You can boost your confidence by using the fact that the provided options all have different units.
 
  • #3
## (\frac{h}{\sqrt{2mqV}} )^2 : \frac{J^2 . s^2}{kg.C.volt} = \frac{kg^2 . m^4}{s^2} \times \frac{A . s^3}{kg. C. Kg. m^2} ##
## = m^2 \times \frac{C/s. s}{C} = m^2 ##
 
  • #4
Well then you have found the answer.
 
  • #5
Thanks :)
 

FAQ: Calculating the De Broglie Wavelength of an Accelerated Particle

What is the De Broglie wavelength?

The De Broglie wavelength, also known as the matter wave, is a concept in quantum mechanics that describes the wavelength associated with a particle. It is named after French physicist Louis de Broglie, who proposed the idea that particles, such as electrons, could have both wave-like and particle-like properties.

How is the De Broglie wavelength calculated?

The De Broglie wavelength can be calculated using the following equation: λ = h/mv, where λ is the De Broglie wavelength, h is Planck's constant, m is the mass of the particle, and v is the velocity of the particle. This equation is based on the de Broglie hypothesis, which states that all particles have a wave-like nature.

What is the significance of the De Broglie wavelength?

The De Broglie wavelength is significant because it helps us understand the wave-particle duality of matter. It shows that particles, such as electrons, can behave like both waves and particles. This concept is crucial in quantum mechanics and has led to many important discoveries and advancements in the field.

What factors can affect the De Broglie wavelength?

The De Broglie wavelength is affected by the mass and velocity of the particle. As the mass of the particle increases, the wavelength decreases, and vice versa. Similarly, as the velocity of the particle increases, the wavelength decreases, and vice versa. Additionally, the De Broglie wavelength can also be affected by external forces, such as electric and magnetic fields.

How does the De Broglie wavelength relate to the uncertainty principle?

The De Broglie wavelength is related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle simultaneously. The De Broglie wavelength is inversely proportional to the momentum of a particle, so if we know the exact wavelength, we can calculate the momentum. However, this means that we cannot know the exact position of the particle, as the wavelength is constantly changing. This demonstrates the wave-particle duality of matter and the limitations of our ability to measure and understand it.

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