Comparing de Broglie Wavelength to Particle Size

In summary, the conversation discusses the comparison between the de Broglie wavelength associated with a particle and the size of the particle. The equation for the de Broglie wavelength is used, and it is considered how the wavelength could depend on the size of the particle. The example of a high energy proton beam probing very fine structure is also mentioned.
  • #1
neelakash
511
1

Homework Statement



It is an MCQ problem:
How does the de Broglie wavelength λ associated with a particle compare to the size of the particle?
(A) λ must be greater than the particle
(B) λ must be less than he particle
(C) λ could be larger and smaller than the particle

Homework Equations



I have used de Broglie's relation and Uncertainty principle.

The Attempt at a Solution



∆x ∆p> h

or, ∆x>(h/∆p)~λ as ∆p~p and ∆x is the particle's size in crude terms...

Please check and tell me if I am correct
 
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  • #2
Use thet equation for the de Broglie wavelength, or just just use logic.
How could the de Broglie wavelength depend on the size of the particle?
 
  • #3
It could depend possibly in the way I showed...
Think of high energy proton beam probing very fine structure...say of the order of picometer or fm

fm is the order of classical proton picture~ nuclear dimension...

It is a problem from Resnick Halliday and I do not find any reason to suspect this problem...
 

1. What is the de Broglie wavelength?

The de Broglie wavelength is a concept in quantum mechanics that describes the wave-like behavior of particles, such as electrons, at the atomic and subatomic level. It is named after French physicist Louis de Broglie, who proposed the idea in the early 20th century.

2. How is the de Broglie wavelength calculated?

The de Broglie wavelength can be calculated using the equation λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is the velocity of the particle.

3. What is the relationship between de Broglie wavelength and particle size?

The de Broglie wavelength is inversely proportional to the size of the particle. This means that as the particle's size increases, its de Broglie wavelength decreases. This relationship is known as the wave-particle duality principle.

4. Why is it important to compare the de Broglie wavelength to particle size?

Comparing the de Broglie wavelength to particle size allows us to understand the wave-like nature of particles and their behavior at the quantum level. It also helps us to better understand the limitations of classical physics in explaining the behavior of particles.

5. Can the de Broglie wavelength be observed in everyday objects?

No, the de Broglie wavelength is only observable in particles with very small masses, such as electrons, protons, and neutrons. Everyday objects have a much larger mass and therefore have a de Broglie wavelength that is too small to be observed.

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