De Broglie wavelength and energy levels

In summary: If you have a standing wave, then you get a discontinuity at every point along the trajectory.In summary, the equations are describing the energy of a particle as a function of its momentum. If you have a standing wave, then at every point along the trajectory you get a discontinuity in the energy.
  • #1
rohanlol7
67
2

Homework Statement


In the earliest circular planetary model of the atom the electron and proton orbited a common centre. The electrostatic forces alone provided the force field. However an accelerating charged body will send out electromagnetic waves and the orbiting charges would consequently lose energy continuously. The model did not, as it stood, predict the existence of discrete energy levels that were known to be a consequence of the discrete system of spectral lines. In the wave particle model the de Broglie wavelength, L, is related to the momentum p ( p = mv) by p =h/L. Assume v < c the speed of light in free space.

i)Use this to find a relationship between the KE of a body and its wavelength. (ii) How, using the de Broglie result, can a discrete energy level model be constructed?
Why are neutrons used to investigate the nature of certain crystals ?

Homework Equations



Equations are given in the question
Ek=mv^2/2
Fc=mv^2/R

The Attempt at a Solution


The first part is fine, i got h^2/2mL^2
for the second part i thought about using electrostatic forces and relate that to Fc but i do not see how this would introduce only discrete values in the model.
I looked online a bit and I found something about standing waves and that it would imply 2*pi*r=nL but i don't understand where this comes from
 
Physics news on Phys.org
  • #2
rohanlol7 said:
I looked online a bit and I found something about standing waves and that it would imply 2*pi*r=nL but i don't understand where this comes from
Remember that you are considering circular orbits. If that condition is not met, then you can't have a standing wave (you have the wave destructively interfering with itself).
 
  • #3
DrClaude said:
Remember that you are considering circular orbits. If that condition is not met, then you can't have a standing wave (you have the wave destructively interfering with itself).
but why should i want standing waves in this situation?
 
  • #4
rohanlol7 said:
but why should i want standing waves in this situation?
Because otherwise you get no solution! The wave will interfere with itself and, on average, you get zero everywhere.

Another way to see it is that the solution should be single valued and continuous at every point along the trajectory.
 
  • Like
Likes rohanlol7

1. What is the De Broglie wavelength?

The De Broglie wavelength is a concept in quantum mechanics that describes the wave-like properties of matter. It is the wavelength associated with a particle, and is given by the equation λ = h/mv, where h is Planck's constant, m is the mass of the particle, and v is its velocity.

2. How is the De Broglie wavelength related to energy levels?

The De Broglie wavelength is related to energy levels through the famous equation E = hf, where E is the energy of a particle, h is Planck's constant, and f is the frequency of the particle's wave function. This equation shows that as the energy of a particle increases, its frequency and therefore its De Broglie wavelength also increases.

3. What is the significance of the De Broglie wavelength in quantum mechanics?

The De Broglie wavelength is significant in quantum mechanics because it shows that particles can exhibit both wave-like and particle-like behavior. This concept is known as wave-particle duality and is a fundamental principle in understanding the behavior of matter at the quantum level.

4. How does the De Broglie wavelength affect the behavior of particles?

The De Broglie wavelength affects the behavior of particles in that it determines the probability of finding a particle in a certain location. This is described by the wave function, which is a mathematical expression that gives the probability of a particle being in a specific location at a given time.

5. Can the De Broglie wavelength be observed experimentally?

Yes, the De Broglie wavelength has been observed experimentally through various experiments such as the double-slit experiment and electron diffraction. These experiments confirm the wave-like nature of particles and the existence of the De Broglie wavelength.

Similar threads

De Broglie wavelength of electron and proton
    • Introductory Physics Homework Help
Replies
14
Views
2K
De Broglie wavelength of an electron
    • Introductory Physics Homework Help
Replies
3
Views
2K
De – Broglie wavelength of O_2
    • Introductory Physics Homework Help
Replies
2
Views
2K
Beam current of positrons and electrons
    • Introductory Physics Homework Help
Replies
5
Views
1K
I De Broglie Wavelength at rest: λ = h/p = h/0 when v=0?
    • Other Physics Topics
Replies
5
Views
874
Wavelength = deBroglie Wavelength?
    • Introductory Physics Homework Help
Replies
11
Views
2K
De Broglie wavelength of a train
    • Introductory Physics Homework Help
Replies
1
Views
1K
De Broglie Wavelength/Electron momentum
    • Introductory Physics Homework Help
Replies
5
Views
2K
Nonrelativistic de Broglie energy Threshold of 1%
    • Introductory Physics Homework Help
Replies
7
Views
1K
Calculating the De Broglie Wavelength of an Accelerated Particle
    • Introductory Physics Homework Help
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top