De Broglie wavelength question.

In summary, the problem involves determining the de Broglie wavelength and quantum number of Earth's orbit using its mass and orbit radius. To find the de Broglie wavelength, the equation lambda = h/mv is used, but the velocity of Earth must be calculated using its period and radius. The quantum number can then be found using the equation n*lambda = 2*pi*r.
  • #1
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Homework Statement



Earth has the mass 6 · 10^24 kg and the orbit radius r = 1.5 · 10^11 m.
(a) Compute its de Broglie wavelength. (b) Apply de Broglie quantization condition
as in the case of the Hydrogen atom and compute the quantum number n for the
orbit of Earth. (c) What is the difference between the radius of nth and n + 1th
orbit?

Homework Equations



lamba=h/p=h/mv

The Attempt at a Solution



I am using the above equation to solve this but I am stuck at getting the velocity of earth. I am completely stumped.
 
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  • #2
Well you know lambda will need to be periodic about the circumference of a circle. So what would you get for lambda if the radius of the circle is 'r'?
 
  • #3
I'm not sure I follow what you are asking.
 
  • #4
If you drew a wave around the circumference of a circle, you will need to connect the wave back to itself. Otherwise you will have a discontinuity when try reattaching the wave back on itself. So the wave will need to be periodic around the circle, so it is continuous the whole way around.
 
  • #5
Yes, but I don't understand the relationship between the wavelength and the radius.
 
  • #6
Well if you straightened out the circumference of the circle into a box of length L. Then you specify that the wave at both ends of the box need to be periodic, you are left with the only possibilities of:

[tex]L = n\lambda[/tex]

where n=1,2,3... Now going back to the circle, ask yourself what is L for a circle?
 
  • #7
Yea L is the circumference of the circle. I understand I use the equation n*lambda=2*pi*r for b. I am stuck at a) because I am not given the velocity for Earth and asked to figure out the de Broglie.
 
  • #8
Well you will have to compute the velocity the old fashioned way. You know the period of the orbit of the earth. It is just 1 year. Using that and the radius, get a speed.
 
  • #9
oh wow. Thank you so much!
 

1. What is De Broglie wavelength?

De Broglie wavelength, also known as matter wave, is a concept in quantum mechanics that describes the wave-like behavior of all matter particles, such as electrons, protons, and neutrons. It is named after French physicist Louis de Broglie, who proposed that particles also have wave-like properties.

2. How is De Broglie wavelength calculated?

The De Broglie wavelength (λ) of a particle is calculated using the following formula: λ = h/mv, where h is Planck's constant, m is the mass of the particle, and v is its velocity. This formula shows that the wavelength is inversely proportional to the momentum of the particle, meaning that particles with higher momentum have shorter De Broglie wavelengths.

3. What is the significance of De Broglie wavelength?

The De Broglie wavelength is significant because it helped bridge the gap between the classical and quantum theories of matter. It showed that particles can exhibit both wave-like and particle-like behaviors, and it laid the foundation for the development of quantum mechanics. De Broglie wavelength is also used to explain various phenomena, such as electron diffraction and tunneling.

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

The De Broglie wavelength is related to the uncertainty principle, which states that the position and momentum of a particle cannot be known simultaneously with certainty. This is because the De Broglie wavelength is inversely proportional to the momentum of the particle, so the more accurately we know the momentum, the less we know about its position. This is a fundamental principle in quantum mechanics.

5. Can De Broglie wavelength be observed?

De Broglie wavelength cannot be directly observed because it is a property of matter particles, which are too small to be seen with the naked eye. However, its effects can be observed in experiments, such as electron diffraction and the double-slit experiment, where particles exhibit wave-like behavior. This provides evidence for the existence of De Broglie wavelength and the wave-particle duality of matter.

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