Derivation of De Broglie wavelength

In summary, the De Broglie wavelength can be derived using the equations E=hf and v=fλ, as well as the equation E=mc^2. However, there is a discrepancy in the derivation when it comes to electrons, as the equation only works for light. To solve this issue, one must assume that the wave-speed is equal to the ratio of c^2 and the physical speed of the electron. Another way to derive the De Broglie wavelength is through Special Relativity, as explained in the provided link.
  • #1
PhiJ
44
0
The De Broglie wavelength was derived like this by our physics teacher.
E=hf v=fλ E=mc^2
so
hf=mc^2
hv=λmc^2
Then the WRONG BIT
h=λmv
h=λρ
λ=h/ρ

But that only works for light (when c=v). There must be a correct way of deriving it for electrons etc. We are expected to use this for electrons.
 
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  • #2
PhiJ said:
The De Broglie wavelength was derived like this by our physics teacher.
E=hf v=fλ E=mc^2
so
hf=mc^2
hv=λmc^2
Then the WRONG BIT
h=λmv
h=λρ
λ=h/ρ
But that only works for light (when c=v). There must be a correct way of deriving it for electrons etc. We are expected to use this for electrons.

It only works if you take: wave-speed = [itex]\frac{c^2}{v}[/tex] where v is the physical
speed of the electron, this is however an ad-hoc assumption here. It's not
that hard to derive λ=h/ρ directly from E=hf but it takes Special Relativity:

http://www.chip-architect.com/physics/deBroglie.pdfRegards, Hans
 

1. What is the De Broglie wavelength?

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

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. This equation is known as the de Broglie relation.

3. What is the significance of the De Broglie wavelength?

The De Broglie wavelength is significant because it shows that matter has wave-like properties, similar to electromagnetic radiation. This concept helped to unify the theories of particle and wave behavior in quantum mechanics and has led to important discoveries in the field.

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

The De Broglie wavelength is closely related to the Heisenberg uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. The De Broglie wavelength is a measure of the momentum of a particle, and the uncertainty principle shows that the more precisely we know the momentum, the less we know about the position.

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

Yes, the De Broglie wavelength can be observed in everyday objects, but it is extremely small for macroscopic objects. For example, the De Broglie wavelength of a baseball traveling at 100 mph is about 10^-34 meters, which is much smaller than the size of an atom. However, it is more noticeable for particles with very small masses, such as electrons, which have a De Broglie wavelength in the nanometer range.

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