DeBroglie Wavelength with Relativistic Electron

In summary: However, even with SI units, your answer would still be wrong because the numerical values you used are too high.$$\vec{p}=\frac{m \vec{v}}{\sqrt{1-\vec{v}^2/c^2}}.$$
  • #1
Oaxaca
8
0
I am trying to find the DeBroglie wavelength of an electron moving at .8c. I have never learned special relativity but I believe the momentum is affected (mass change). I used the formula p= (mv)/(1-v^2/c^2) and got a momentum of p = 2.733 E-22 and a wavelength of lamda = 2.4149 E-12. Did I apply the formula correctly for the relativistic momentum?

Thanks for any help
 
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  • #2
Neither ##p=2.733\times{10}^{-22}## grain-furlongs per fortnight nor ##\lambda=2.4149\times{10}^{-12}## parsecs would be correct, but I'm pretty sure you didn't use those units. What units did you use?

The ##m## in the formula you cite is the rest mass, not the relativistic mass (and we have a FAQ on why relativistic mass is seldom used - look for a link to it in the sticky thread at the top of this forum). As long as you get that right and pay attention to the units, you should come to the right answer.
 
  • #3
Nugatory said:
Neither ##p=2.733\times{10}^{-22}## grain-furlongs per fortnight nor ##\lambda=2.4149\times{10}^{-12}## parsecs would be correct, but I'm pretty sure you didn't use those units. What units did you use?

The ##m## in the formula you cite is the rest mass, not the relativistic mass (and we have a FAQ on why relativistic mass is seldom used - look for a link to it in the sticky thread at the top of this forum). As long as you get that right and pay attention to the units, you should come to the right answer.
I used kg and m/s for the electron, with momentum therefor being kg*m/s - and meters for my wavelength. Thanks for the response!
 
  • #4
The correct formula is
$$\vec{p}=\frac{m \vec{v}}{\sqrt{1-\vec{v}^2/c^2}}.$$
I'm to lazy to check your formula with quantities given in SI units which are not very intuitive to use in high-energy physics and thus why I've never seen anybody using them there in scientific work in this field ;-)).
 

Related to DeBroglie Wavelength with Relativistic Electron

1. What is DeBroglie Wavelength with Relativistic Electron?

The DeBroglie Wavelength with Relativistic Electron is a concept in physics that describes the wavelength of a particle, specifically an electron, in motion at relativistic speeds. This is based on the theory of wave-particle duality, which states that all particles have both wave-like and particle-like properties.

2. How is DeBroglie Wavelength with Relativistic Electron calculated?

The DeBroglie Wavelength with Relativistic Electron can be calculated using the formula: 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 formula takes into account the relativistic effects on the electron's motion, such as its increased mass and energy.

3. What is the significance of DeBroglie Wavelength with Relativistic Electron?

The DeBroglie Wavelength with Relativistic Electron is significant because it helps us understand the behavior of particles at high speeds and in quantum systems. It also provides a link between classical and quantum mechanics, as it shows that even particles with mass have wave-like properties.

4. What is the relationship between DeBroglie Wavelength with Relativistic Electron and Heisenberg's Uncertainty Principle?

The Heisenberg's Uncertainty Principle states that it is impossible to know both the position and momentum of a particle with certainty. The DeBroglie Wavelength with Relativistic Electron is related to this principle as it shows that the wavelength of a particle is inversely proportional to its momentum. This means that the more accurately we know the momentum of the particle, the less we know about its position, and vice versa.

5. Can the DeBroglie Wavelength with Relativistic Electron be observed in experiments?

Yes, the DeBroglie Wavelength with Relativistic Electron has been observed in various experiments, such as the double-slit experiment. In this experiment, electrons are fired through two slits and their interference pattern is observed, indicating their wave-like behavior. This supports the concept of DeBroglie Wavelength with Relativistic Electron and the wave-particle duality theory.

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