What Makes a Proton's Velocity Relativistic?

In summary, the conversation discusses calculating the de Broglie wavelength of a proton at two different velocities: 2 x 10^4 m/s and 2 x 10^7 m/s. The second velocity is considered relativistic due to its significant fraction of the speed of light. It is explained that any nonzero velocity can be considered relativistic, but the factor gamma is close to 1 for small beta. However, for larger values of beta, there may be a significant difference in calculations.
  • #1
jimmy_neutron
10
0
I have been instructed to calculate the de Broglie wavelength of a proton moving at 1) 2 x 10^4 m/s and 2) 2 x 10^7 m/s

For the first velocity, the particle is not relativistic, but for the second velocity the particle is.

can someone explain to me what makes velocity 2 relativistic?
thanks.
 
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  • #2
Its a significant fraction of the speed of light basically. velocity 2 is approx. 7% the speed of light while the first is 0.007%.
 
  • #3
ah I see, is there a set percentage that makes a velocity relativistic?
 
  • #4
To be Truthful, ANY nonzero velocity is relativistic ...
but the factor gamma (1/sqrt(1-beta^2)) is CLOSE to 1
for small beta ...
if beta = v/c = 50 %, for example, then gamma = 1.15 ...
you might be off by 15% if you calculated non-relativistically.
 

Related to What Makes a Proton's Velocity Relativistic?

What is the De Broglie wavelength?

The De Broglie wavelength is a concept in quantum mechanics that describes the wavelength associated with particles, such as electrons, that exhibit wave-like behavior.

Who was Louis de Broglie?

Louis de Broglie was a French physicist who proposed the theory of wave-particle duality, which states that particles can exhibit both wave-like and particle-like behavior.

What is the equation for calculating the De Broglie wavelength?

The equation for calculating the De Broglie wavelength is: 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.

What is the significance of the De Broglie wavelength?

The De Broglie wavelength helps to explain the wave-like behavior of particles, which is a fundamental concept in quantum mechanics. It also allows us to calculate the wavelength of a particle and understand how it interacts with its surroundings.

How does the De Broglie wavelength relate to the Heisenberg uncertainty principle?

The De Broglie wavelength is 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 uncertainty in the momentum of a particle is inversely proportional to its De Broglie wavelength.

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