What Makes a Proton's Velocity Relativistic?

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A proton's velocity is considered relativistic when it approaches a significant fraction of the speed of light, typically around 10% or more. In the discussion, a proton moving at 2 x 10^4 m/s is not relativistic, while at 2 x 10^7 m/s, it reaches approximately 7% of the speed of light, thus becoming relativistic. The concept of the Lorentz factor (gamma) is introduced, indicating that even at lower velocities, any nonzero speed can be treated as relativistic, but the effects are negligible when beta (v/c) is small. For instance, at 50% of the speed of light, the Lorentz factor is 1.15, suggesting a 15% deviation from non-relativistic calculations. Understanding these distinctions is crucial for accurate physics calculations involving high-speed particles.
jimmy_neutron
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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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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%.
 
ah I see, is there a set percentage that makes a velocity relativistic?
 
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.
 

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