De Broglie wavelength question

1. Jun 8, 2006

jimmy_neutron

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.

2. Jun 8, 2006

Kurdt

Staff Emeritus
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. Jun 8, 2006

jimmy_neutron

ah I see, is there a set percentage that makes a velocity relativistic?

4. Jun 8, 2006

lightgrav

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.