DeBroglie wavelength and nucleon velocity

[atomicpedals]

Homework Statement

Atomic nucleus consists of nucleons. What velocity (order of magnitude estimate) will a nucleon have inside a nucleus?

Homework Equations

$\lambda$ = h/mv

v = h/m$\lambda$

The Attempt at a Solution

The wavelength of a nucleus is on the order of 10^-15/m, nucleons have a mass on the order of 10^-27 kg, and h is Plancks Constant. If I do a straight plung-n-chug I get that the velocity should be on the order of 10^-22 m/s.

It seems reasonable to me, but recently that's been a guarantee that it isn't. So does that look reasonable to anyone else?

 

[vela]

No, that's not correct. A length scale of 1 fm corresponds to an energy of 197 MeV, which is a good chunk of the 1 GeV mass of a nucleon. You should expect the nucleon to be moving relativistically.

 

[atomicpedals]

Ok, ran it again this time assuming a wavelength for the nucleus of ~10^-14m (a big-ish nucleus), and a nucleon mass of 1GeV/c^2 and came up with a velocity of ~0.4c. Which makes considerably more sense than my first answer.