Question

A proton is confined within an atomic nucleus of diameter 3.60 fm. part a estimate the smallest range of speeds you might find for a proton in the nucleus.

Answer 1

The answer for this problem would be:
Assuming non-relativistic momentum, then you have: 
ΔxΔp = mΔxΔv = h / (4) 
Δv = h / (4πmΔx) 
m ~ 1.67e-27 h ~ 6.62e-34,Δx = 4e-15 --> 
Δv ~ 6.62e-34 / (4π * 1.67e-27 * 4e-15) ~ 7,886,270 m/s ~ 7.89e6 m/s 
That's about 1% of the speed of light, the assumption that it's non-relativistic.