Uncertainty principle and an electron

[thenewbosco]

question is:
use the uncertainty principle to show that if an electron were confined inside and atomic nucleus, diameter of $$2 x 10^{-15}m$$, it would have to be moving relativistically i.e. more than 0.1c.
what i have done is the following:
$$\Delta x \Delta p = \frac{\hbar}{2}$$
then i set $$\Delta x = 2 x 10^{-15}$$ and solved for $$\Delta p$$

from this i don't know how to solve for the speed, i considered replacing $$\Delta p$$ with $$\gamma m\Delta v$$ but this doesn't seem to work with the gamma in there.
what is a better way to solve this?
thanks

 

[robphy]

Must you actually solve for the speed? [it can be done, since you can write $$\gamma$$ in terms of v... but do you need to?]
While v>0.1c may characterize "relativistic", is there another way?

 

[thenewbosco]

this was the hint that was given, that relativistic speeds were > 0.1c, but if you could give me a hint on comparing something else it would be appreciated.

 

[robphy]

What is the corresponding inequality for $$\gamma$$?

 

[thenewbosco]

i don't know of anything similar, but gamma will be less than or equal to 1. is this close to the right track?

 

[Gamma]

Find $\frac{\gamma v}{c}$ (= $\frac{\Delta p}{mc}$)

Squre both sides and solve for v/c.

 

[Gamma]

gamma will be less than or equal to 1.

v < c
Therefore, gamma > 1