Solving the Uncertainty Principle Homework

[Epif]

Homework Statement

http://img340.imageshack.us/img340/3249/question.jpg

Homework Equations

P=h/lambda
E=p^2/2m

The Attempt at a Solution

Well, I calculated P using a wavelength of .1 femtometer. Then I plugged it into the energy equation. However, I got 1.5e14 eV, while the answer sheet says it's supposed to be 12 GeV. Have I done something wrong wrong? On the answer sheet my professor calculated P, and I got the same answer he got, but after that he just says therefore E=12GeV, not showing how he came to that conclusion.

Thanks for any help!

 

[Fightfish]

You cannot neglect relativistic effects at such high energies, thus the equation
$$E = \frac{p^{2}}{2m}$$ does not hold.
Instead you should use the relativistic equation
$$E^{2} = m_{0}^{2} c^{4} + p^{2} c^{2}$$

 

[Epif]

Ahh that makes sense and gives e the right answer. Thanks!