jk4

**1. Homework Statement**

In its own frame of reference, a proton takes 5 min to cross the Milky Way galaxy, which is about [tex]10^{5}[/tex] light-years in diameter.

(a) What is the approximate energy of the proton in electronvolts?

(b) About how long would the proton take to cross the galaxy as measured by an observer in the galaxy's reference frame?

mass of proton = [tex]1.6726 x 10^{-27} kg[/tex]

[tex]1eV = 1.602 x 10^{-19} J*s[/tex]

**2. Homework Equations**

It says the problem belongs to the "Energy and Momentum" section, so here are those equations:

[tex]E = \gamma mc^{2}[/tex]

[tex]p = \gamma mv[/tex]

[tex]E^{2} = (mc^{2})^{2} + p^{2}c^{2}[/tex]

[tex]E = pc[/tex]

*(Massless particle, probably doesn't apply to this problem)*

**3. The Attempt at a Solution**

well, I'm pretty confused. I calculated that the distance of [tex]10^{5}[/tex] light-years corresponds to about [tex]9.45 x 10^{15} m[/tex]. But I can't figure out how to proceed from here.

I'm not necessarily looking for an answer but a little help.

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