Position of a proton in Quantum mechanics.

[Skullmonkee]

Homework Statement

Find the maximum accuracy that can be found to a proton's position without changing it's (not-realativistic) kinetic energy by more that 1 keV

I think this involves Heisenberg's uncertainty principle $$\Delta x\Delta p=hbar/2$$ but I am not sure at all.

Now to find the momentum p of a non-realativistic kinetic energy we can use $$E(kinetic) = 1/2mv^2 = p^2/2m$$
which gives $$p = \sqrt{}2mE$$
however this is as far as i got.

 

[yogeshbua]

Usually, professors expect you to realize that $$p\ge\Delta p$$. Use this and see whether the answer matches!

 

[yogeshbua]

That is, use that
$$p\Delta p=m\Delta E$$
$$\Rightarrow \Delta p\le\sqrt{m\Delta E}$$
$$\Rightarrow \Delta x\ge \frac{\hbar}{2\sqrt{m\Delta E}}$$