# Uncertainty - Finding Momentum and KE

1. Homework Statement

An electron is conned inside a cubic region of size an atomic radius L = 0.5 nm.

2. Homework Equations

What is the uncertainty in the momentum p of the electron? Remember that $$\Delta p \Delta x \approx h$$.

3. The Attempt at a Solution

I am confused when to use $$\Delta p \Delta x \approx h$$ or $$\Delta p \Delta x \approx \frac{\hbar}{2}$$.

So first I solved for p using $$\Delta p \Delta x \approx h$$ since that's what was suggested in the problem.

From the momentum I found there, I then solved for speed using $$\Delta p \Delta x \approx h$$ along with the electron's mass. This gave me a non-relativistic speed.

The next part of the problem reads: what is its minimum kinetic energy? Is the electron relativistic? For this I just used the regular KE=1/2mv2.

Then I got thinking about the minimum KE as asked in the question and that is where my confusion came in. Should I be using the second equation instead? I read the wiki page for the Uncertainty Principle and that confirmed my worry that I should be using the second one.

My question is....is my logic for this problem correct (the way I have already solved it)? And when is one used over the other?