# Homework Help: Setting up an Uncertainty Problem

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1. Nov 2, 2016

### talrefae

1. The problem statement, all variables and given/known data
A proton is known to lie within the nucleus of a gold atom. The radius of a gold nucleus is approximately 6 fm. What is the minimum uncertainty in the proton’s velocity [you may treat the problem as one-dimensional and you should express your answer as a fraction of c].

2. Relevant equations
ΔxΔp ≥ ħ/2

3. The attempt at a solution
I think I got this, but Chegg is showing up weird inconsistent answers. I just want to make sure my logic is sound:

So since we can treat this one dimensionally, we know that the proton lies within a 6fm range. For simplicity, we can (in our imaginations) draw a 6 fm line and put a point on the center. On that center, our uncertainty of the position of the proton is ± 3 fm. So our Δx should be 3fm instead of 6 fm!

The rest of the work is rather simple, I just want to make sure I'm setting this up properly.

2. Nov 2, 2016

### TSny

The 6 fm represents the radius of the nucleus.

3. Nov 2, 2016

### talrefae

Not very helpful. I think my work shows that I understand this.

4. Nov 2, 2016

### haruspex

No, it shows you thought the 6fm was a diameter.

5. Nov 3, 2016

### kuruman

Not that it would make a difference to this order of magnitude calculation, but if someone gave me a proton in a one-dimensional box that extends, say, from zero to 12 fm and asked "where is the proton?", I would say "somewhere between zero and 12 fm". So in such situations, I consider the position uncertainty to be the entire range in which the particle can be without me knowing any better.

6. Nov 3, 2016

### talrefae

You're 100% right. Thanks for that!