Setting up an Uncertainty Problem

[member 545369]

Homework Statement

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].

Homework Equations

ΔxΔp ≥ ħ/2

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.

 

[TSny]

The 6 fm represents the radius of the nucleus.

 

[member 545369]

The 6 fm represents the radius of the nucleus.

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

 

[haruspex]

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

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

 

[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.

 

[member 545369]

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

You're 100% right. Thanks for that!