# Homework Help: Minimum energy of electron bound in nucleus

1. Nov 11, 2012

### phosgene

1. The problem statement, all variables and given/known data

An electron is confined to a nucleus of radius 4 femtometres. Estimate its minimum energy.

2. Relevant equations

$ΔxΔp_x=h/4\pi$
$E^2=p^2c^2 + m^2c^4$

As the electron's rest energy will be much less than it's kinetic energy,

$E=pc$

3. The attempt at a solution

So I understand that I'm supposed to use the uncertainty principle to find the average momentum, and then plug it into the energy equation. What I don't understand is that the solutions use Δpx/2 instead of just Δpx. Why is this?

2. Nov 11, 2012

### Staff: Mentor

I think that Δpx/2 in both directions gives a difference of Δpx, which is "somehow" equivalent to a momentum uncertainty.
Using Δpx is probably fine, too.