Minimum energy of electron bound in nucleus

[phosgene]

Homework Statement

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

Homework 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,

$E=pc$

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 Δp_x/2 instead of just Δp_x. Why is this?

 

[mfb]

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