# Minimum energy of electron bound in nucleus

#### phosgene

1. Homework Statement

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

2. 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,

$E=pc$

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?

Related Introductory Physics Homework Help News on Phys.org

#### mfb

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.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving