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Minimum energy of electron bound in nucleus

  • Thread starter phosgene
  • Start date
141
1
1. Homework Statement

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

2. Homework Equations

[itex]ΔxΔp_x=h/4\pi[/itex]
[itex]E^2=p^2c^2 + m^2c^4[/itex]

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

[itex]E=pc[/itex]

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?
 
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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.
 

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