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Minimum energy of electron bound in nucleus

  1. Nov 11, 2012 #1
    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

    [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?
     
  2. jcsd
  3. Nov 11, 2012 #2

    mfb

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    2016 Award

    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.
     
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