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Uncertainty Principle and energy of an electron

  1. Sep 22, 2009 #1
    Using the uncertainty principle find the energy required for the electron to be confined inside the hydrogen atom. Use the radius of the atom 1 x 10-10 m for Δr. Express your answer in eV, rounded up to the nearest hundredth.

    Equations used

    Δx(Δp) ≥ h/4pie

    1 x 10^-10 m x p ≥ 4.14 x 10^-15 eV / 12.56

    Δp ≥ 3.3 x 10^-6

    I'm not really sure what to do from here or if I even did this correctly. My teacher did a horrible job explaining this to me and I am really confused. I found the momentum Δp = mv

    What do I do from here?
     
  2. jcsd
  3. Sep 22, 2009 #2
    Maybe p2/2m is an estimation of kinetic energy. Maybe e2/delta_x is an estimation of the potential energy?
     
  4. Sep 22, 2009 #3
    This problem is rather confusing and basically it's way of approximating values using the uncertainty principle so I wouldn't worry too much the first time you encounter it!

    Think in terms of energy.

    For example say you want to know how much energy it takes to leave the earth's atmosphere. Well the earth has some potential energy right? We can consider this like a potential energy well, the earth is a well and in order to escape we must put in energy to overcome the potential. So if start from the ground and wanted to leave the earth's atmosphere we would need a greater amount of kinetic energy than potential energy. Or conversely in order to stay in the earths atmosphere the potential energy of the earth would need to be greater than our kinetic energy.

    So back to your problem. In order for the electron to stay in the hydrogen atom there must be a greater or equal amount of potential energy compared to kinetic energy does this make sense?
     
  5. Sep 22, 2009 #4
    Ok so

    Δp ≥ 3.3 x 10^-6 eVs

    p^2/2m = Ke
    (3.3x10^-6)^2 eVs / 2 (1.01)

    Ke = 5.5 x 10^-12 eVs

    So U ≥ 5.5 x 10^-12 eVs?
     
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