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De broglie waves

  1. Oct 28, 2005 #1
    for the following question:
    a hydorgen atom is 5.3*10^(-11) m in radius. use the uncertainty principle to estimate the minimum energy an electron acan have in this atom.

    my problem:
    to calculate the kinetic energy, do you use Ek=(p^2)/2m or Ek=pc????
     
  2. jcsd
  3. Oct 28, 2005 #2
    The uncertainty principal is: /\x/\p = h/2*pi.

    /\x is the radius you have stated.

    /\p is the uncertainty of momentum. p = mv, mass is known, so /\p = m/\v.

    So: /\v = h/(2 * pi * m * /\x)

    where m is the mass of the electron.

    Find /\v, then you can find the minimum energy:

    energy = 0.5 * m * /\v^2.
     
    Last edited: Oct 28, 2005
  4. Oct 29, 2005 #3
    is that the same as just calculating the kinetic energy=p^2/2m?
     
  5. Oct 29, 2005 #4
    Yep, that's another way.
     
  6. Oct 31, 2005 #5
    ok~ that's cool!
     
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