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Homework Help: Expectation values of the electron.

  1. Feb 5, 2009 #1
    1. The problem statement, all variables and given/known data

    The expectation value <r> of the electron-nucleus separation distance 'r' is:

    <r> = ʃ r |ψ|² dV.

    (a) Determine <r> for the 1, 0, 0 state of hydrogen.





    3. The attempt at a solution

    Right, I've obtained the value for ψ = (1/πa³)^1/2 exp(-r/a)

    I then replace dv by 4πr² dr.

    I then put all of that in the equation above and try to integrate but I cant seem to go any further from here. Any help?

    Thanks very much.
     
  2. jcsd
  3. Feb 5, 2009 #2

    Gokul43201

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    Are you having trouble with the integral? Remember how to integrate by parts?
     
  4. Feb 5, 2009 #3
    I think it might be the integral. The problem is, I have an exponential term in the integral which I can't solve by parts? if so how?
     
  5. Feb 5, 2009 #4

    Gokul43201

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    How are you trying to integrate, and what's the problem? Show us what you are doing.
     
  6. Feb 5, 2009 #5
    Your integral should be of the form:

    u dv = exp(-2r/a) r^3 dr

    All you have to do is assign u and v. Hint: you will have to integrate by parts several times.
     
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