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Electron probability

  1. Apr 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider an electron in the n = 5, ℓ = 2, mℓ = -1 state.
    What is the probability that the electron is located in a cone
    of half angle 41◦ about the z axis? (In other words, what is the
    probability that θ ≤ 41◦
    ?)
    2. Relevant equations

    P=∫∫∫R(r)^2 * Y[θ,phi]^2


    3. The attempt at a solution

    I'm not quite sure what I'm doing here, but this is as far as I got:

    I said R(r) is a constant because the angle doesn't depend on the radius.

    Next I found an expression for Y(theta,phi) from my textbook based on l and m_l:

    Y(θ,f)=.5*sqrt(15/2pi)SinθCosθ * e^-i*f

    I integrated Y^2, .7156<θ<pi, 0<f<pi

    This probability is not right.

    ANy ideas?
     
  2. jcsd
  3. Apr 18, 2013 #2

    Simon Bridge

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    You have assumed the radial wavefunction is a constant for that state... did you check, say, by looking it up or computing it? Did you remember to take the complex conjugate for the complex parts of the wavefunction?
     
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