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Probability Electron at Point: H Atom

  1. Feb 2, 2014 #1
    The problem I'm working on asks: At what radius does the probability of finding an electron at a point in the hydrogen atom fall to 50% of its maximum?

    I've already worked through the problem to find the probability at the maximum, which was to take the first derivative of r^2 e^(-2r/a) and then set it equal to zero and solve for r (results in r = a). For the 50% of maximum do I simply set that derivative equal to 0.5?


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  2. jcsd
  3. Feb 2, 2014 #2

    BruceW

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    ah, no that wouldn't get the right answer. the question is about probability. you have the wavefunction, so how do you calculate the probability of finding the electron at a certain place?
     
  4. Feb 2, 2014 #3
    Integral of the probability density; from 0 to 2pi in this case (I think).
     
  5. Feb 2, 2014 #4

    BruceW

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    you don't need to do any integration. what's important is the probability density. if the probability of finding an electron in one place is 1/2 the probability of finding it in another specific place, then what can you say about the ratio of the probability density at these two points?
     
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