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Probability of finding electron inside bohr radius

  1. Sep 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider an hydrogen atom in its ground state, what is the probability that the electron is found inside the Bohr Radius?


    2. Relevant equations

    The probability of finding the electron at bohr radius is maximum. but the probability over the range from 0 to bohr radius, is hard to visualize.

    3. The attempt at a solution

    http://www.physics.uc.edu/~sitko/CollegePhysicsIII/28-AtomicPhysics/AtomicPhysics_files/image024.jpg
    graphically, the probability is area under the curve from 0 to bohr radius, but how to do it mathematically?
     
  2. jcsd
  3. Sep 11, 2009 #2

    gabbagabbahey

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    Hint: The area under the curve [itex]f(x)[/itex] between [itex]x_0[/itex] and [itex]x_1[/itex] is

    [tex]\int_{x_0}^{x_1} f(x)dx[/tex]
     
  4. Sep 11, 2009 #3
    i know this, is a calculus. but the real things is how to represent the wavefunction of hydrogen atom?

    [tex]Probability=\int\psi*\psi dx[/tex]
     
  5. Sep 11, 2009 #4

    gabbagabbahey

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    The ground state wavefunction for a hydrogen atom is computed (at least approximately) in every introductory QM text I've seen....surely you've come across it before?
     
  6. Sep 11, 2009 #5
    alright then, will flip through it, in case i miss out. thanks. by the way, i should be working in spherical coordinate right?
     
  7. Sep 11, 2009 #6
    ok, that would be [tex]\psi_{100}=\frac{1}{\sqrt{\pi a^{3}}e^{\frac{-r}{a}}[/tex]
    bingo!


    [itex]\psi_{100}=\frac{1}{\sqrt{\pi a^{3}}e^{\frac{-r}{a}}[/itex]
     
    Last edited: Sep 11, 2009
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