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Probability of finding electron.

  1. May 15, 2013 #1

    The picture shows the first few hydrogen atom orbitals (energy eigenfunctions). These are cross-sections of the probability density that are color-coded (black=zero density, white=highest density).

    according to the picture -Do s orbital electrons have highest probability density in the nucleus?

    (i am totally new to quantum mechanics.So please tell if i am wrong.)
    Last edited: May 15, 2013
  2. jcsd
  3. May 15, 2013 #2


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    Staff: Mentor

    If you take the radial part of the wave function only, then yes, the probability density ##|\psi|^2## is maximum at ##r=0## for s electrons. But that doesn't mean that the expectation value ##\langle r \rangle## is 0. A measurement will most likely find the electron at a certain distance from the nucleus.

    Another way to see it is to consider the radial distribution too. As s orbitals are spherical, the surface of the sphere increases as ##r## increases, so the probability of finding the electron at a certain distance of the nucleus goes through a maximum away from the nucleus.
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