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Atomic Orbitals

  • Page ID
    32705
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    (2) radial density versus r.
    1. Density versus radius r: In this case, the square of the wave function is plotted against r. These plots are sometimes misleading. For example, the 1s orbital plot looks like
      probability
        |
        |.
        |
        | .
        |
        |   .
        |
        |      .
        |          .
        |               .
        |                     .
        |                             .
        |________________________________________._______ r
      
      You may feel the probability of finding the electron is the highest in the nucleus, yet you have learned that the electron is most likely at a distance r = 53 pm from the center of the atom.
    2. Radial density (RD) versus r: To really represent the probability of finding the electron at r at a given time, the radial distribution against r is often plotted. In this plot, instead of plotting square-of-the-wave-function, we modify square-of-the-wave-function by the volume associated with r, (4*pi*r2). This modification converts electron density to radial electron density.

      The radial density plot of 1s orbital has a shape as shown below:

      probability
        |
        |
        |
        |
        |
        |        .  '   .
        |     .           .
        |   .                 .
        | .                            .
        |________________________________________._______ r
      
      
      At the center of the atom, the value of the wavefunction is large, but when r = 0, the volume element (4*pi*r2) is almost zero when r -> 0. Thus, the radial distribution rises as r increases, reaching a maximum at some value of r. For the H atom, the maximum of the radial distribution is at r = 53 pm.

    Contributors and Attributions


    This page titled Atomic Orbitals is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Chung (Peter) Chieh.

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