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I Why is the s state spherically symmetric?

  1. Sep 8, 2016 #1

    KFC

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    Hi there,
    I am reading something about quantum numbers, there the author introduce the quantum number by solving Schrodinger equation for Hydrogen atom. It gives me an example when the principal quantum number n=4, there are four different sub-level ##s, p, d, f##. It also depicts the sublevel for them. It is said that for s state which ##\ell=0##, the shape is something like a completely flattened ellipse going through the nucleus. But since ##\ell=0##, there is no angular momentum, the electron is not "orbiting" anything; hence, it must be totally radially so s state is spherically symmetric.

    It is quite confusing for me. Since it is said at the beginning it is flatten ellipse but later becomes spherically symmetric.

    reference: http://web.pdx.edu/~pmoeck/lectures/312/chapter 7 part 3.doc
    page 3 and page 8
     
    Last edited: Sep 8, 2016
  2. jcsd
  3. Sep 8, 2016 #2

    Doc Al

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    Where does your reference say that?
    Right. s orbitals are spherically symmetric.
     
  4. Sep 8, 2016 #3

    KFC

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    Sorry that I give the wrong reference. I just get it corrected. And in the document given by the link, in page 3, note below the caption of FIGURE 7.3, it is said that "for l=0 we have a completely flattened ellipse that goes through the nucleus, this will be later called an s state."
     
  5. Sep 8, 2016 #4

    Doc Al

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    Those elliptical orbits are remnants of the Bohr-Sommerfeld model of the atom. (Old stuff!) Note the diagram on page 20 of your reference, which shows the s orbitals as spherical.
     
  6. Sep 8, 2016 #5

    KFC

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    Thanks a lot.
     
  7. Sep 9, 2016 #6

    vanhees71

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    According to my prejudices, I always warn against physics manuscripts written with Word. This one cements my prejudice. SCNR.
     
  8. Sep 10, 2016 #7

    DrDu

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    Classically, an orbit with l=0 corresponds to the electron falling straight on or through the nucleus. Quantum mechanically, the orientation of this line becomes completely undetermined.
     
  9. Sep 10, 2016 #8

    vanhees71

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    Quantum mechanically ##l=0## means that your wave function and thus the probability distribution for the particle's position (and momentum) is spherically symmetric.
     
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