in atom why p orbital have dumb bell shape

Discussion in 'Physics' started by sabbi, Feb 7, 2010.

  1. sabbi

    sabbi Thread Starter New Member

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    i have a question that why we said that s orbital have spherical while p orbital have dumb bell shape?
  2. studiot

    studiot E-book Developer

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    Hello Sabbi , here is a non mathematical explanation, if you want mathematical post again.

    Orbitals are a bit like seats on a bus. They are fixed in place and the passengers (electrons) have to sit where there is an empty space. They cannot start rearranging the seats to suit themselves as if they were in a lounge.

    The rules of placement are different though. In a bus clear space (the aisle) has to be allocated to allow passengers to wald to their seats. Electrons do not need this - they have the ability to jump instantly to their correct positions. This is called tunneling.

    The main difference between passengers and electrons is that passengers are neutral they neither attract or repel each other. Electrons have a negative charge so repel each other. They are also attracted by the positive charge in the nucleus.

    So the placement of electron orbitals is determined by the conflicting requirments of electrons to get close to the nucleus, but far from each other.

    Note that there is one S orbital but three P orbitals in each shell (one for each axis)

    If we look at my sketch and imagine the electron to be smeared out over the whole orbital (this is the easiest representation for this purpose) then we can see that the S orbital satisfies this for the first electrons. Once this is filled there are three P orbitals. The shapes can be seen to be as close to the centre as being distant from each other allows.

    If you were to ask why do the electrons not just fly into the nucleus because of the attraction? This because the electrons posess energy. This energy allows them to remain apart from the positive nucleus. There is thus an inner core volume where there are no electrons. The S orbital is hollow.

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  3. sabbi

    sabbi Thread Starter New Member

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    Thanks for reply. i satisfies with your expalation but my question is at his place. you dont tell me why we ask p orbital has dumb bell shape and not spherical. also tell me please what is sheilding effect?
  4. studiot

    studiot E-book Developer

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    I just spent quite some time composing further explanation so I was pretty peeved that the site just ate my reply.

    I will have another go later.
    Last edited: Feb 9, 2010
  5. BillO

    BillO Well-Known Member

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    This has been happening quite a bit lately.
  6. jpanhalt

    jpanhalt E-book Developer

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    Perhaps Schrödinger's Cat knows where the posts went?

    John
  7. Papabravo

    Papabravo AAC Fanatic!

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    The simple answer is that in quantum mechanics things like energy and angular momentum are constrained to have discrete values. When those discrete values are assigned to an electron it's statistics imply a high probability of being where it is supposed to be. The dumbell shape is just the set of points where the electron is likely to be. In order for it to be somewhere else it must change it's quantum numbers or it must be an extremely unlikely event.
    Last edited: Feb 10, 2010
  8. KL7AJ

    KL7AJ E-book Developer

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    So it's actually a "smartbell" shape. :D:cool:
  9. davebee

    davebee Well-Known Member

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    Here's a slightly more involved answer for why dumbbell shapes are described.

    You can study atoms by examining the light that is absorbed or emitted by the atom. When people started doing this, it was immediately apparant that atoms do not emit all colors; they only emit specific wavelengths of light (but there were many different of these specific wavelengths emitted).

    The wavelength (color) of the light is exactly related to the energy gained or lost by the atom.

    If all kinds of experiments are done on the atom, and adding and removing energy while the atom is relatively free of fields, and is in electric fields and in magnetic fields of all different strengths, charts can be made up of the wavelengths observed.

    An explanation of why this is came up with the idea that electrons only "orbit" the nucleus in specific paths, each corresponding to a specific energy and angular momentum. Changing orbitals emits or absorbs energy, which results in light of a wavelength corresponding to the change in energy of the electron jumping from one orbital to another.

    Then, by analyzing many different wavelengths seen, plugging them into formulas to try to explain what sort of orbitals and orbital changes may exist that would emit the exact wavelengths seen, it turns out that mathematical solutions to those formulas describe spheres and a number of elaborate dumbbell shapes.

    That's why the p orbitals are drawn as dumbbell shapes.
  10. studiot

    studiot E-book Developer

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    This is a good question which deserves a good answer.

    But first the answer to your second question - what is shielding?

    In a multi electron atom the electrons are arranged in 'shells'

    These are numbered 1,2 3 etc and each higher number is further from the nucleus than the previous one.

    Now imagine we have a nucleus with multiple positive charges.

    When we fill the first shell the electrons see the full strength of the combined attraction of the positive charges in the nucleus.

    When we fill the next shell there is some negative charge between the electrons and the nucleus. This has less negative charge than the total positive nuclear charge so these electrons see an effectively reduced positive charge.

    This is called shielding.
    The effect increase with each shell as we move outward from the nucleus.
    A partly filled shell has a smaller shielding effect than a fully filled shell.
  11. studiot

    studiot E-book Developer

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    You need to understand that orbitals are the graphical representation of solutions to the Schroedinger Wave Equation (SWE)

    This is a difficult mathematical equation so I will try to illustrate with reference to the ordinary Wave Equation, which is much simpler. The solutions are not exactly the same but sufficiently similar for our purposes.

    Image an elastic string stretched tightly between two fixed walls, as in sketch 1 in my attachment.

    Now apply a displacement by 'twanging' the elastic in the centre as shown.
    You will see a vibrating standing wave in the string. Maximum amplitude occurs in the centre and the ends have zero amplitude.
    This is shown in sketch 2.

    Also in sketch 2 is a density plot of density or probability corresponsing to an SWE. This has max density in the centre tailing off to zero at the edges.

    If you now twang the string at a different place you will see a different standing wave.
    Sketch 3

    I have drawn the standing wave and density plot in sketch 4.
    This corresponds to the dumbell shape you are asking about.

    In a simple wave equation a wavenumber (n) is given to each possible solution or vibration pattern. This number also appears in SWE as a quantum number. The simple WE only has one such number, n. This corresponds to the number of nodes in the standing wave.

    So for sketch 1/2 n = 1 and for sketch 3/4 n = 2.

    The SWE is more complex and gives rise to several quantum numbers.

    We call the case of n = 1 the S orbital and the case of n = 2 the P orbitals.

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