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Question about electrons per shell

  1. May 15, 2008 #1
    why is it the maximum electrons per shell is 2,8,18,32,50 ... Wouldn't 2,8,16,32,50 make more sense mathematically?

    Are there any equations the show why this occurs?
  2. jcsd
  3. May 15, 2008 #2


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    It is due, first due to the degeneracy of the energy shell (i.e. how many energy states that have that shell's energy) and also due to the pauli exclusion principle.

    First, the higher energy shells have bigger degeneracies. In simple terms, there are more orbitals in the n=2 shell than there are in the n=1 energy shell. Thus, they can hold more electrons. Each orbital can hold a maximum of two electrons with opposite spin due to the Pauli principle. So the end result is:

    n=1 Shell: 1 orbital = 2 electrons

    n=2 Shell: 4 orbitals= 8 electrons

    n=3 Shell: 9 orbitals= 18 electrons

    The number of orbitals is determined by the number of possible angular momentum states for the electrons in the atom, which is predicted by the Schrödinger Equation. So, while your pattern may seem nicer or more aesthetic, it is not what the Schrödinger Equation predicts, so it does not make more sense mathematically in the end.
    Last edited: May 15, 2008
  4. May 15, 2008 #3
    Is this possible? n=6
    71.5 electrons?
  5. May 15, 2008 #4


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    That might be a bit difficult; splitting an electron in half is not something that you just do with a hammer and chisel...
  6. May 15, 2008 #5
    Lol. nevermind
    Last edited: May 15, 2008
  7. May 16, 2008 #6

    dont forget that the nucleus also has shells and subshells.
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