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Chemistry: Quantum Numbers

  1. Oct 7, 2012 #1
    1. The problem statement, all variables and given/known data

    In a universe different from ours, the laws of quantum mechanics are the same as ours with one small change. In this different universe the m ℓ quantum number obeys this rule.

    mℓ = (-ℓ-1), (-ℓ),..,0,...(ℓ), (ℓ+1)

    In this different universe, what is the maximum number of electrons required to fill the 2p orbitals?

    Determine only the electrons in the indicated p orbitals not any in other orbitals




    3. The attempt at a solution

    How do I do this question? I though m ℓ didn't affect the number of electrons in the p orbitals, so i put that the answer for the maximum number of electrons in 2p orbital was 6, however that was wrong. So, how do I do this? How does the m ℓ affect the maximum number of electrons? Would the answer be 10, since m ℓ would be values of -2, -1, 0, 1, 2? This really makes no sense to me. Any help would be appreciated. Thanks in advance.
     
  2. jcsd
  3. Oct 7, 2012 #2

    Borek

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    Staff: Mentor

    That's the intended logic behind.

    It makes exactly as much sense as three orbitals for three possible ml values of -1, 0, 1 (at least as long as you don't know where the rule limiting possible values of ml comes from).
     
  4. Oct 7, 2012 #3
    But i don't understand. Does each m ℓ value correspond to 2 electrons? Like in a normal universe?
     
  5. Oct 7, 2012 #4

    Borek

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    Staff: Mentor

    Yes.
     
  6. Oct 7, 2012 #5
    I don't follow this logic. For example, if it was 3p insetead of 2p, m ℓ would be -2, -1, 0, 1, 2 in normal universe. This would mean the max is 10, which is not true. The max is still 6.
     
  7. Oct 7, 2012 #6

    Borek

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    Staff: Mentor

    The way it works here is that we always have three p orbitals (regardless of n) - usually denoted px, py and pz. But we can write them as p-1, p0 and p1 as well. In the other universe there would be p-2, p-1, p0, p1 and p2.

    Perhaps you are confused by the fact that "orbital" can mean either 3p or 3px (or just px, without any more detailed specification).
     
  8. Oct 7, 2012 #7

    AGNuke

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    Gold Member

    What's the value of m for 3p. Its 1. So, the values of l are -1, 0 and +1.

    You took it wrong. Think again!
     
  9. Oct 7, 2012 #8
    ohh right. yes, i was thinking of it wrong. but if i have something like 2s. then l= 0, and ml is also 0, right? so there's only 1 possible ml value there, so according to the original question, in a regular universe the max electrons is 2, so in this alternate universe, it would also be 2?
     
  10. Oct 7, 2012 #9

    AGNuke

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    Gold Member

    Since it is not stated that each orbital can hold x electrons, so yes, its 2.
     
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