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Quantum Numbers and Total number of Orbitals

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data

    How many orbitals have the values n = 4, l = 3, and m_l = -2?

    2. Relevant equations

    First of all, is this question asking me how many orbitals there are with the given quantum numbers? Second, how do I go about finding that out

    3. The attempt at a solution

    I thought that I could figure out the number of orbitals by using 2*l +1 but the answer I get is wrong? Help please :)
     
  2. jcsd
  3. Feb 25, 2010 #2
    I think your answer would be correct if only n and l were given. The reason that 2*l + 1 does not apply is because the magnetic quantum number (m_l) is specified. The magnetic quantum number has to do with energy level within a subshell, and if I remember correctly, each orbital is associated with a single m_l.

    So what does that tell you about the number of orbitals that meet the criteria above?
     
  4. Feb 25, 2010 #3
    Hi! Thanks for your reply...I'm not quite sure at what you're trying to get at here...sorry :S I wish I did.
     
  5. Feb 25, 2010 #4
    The four quantum numbers are used to describe an electron.

    1st QN tells you what shell it is in. n = 1,2,3,...
    2nd QN tells you what subshell it is in. l = 0,1,2,...
    3rd QN specifies an orbital. m_l can be anywhere from -l to positive l, including 0. This is the reasoning behind the 2l + 1 equation. That equation tells you how many possible m_l values there are for a specific subshell, and thus how many orbitals are in a subshell.
    4th QN tells you the spin of the electron. m_s = +1/2 or -1/2

    In your problem, they told you what the m_l value was. The possible m_l values for the given subshell were -3,-2, -1, 0, 1, 2, 3, but they narrowed it down and told you that it was -2.

    How many orbital choices does that leave you with?
     
  6. Feb 26, 2010 #5
    Just one! That makes perfect sense! Thanks so much!
     
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