1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Working out magnetic moment and electric quadrupole moment

  1. May 14, 2015 #1
    Could somebody check if I have done this correctly please?

    1. The problem statement, all variables and given/known data

    Draw the shell filling for oxygen isotopes and make predictions of their nuclear spin, parity, magnetic moment and electric quadrupole moment.

    2. Relevant equations
    Magnetic moment μ = gj j μN
    Electric quadrupole moment Q ≈ -<r2>[itex]\frac{2j - 1}{2(j + 1)}[/itex]

    3. The attempt at a solution
    So starting off with the isotopes of oxygen: 16O, 17O, 18O

    This fills the 1p[itex]\frac{1}{2}[/itex] shell.

    spin = 0 because it is even-even
    parity = 1 because even-even
    μ = 0 because even-even
    Q = 0 because it is a closed shell

    This corresponds to the 1d[itex]\frac{5}{2}[/itex] shell.

    Same values as above except for the electric quadrupole moment:

    Q ≈ -<r2>[itex]\frac{2(0) - 1}{2((0) + 1)}[/itex] = -<r2>[itex]\frac{-1}{2}[/itex] = [itex]\frac{1}{2}[/itex]<r2>

    This corresponds to a valence neutron in the 1d[itex]\frac{5}{2}[/itex] shell.

    spin = j = [itex]\frac{5}{2}[/itex]
    parity = (-1)l = (-1)2 = 1

    μ = [itex]\frac{5}{2}[/itex] gj μN (I won't work out gj or put the value of μN in)

    Q ≈ -<r2>[itex]\frac{2(\frac{5}{2}) - 1}{2((\frac{5}{2}) + 1)}[/itex] = -[itex]\frac{4}{7}[/itex]<r2>
  2. jcsd
  3. May 15, 2015 #2
    I think I may be wrong about the electric quadrupole moments, it's possible that only protons contribute to Q. So because the only thing that changes with oxygen isotopes is neutron number Q will be 0 for all of them?

    EDIT: scratch that neutrons do actually contribute as they attract the protons slightly.
    Last edited: May 15, 2015
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted