1. Not finding help here? Sign up for a free 30min 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!

How do you calculate the magnetic moment of the ground state of Calciu

  1. Dec 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Calculate the magnetic moment of the ground state of [itex]\,_{20}^{39}Ca[/itex]. Compare to the experimental value in table 1.

    2. Relevant equations

    Nuclear Shell Model knowledge

    3. The attempt at a solution

    Well firstly the magnetic moment of the nucleus similar to the spin is based only on the unpaired nucleon. With the above having one unpaired neutron in the 1d3/2 giving it spin 3/2 and parity +.

    I thought the formulae for magnetic moment was:

    [itex] \mu_{n} = \dfrac{g_{n}\mu_{N}\vec{s}}{\hbar}[/itex]

    but that would only involve googling the g value and multiplying it by 3/2 I think which would not get me all the marks this question is worth. Please give me a point in the right direction.
     
    Last edited: Dec 5, 2013
  2. jcsd
  3. Dec 7, 2013 #2
    I thought the subshell it would be in would be 0d3/2
     
  4. Dec 7, 2013 #3
    Yes sorry the subshell is 0d3/2 also its total angular momentum is 3/2 not its spin which I said before. I continued studying on my own when I didnt get an answer and in case anyone is interested the answer (I think) would be to use this formula (derived from the first equation I mentioned taking into account that s and l are not exactly defined in a system where j is, so replacing all terms in quantities related to j using vectors and expectation values);

    [itex]\mu_{n} = \left[g_{l}\dfrac{j(j+\dfrac{1}{2})}{(j+1)}-\dfrac{1}{2}\dfrac{1}{j+1}g_{s}\right]\mu_{N}[/itex]
     
  5. Dec 8, 2013 #4
    for the magnetic moment i got μn=3.865x10^-27 J/T
    where gl=0 and gs=-3.8261
     
  6. Dec 8, 2013 #5
    That is what I got if you convert to those units. Though the comparison against the experimental value in table 1 is unitless i.e. magnetic moment/nuclear magneton and the equation above gives you an answer in units of nuclear magneton(if you dont put in the number of mu_N and just leave it as mu_N). So its just that number(0.76526)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How do you calculate the magnetic moment of the ground state of Calciu
Loading...