Hyperfine Splitting

  • #1

Summary:

I'm trying to figure out how to find the energy difference of Titanium-48(22 protons/electrons & 26 neutrons) hyperfine splits of the ground state. It has 2 unpaired electrons(d orbital) and angular momentum of 2(l=2) so the total splits(2l+1) are 5.

Main Question or Discussion Point

I've looked around for help on sites and youtube but I don't really understand how to figure it out.
 

Answers and Replies

  • #2
anuttarasammyak
Gold Member
199
82
The formula of hyperstructure splitting
[tex]{\displaystyle \Delta E_{hfs}=-{\vec {\mu }}_{I}{\vec {B}}_{J}={\frac {a}{2}}[F(F+1)-I(I+1)-J(J+1)],}[/tex]
where
[tex]{\displaystyle a={\frac {g_{I}{\vec {\mu }}_{N}{\vec {B}}_{J}}{\sqrt {J(J+1)}}},}[/tex] , J is the rotational quantum number and F is the total rotational quantum number inclusive of nuclear spin I via
https://en.wikipedia.org/wiki/Hyperfine_structure.

How about finding these I,J and F in your case ?
 
  • #3
DrClaude
Mentor
7,337
3,516
Titanium-48 has no nuclear spin, ##I=0##, so there will be no hyperfine splitting.
 

Related Threads on Hyperfine Splitting

  • Last Post
Replies
1
Views
1K
Replies
1
Views
1K
Replies
4
Views
849
  • Last Post
Replies
0
Views
3K
Replies
3
Views
3K
Replies
1
Views
468
Replies
9
Views
3K
  • Last Post
Replies
1
Views
762
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
3K
Top