Undergrad Hyperfine Splitting: Get Help Understanding It

[privategenius]

TL;DR

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.

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

 

[anuttarasammyak]

The formula of hyperstructure splitting
{\displaystyle \Delta E_{hfs}=-{\vec {\mu }}_{I}{\vec {B}}_{J}={\frac {a}{2}}[F(F+1)-I(I+1)-J(J+1)],}
where
{\displaystyle a={\frac {g_{I}{\vec {\mu }}_{N}{\vec {B}}_{J}}{\sqrt {J(J+1)}}},} , 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 ?

 

[DrClaude]

Titanium-48 has no nuclear spin, $I=0$, so there will be no hyperfine splitting.