Hyperfine Structure of $^133Cs$: Find I & J

[Yaste]

Homework Statement

A transition happens for $\lambda = 494nm$ in the Cesium ions ($^133 Cs$) between a term in the $5p^5 6s$ configuration and term in the $5p^5 6p$ configuration. Five components are observed with the following energies (relative to the transition of least energy): 0, 2.40Ghz, 5.75GHz, 10.07GHz, 15.35GHz.

Find the value of the nuclear spin of $^133 Cs$ as well as the value of J for the term in the $5p^5 6s$ configuration

Homework Equations

The Attempt at a Solution

I am not sure how to solve this. I probably have to use $F = I + J$, with $I$ being the nuclear spin, which I have to find. I therefore need the value of $F$ and $J$.

One of the problems here is that I do not know how to find the S and L for the above configurations.. Any help would be huge!

 

[unscientific]

What are the $L,S,J$ numbers for the two configurations? What are the selection rules for transitions between them?