I’m not sure I’m following the question, but I’ll try to answer.
We can measure the value a, defined in the slides. This a depends on mu, B_J, I and J. We considered B_J as being known, or something we can calculate. I assume this is the same for the new isotope (same for J), and hence also known from earlier. We are given the value of I, and hence from our measurements of a, we can determine the value of mu.
I’m not sure about this, I was also thinking we could measure the energy splitting, maybe this would give us also some information we could use, but I don’t see how exactly.
I see others that are also assuming J and B_J to be the same for both isotopes, and some mention that it is indeed since we only change the number of neutrons, and this would not affect the electron cloud. But I would like more clarification on this, I’m not 100% convinced since I have no clue on how these J and B_J behave.
Moreover, J is the spin of the electron cloud, but how exactly is this defined? Can we be sure it remains constant? More info is always welcome!