We need to find the nuclear magnetic moment μ2 and we already know the nuclear spin I1 and magnetic moment μ1.
From our experiment we can also find the hyperfine coupling constant a and I2. We can also deduce J from the energy level spacing and have B, the magnetic vector.
We now have enough informations to calculate the magnetic moment of this different isotope of the same element. We can first calculate the Hamiltonian H= a*I*S, then from this equation: H=-μ*B we can find the magnetic moment μ2.