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If we can measure for both elements the difference between the closest energy levels a, let us label them a1 and a2, we are as good as there. a1=mu_1B_J/(I_1 J), and
a2=mu_2B_J/(I_2 J), since they are Isotopes J and B_J, the electron parts, should stay the same. Only the nuclear part changes, but since we know I_1, I_2 and mu_1, it is pretty easy to find mu>_2, take a1/a2=mu_1I_2/(mu_2 I_1), so that mu_2=(mu_1 I_2/I_1)(a2/a1).
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