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The task mentions that it is possible to measure the hyperfine coupling constant ‘a’.
If you know I_1, mu_1 and measure a_1, you can infer the rest of the values in this constant, i.e. B_J/J. The information of the electron-cloud does not change between isotopes, so we can use the inferred value for B_J/J for the second isotope. We also know I_2. The only unknown left now is mu_2. From measuring a_2, we can infer the value for mu_2.
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