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Firstly we measure the hyperfine coupling constant a for the isotope with the known nuclear spin and magnetic moment. From this hyperfine coupling constant a, the nuclear spin and magnetic moment we can calculate the hyperfine field for this isotope. We can then use this hyperfine field value for the other isotope as they have the same electron cloud configurations and thus the same hyperfine fields.
We can then use this value in combination with the values for the hyperfine coupling constant we measure for the second isotope and for its nuclear spin to derive its magnetic moment.
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