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For isotope 1 we have a_1 = (mu_1 / I_1) * (B_J / J). a_1 can be experimentally measured and mu_1, I_1 is known which allows us to determine the ratio of (B_J / J).
For isotope 2 we have a_2 = (mu_2 / I_2) * (B_J / J). The ratio of (B_J / J) remains the same for this isotope because we have the same electron cloud. Rewriting this expression gives mu_2 = a_2 * I_2 * (J / B_J). a_2 can be measured, I_2 is known and the ratio was calculated using isotope 1.
This allows you to find the value of mu_2
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