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We have B1/J1 = a1*I1/mu1
B1/J1 is the magnetic field from the electron cloud. For an isotope we have different amount of neutrons, but equal amount of protons, so also equal amount of electrons. The electron cloud is therefore the same, so
B1/J1 = B2/J2
So a1*I1/mu1 = a2*I2/mu2
So we find
mu2 = a2*I2*mu1/(a1*I1)
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