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The magnetic moment can be calculated using the formula ( \mu = \sqrt{n(n+2)} ), where ( n ) is the number of unpaired electrons. For Fe³⁺, which has a configuration of ( [Ar] 3d^5 ), there are 5 unpaired electrons, giving a magnetic moment of approximately ( \mu_{Fe^{3+}} \approx 5.92 ). For Co²⁺, with a configuration of ( [Ar] 3d^7 ), there are 3 unpaired electrons, resulting in a magnetic moment of about ( \mu_{Co^{2+}} \approx 3.87 ). Therefore, the ratio of the magnetic moments ( \mu_{Fe^{3+}} : \mu_{Co^{2+}} ) is approximately ( 5.92 : 3.87 ) or roughly ( 1.53 : 1 ).

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