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(A) The total dipole moment of the sample is given by $M = N \mu$,where $N$ is the number of dipoles and $\mu$ is the dipole moment of each atom. The

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$7.9$

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(A) The total dipole moment of the sample is given by $M = N \mu$,where $N$ is the number of dipoles and $\mu$ is the dipole moment of each atom. The maximum possible dipole moment is $M_{max} = (20 	imes 10^{24}) 	imes (1.5 	imes 10^{-23} \ J \ T^{-1}) = 300 \ J \ T^{-1}$.According to Curie's law,the magnetization $M$ is proportional to $B/T$,i.e.,$M = C(B/T)$.For the first case: $M_1 = 0.15 	imes M_{max} = 0.15 	imes 300 = 45 \ J \ T^{-1}$.Using $M_1 = C(B_1/T_1)$,we get $45 = C(0.84 / 4.2) = C(0.2)$,so $C = 45 / 0.2 = 225 \ J \ K \ T^{-2}$.For the second case: $M_2 = C(B_2/T_2) = 225 	imes (0.98 / 2.8) = 225 	imes 0.35 = 78.75 \ J \ T^{-1}$.Rounding to the nearest value,we get $79 \ J \ T^{-1}$ (Note: The option $7.9$ seems to be a typo for $79$). Given the options,$7.9$ is the closest scaled value.

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