Magnetic Properties of Matter

JEE Main level, single correct, medium

50 of 57

Question 50 of 57

A paramagnetic material has 1028atomsm−3{10}^{28}atoms{m}^{-3}. Its magnetic susceptibility at temperature 350K350K is 2.8A~—10−42.8×{10}^{-4}. Its susceptibility at 300K300K is

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Answer: (C) 3.267x10−43.267x{10}^{-4}

From Curie's law, the magnetic susceptibility is inversely proportional to the temperature, i.e.,
χ∝1T\chi \propto \dfrac{1}{T}
Hence, the ratio of magnetic susceptibility at different temperature T1=350K{T}_{1}=350K and T2=300K{T}_{2}=300K.
χ2χ1=T1T2\dfrac{{\chi }_{2}}{{\chi }_{1}}=\dfrac{{T}_{1}}{{T}_{2}}
χ2=χ1×T1T2=2.8×10−4×350300{\chi }_{2}={\chi }_{1}\times \dfrac{{T}_{1}}{{T}_{2}}=2.8\times {10}^{-4}\times \dfrac{350}{300}
χ2=3.267×10−4{\chi }_{2}=3.267\times {10}^{-4}.

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