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The susceptibility of magnesium at 300 K is 1.2 × 10^{−5}. At what temperature will the susceptibility increase to 1.8 × 10^{−5}?

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#### Solution

Given,

Susceptibility of magnesium at 300 K,

\[\chi_1= 1.2 × 10^{−5}\]

Let T_{1} be the temperature at which susceptibility of magnesium is 1.2 × 10^{−5} and T_{2 }be the temperature at which susceptibility of magnesium is 1.8 × 10^{−5}.

According to Curie's law,

\[\chi = \frac{C}{T}, \]

where C is Curie's constant.

\[\Rightarrow \frac{\chi_1}{\chi_2} = \frac{T_2}{T_1}\]

\[ \Rightarrow \frac{1 . 2 \times {10}^{- 5}}{1 . 8 \times {10}^{- 5}} = \frac{T_2}{300}\]

\[ \Rightarrow T_2 = \frac{12}{18} \times 300\]

\[ \Rightarrow T_2 = \frac{2}{3} \times 300 = 200 K\]

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