# The magnetic susceptibility of magnesium at $\inline 300\; K$ is  $\inline 1.2\times 10^{5}$. At what temperature will its magnetic susceptibility become $\inline 1.44\times 10^{5}$ ?

We have given the temperature :

Temperature $T_{1}=300K$

Temperature $T_{2}=?$

Given: the magnetic susceptibility at a temperature

$T\ \text{is}\ \\\chi_{1}=1.2\times 10^{5}$

and at temperature

$\\T_{2}\ \text{is}\\\chi_{2}=1.44\times 10^{5}$

We know that,

According to curies law at far away from saturation Susceptibility $\chi$ of paramagnetic material is inversely proportional to temperature (T).

$\chi=\frac{C}{T}$      Where, $C$ is curies constant and $T$ is temperature

Hence, we can say that,

$\frac{\chi_{1}}{\chi_{2}}=\frac{T_{2}}{T_{1}}$

On putting the values of $\chi_{1},\chi_{2}$ and $T_{1},$ we can have $T_{2}$.

$\frac{1.2\times 10^{5}}{1.44\times 10^{5}}=\frac{T_{2}}{300}$

$T_{2}=\frac{1.2}{1.44}\times 300=250K$

Therefore, the magnetic susceptibility become $1.44\times 10^{5}$ at the temperature $250K$

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