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Q.

A paramagnetic material has $10^{28} a t o m s / m^{3} .$ Its magnetic susceptibility at temperature $350 K$ is $2.8 \times 10^{- 4} .$ Its susceptibility at $300 K$ is

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a

$3.672 \times 10^{- 4}$

b

$3.267 \times 10^{- 4}$

c

$3.726 \times 10^{- 4}$

d

$2.672 \times 10^{- 4}$

answer is C.

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Detailed Solution

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We know that susceptibility of a material is given as
$X α \frac{1}{T_{C}}$
$\Rightarrow \frac{X_{1}}{X_{2}} = \frac{T_{C_{2}}}{T_{C_{1}}}$

$\Rightarrow \frac{2.8 \times 10^{- 4}}{X_{2}} = \frac{300}{350}$
$\Rightarrow X_{2} = \frac{2.8 \times 350 \times 10^{- 4}}{300}$
$\Rightarrow X_{2} = 3.266 \times 10^{- 4}$

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