A paramagnetic material has $$10^{28}$$ atoms m$$^{-3}$$. Its magnetic susceptibility at temperature 350 K is $$2.8 \widetilde{A} \times 10^{-4}$$. Its susceptibility at 300 K is

For a paramagnetic substance we use Curie’s law, which states that the magnetic susceptibility $$\chi$$ varies inversely with the absolute temperature $$T$$:

$$\chi = \dfrac{C}{T},$$

where $$C$$ is Curie’s constant (a material‐specific constant).

Because the same specimen is observed at two different temperatures, the value of $$C$$ remains unchanged. Thus we may write for the two sets of observations

$$\chi_1 T_1 = C = \chi_2 T_2.$$

Rearranging to obtain the unknown susceptibility $$\chi_2$$ at temperature $$T_2$$ we get

$$\chi_2 = \chi_1 \dfrac{T_1}{T_2}.$$

The data provided are

Initial susceptibility: $$\chi_1 = 2.8 \times 10^{-4}.$$

Initial temperature: $$T_1 = 350 \text{ K}.$$

Required temperature: $$T_2 = 300 \text{ K}.$$

Substituting these values into the rearranged Curie’s law expression:

$$\chi_2 = \left(2.8 \times 10^{-4}\right)\dfrac{350}{300}.$$

First evaluate the fraction $$\dfrac{350}{300}$$:

$$\dfrac{350}{300} = \dfrac{35}{30} = \dfrac{7}{6} = 1.166\overline{6}.$$

Now multiply this factor with $$2.8 \times 10^{-4}$$:

$$\chi_2 = 2.8 \times 10^{-4} \times 1.166\overline{6}.$$

Carrying out the multiplication step by step:

$$2.8 \times 1.166\overline{6} = 3.266\overline{6}.$$

Hence

$$\chi_2 \approx 3.266\overline{6} \times 10^{-4}.$$

Rounding to three significant figures,

$$\chi_2 \approx 3.267 \times 10^{-4}.$$

This value matches the entry in Option C.

Hence, the correct answer is Option C.