The susceptibility of magnesium at 27°C is $1.2 × 10^{-5}$. Its susceptibility at 200 K will be

$1.8 × 10^{-5}$

The correct answer is Option (2) → $1.8 × 10^{-5}$

Given:

Temperature 1, $T_1 = 27°C = 27 + 273 = 300\,K$

Susceptibility at $T_1$, $\chi_1 = 1.2 \times 10^{-5}$

Temperature 2, $T_2 = 200\,K$

For a paramagnetic material, $\chi \propto \frac{1}{T}$

Therefore, $\frac{\chi_1}{\chi_2} = \frac{T_2}{T_1}$

Substituting values:

$\frac{1.2 \times 10^{-5}}{\chi_2} = \frac{200}{300}$

$\chi_2 = 1.2 \times 10^{-5} \times \frac{300}{200}$

$\chi_2 = 1.8 \times 10^{-5}$

Final Answer:

${\chi_2 = 1.8 \times 10^{-5}}$