From the Wien displacement law,

$\begin{align*}\lambda^{\text{max}}_1 T_1 = \lambda^{\text{max}}_2 T_2\end{align*}$
$T_1 = 6000 \mbox{ K}$ , $T_2 = 300 \mbox{ K}$ , and $\lambda^{\text{max}}_1 = 500 \mbox{ nm}$ , so
$\begin{align*}\lambda^{\text{max}}_2 = 500 \mbox{ nm} \cdot \frac{6000 \mbox{ K}}{300 \mbox{ K}} = \boxed{10000 \mbox{ nm}}\e...$
Therefore, answer (A) is correct.

Solution to 2008 Problem 19