The blackbody emission curves for two newly discovered exoplanets, Planet X and Planet Y, are shown below. Planet X has a peak emission wavelength of λmax, X=10 μm\lambda_{\text{max, X}} = 10\ \mu\text{m}λmax, X=10 μm and Planet Y has a peak emission wavelength of λmax, Y=25 μm\lambda_{\text{max, Y}} = 25\ \mu\text{m}λmax, Y=25 μm.
Assuming both planets act as perfect blackbodies, what is the ratio of the power radiated per unit surface area by Planet X to that by Planet Y, PXPY\displaystyle \frac{P_{\text{X}}}{P_{\text{Y}}}PYPX?
0.0260.0260.026
2.52.52.5
6.36.36.3
393939