Consider a Hot Jupiter with a temperature of 3009 K orbiting the star Vega. At what wavelength in nanometers) would the Hot Jupiter would be brightest?

Answer 1

Wien's Law states that the peak wavelength and temperature are inversely proportional:

lambda = b/T where b is a proportionality constant and T is the temperature of the planet (3009 K in this case). b = 2.897771955...×10⁶ nm⋅K (from Wikipedia), so plugging these in will give you the wavelength in nm.