If we measure the spectrum of radiation coming from different clouds in Jupiter's atmosphere,and we find that a cloud that appears white in visible light emits the largest number of photons at a wavelength of ,while a cloud that appears brown in visible light emits the largest number of photons at a wavelength of ,how do the temperatures of the clouds compare?

Question

If we measure the spectrum of radiation coming from different clouds in Jupiter's atmosphere,and we find that a cloud that appears white in visible light emits the largest number of photons at a wavelength of  ,while a cloud that appears brown in visible light emits the largest number of photons at a wavelength of  ,how do the temperatures of the clouds compare?

Quizplus · Accepted Answer

The wavelength of the photons emitted by a cloud is related to the temperature of the cloud through Wien's law, which states that the wavelength at which the maximum number of photons is emitted is inversely proportional to the temperature. The formula for Wien's law is λmax = b/T, where λmax is the wavelength at which the maximum number of photons is emitted, T is the temperature, and b is Wien's displacement constant. Since both clouds emit at the same wavelength in the infrared, we can set their expressions for T equal to each other and solve for the ratio:

b/11eaa3e3_4196_638f_a4ea_f72760680a2d_TB4068_11 = b/11eaa3e3_4196_6390_a4ea_658e749ea4a9_TB4068_11

11eaa3e3_4196_6390_a4ea_658e749ea4a9_TB4068_11/11eaa3e3_4196_638f_a4ea_f72760680a2d_TB4068_11 = T_white/T_brown

Simplifying the left side:

10/638f_f72760680a2d_TB4068_11 = T_white/T_brown

T_white = (T_brown)(10/638f_f72760680a2d_TB4068_11)

T_brown/T_white = (638f_f72760680a2d_TB4068_11)/(10) = 390

This means that the brown cloud is 1.5 times hotter than the white cloud, so the answer is (B).

If We Measure the Spectrum of Radiation Coming from Different