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 3 × 10⁻⁵ m,while a cloud that appears brown in visible light emits the largest number of photons at a wavelength of 1.9 × 10⁻⁵ m,how do the temperatures of the clouds compare?

Question

Quizplus · Accepted Answer

This is a question about Wien's Law, which states that the wavelength of the peak of the radiation emitted by a black body is inversely proportional to its temperature. The formula for this relationship is:

λmax = b/T

where λmax is the wavelength of the peak radiation, T is the temperature of the black body, and b is a constant known as Wien's displacement law constant.

Since we are given the wavelengths λ1 and λ2 at which the two clouds emit the largest number of photons, we can set up the following equation:

λ1 = b/T1
λ2 = b/T2

Dividing these two equations, we get:

λ1/λ2 = T2/T1

Substituting the values of λ1 and λ2, we get:

(3 × 10^-15 m) / (1.9 × 10^-15 m) = T2/T1

Simplifying this equation, we get:

1.6 = T2/T1

So the brown cloud is 1.6 times hotter than the white cloud, which is equivalent to saying that the white cloud is (1/1.6) = 0.625 times (or about 60%) as hot as the brown cloud. Therefore, the correct answer is B: The brown cloud is 1.6 times hotter than the white cloud.

If We Measure the Spectrum of Radiation Coming from Different