energy per range dλ of wavelengths, where wavelength and frequency are relatedby f= c. Show that Planck's formula in terms wavelength is given by:dU 8rVhc 1phc/λk ₂I - 12³dλ=[Note: Don't worry if you're off by an overall minus sign.](b) Show that Wien's Law follows from the spectral energy density dU/dλ from (a).[Hint: Make use of the fact (not to be proven here) that the emission strength of ablack body at a given wavelength λ, is proportional to dUldλ.](c) Which is hotter: "red hot" or "white hot"? Explain your reasoning.(d) Estimate the surface temperature of the star Arcturus, one of the brightest in thenighttime sky, if the dominant wavelength (=wavelength of maximum emissionstrength) of light it emits is 676 nm. In 1893, physicist Wilhelm Wien showed that the wavelength of maximum thermalemission strength of electromagnetic radiation from a blackbody at temperature Tobeys:Amax T 2.898 mm.K.=This result, known today as Wien's Law, is very useful for, among other things, esti-mating the temperature of distant objects based on the color of light they emit.(a) Planck's spectral energy density function is usually written as an energy per rangedf of frequencies. Quite often, however, it is more convenient to express it as an

In 1893, physicist Wilhelm Wien showed that the wavelength of maximum thermal emission strength of electromagnetic radiation from a blackbody at temperature T obeys: Amax T = 2.898 mm.K. This result, known today as Wien's Law, is very useful for, among other things, esti- mating the temperature of distant objects based on the color of light they emit. (a) Planck's spectral energy density function is usually written as an energy per range df of frequencies. Quite often, however, it is more convenient to express it as an

In 1893, physicist Wilhelm Wien showed that the wavelength of maximum thermal emission strength of electromagnetic radiation from a blackbody at temperature T obeys: Amax T = 2.898 mm.K. This result, known today as Wien's Law, is very useful for, among other things, esti- mating the temperature of distant objects based on the color of light they emit. (a) Planck's spectral energy density function is usually written as an energy per range df of frequencies. Quite often, however, it is more convenient to express it as an