(Solved): 3. (Blackbody Radiation) Max Planck proposed the first "quantum" hypothesis to explain the observed ...

3. (Blackbody Radiation) Max Planck proposed the first "quantum" hypothesis to explain the observed emission spectrum from a blackbody emitter. a. Use your own words to describe why the experimental spectrum of a blackbody emitter does not agree with classical physics predictions. b. The color of stars depends on the radiation they can emit. These phenomena can be explained by blackbody emitter model at different temperature. Let's say the emission spectrum of our sun peaks at around \( 480 \mathrm{~nm} \). What is the temperature of the sun surface? Compared to the sun surface, what is the metal surface temperature of Tungsten incandescent light bulb emitting light peaked at \( 900 \mathrm{~nm} \) ? c. If a thermonuclear explosion happens \( (e, g \). hydrogen bomb), the temperature can reach up to approximately 100 million \( \mathrm{K} \). What is the peak emission wavelength for the blast? What region of the electromagnetic spectrum does this pertain to? If you are near thermonuclear explosion, is any risk can arise from the blast? d. Correspondence principle is a concept we'll encounter this semester. Basically, it states that when the energy gaps between quantum states are so small. The absorption/emission spectra appear to be continuous, behavior described by classical mechanics. As an example of this concept, show that Planck's quantum expression for describing the density of states of a blackbody emitter at a frequency \( v \) : \[ \rho(v)=\frac{8 \pi h v^{3}}{c^{3}}\left(\frac{1}{\mathrm{e}^{k / / k_{0} T}-1}\right) \] reverts to the classical Rayleigh-Jeans law: \[ \rho(v)=\frac{8 \pi k_{B} T}{c^{3}} v^{2} \] as \( v \rightarrow 0 \) (i.e. as the spacing between states becomes smali). Hint: Think about using a Taylor series in the denominator. If you've forgotten how to do a Taylor expansion (or never learned it in the first placel) check out Barrante, Section 7-4 (or all of Chapter 7 for that matter...).