Chapter 4, Problem 64RE

Any body radiates energy at various wavelengths. Figure 4.6 shows the intensity of the radiation of a black body at a temperature T = 3000 kelvins as a function of thewavelength. The intensity of the radiation is highest in the infrared range, that is, at wavelengths longer than that of visible light (0.4–0.7μm). Max Planck’s radiation law, announced to the Berlin Physical Society on October 19, 1900, states that

$r(\lambda )=\frac{a}{{\lambda }^5(e^{b/\lambda }-1)}.$

Find constants a and b so that the formula fits the graph. (Later in 1900 Planck showed from theory that a = 2πc²ℎ and $b=\frac{hc}{Tk}$ where c = speed of light, ℎ = Planck’s constant, and k = Boltzmann’s constant.)

Figure 4.6