We need to solve the problem in Colab! Exercise 6.13: Wien's displacement constant Planck's radiation law tells us that the intensity of radiation per unit area and per unit wavelength from a black body at temperature T is 27thc22-5 I() = ehc/ART-1' where h is Planck's constant, c is the speed of light, and kp is Boltzmann's constant. a) Show by differentiating that the wavelength 1 at which the emitted radiation is strongest is the solution of the equation hc 5e-he/AXT + -5=0. AkgT Make the substitution x = hc/ AkgT and hence show that the wavelength of max- imum radiation obeys the Wien displacement law: b X T e lo ste for phy y do dort end dhe . amer where the so-called Wien displacement constant is b = hc/kpx, and x is the solution to the nonlinear equation 5e * +x-5= 0. b) Write a program to solve this equation to an accuracy of e = 10-6 using the binary search method, and hence find a value for the displacement constant. c) The displacement law is the basis for the method of optical pyrometry, a method for measuring the temperatures of objects by observing the color of the thermal radiation they emit. The method is commonly used to estimate the surface tem- peratures of astronomical bodies, such as the Sun. The wavelength peak in the Sun's emitted radiation falls at = 502 nm. From the equations above and your value of the displacement constant, estimate the surface temperature of the Sun. ethel when al dal 20 thadir til des parison