Question

6. For photons in equilibrium at temperature Tin a cavity of volume V Eq. (7.22) gives the energy density of photons with angular frequency in the range ω to ω + do. Show that the energy density of photons with wavelength in the range λ to λ + dÀIs given (a) dh. Explicitly show the value of A in your result. [4 marks] (b) Show that at temperature T. the maximum intensity occurs at wavelength /w , where and find the value of the constant b. [4 marks]

Answer 1

According to clerical Rayleigh Jeans formal energy density: - U (delta, T) = B pi r^2/c^3 kT Where delta - frequency k - Batsman constant This formula is product of two tames The No of degree of freedom: - B pi delta^2/c^3 rightarrow and the average energy E^which is kT E^bar = integral^infinity_0 E e - E/kT d E/ integral^infinity_0 e - F/kT df = KT according to plants quantum energy is given by - E = ph v h = planks constant n = 0, 1, 2 So E^bar = sigma^infinity_n = 0 n E e^- n E/k T/sigma^infinity_n = 0 e -n E/kT But x = e^-e/k T E^bar = sigma^infinity_n = 0 n H^h/sigma H^n Vertical-bar 1/1 - x = 1 + x + x^2 + x/(1 - x)^2 = x + 2 x^2 + 3 x^3 E^bar = h delta/e h delta/k T - 1 Now Replace kT by New E^bar 4 (delta, T) = B pi delta 3/C^3 h delta/