Question

Question 11 Assuming that your surface temperature is 98.4 F and that you are an ideal blackbody radiator (you are close), find (a) the wavelength at which your spectral radiancy is maximum, (b) the power at which you emit thermal radiation in a wavelength range of 0.940 nm at that wavelength, from a surface area of 3.90 cm?, and (c) the corresponding rate at which you emit photons from that area. Using a wavelength of 500 nm (in the visible range), (d) recalculate the power and (e) the rate of photon emission. (As you have noticed, you do not visibly glow in the dark.) (a) Number Units (b) Number Units (c) Number (d) Number Units Units Units (e) Number

Answer 1

@ We have, maximum wavelength, & max = 1/2 where, b is a constant = 2.897 x 10-3 mk T = 98.4 F = (98.4 x 273:15) K (:' 32°F = 273'15k) = 839-94K 2. 897810-3 839.94 = 3.45x10-6 m = 3.45 um 32 X © Power radiated, P = 2.be? As A x abyAKT-1 where, 1 = 3'45x10-6m, Ad = 0.940 nm = 0.940x10°m, A = 3:90 cm*= 3-9x109 m h = 66X 10–34Js, c=3x 108 m/s, T = 839.94 K, 2x3-14866x10-34X(3x108)* X094x10-9X3'9x104 - 23.45x10-65 166x10 34x3x108 9:45x10X1-38%1672 X839094 1367.535 X10-31 68602.325810-30 Watt = 1.993210-3 Watt 1993 mW. © Rate of photon emission = cc. TA, where, T=839-94 k, A=359.10 09=1° 52x1015 photons/s. m? K3 .: Rate of emission = (1-52x1015 (839.943 x 39 x 10-49 photons is = 3.58 1020 photons/

@ We have, maximum wavelength, & max = 1/2 where, b is a constant = 2.897 x 10-3 mk T = 98.4 F = (98.4 x 273:15) K (:' 32°F = 273'15k) = 839-94K 2. 897810-3 839.94 = 3.45x10-6 m = 3.45 um 32 X © Power radiated, P = 2.be? As A x abyAKT-1 where, 1 = 3'45x10-6m, Ad = 0.940 nm = 0.940x10°m, A = 3:90 cm*= 3-9x109 m h = 66X 10–34Js, c=3x 108 m/s, T = 839.94 K, 2x3-14866x10-34X(3x108)* X094x10-9X3'9x104 - 23.45x10-65 166x10 34x3x108 9:45x10X1-38%1672 X839094 1367.535 X10-31 68602.325810-30 Watt = 1.993210-3 Watt 1993 mW. © Rate of photon emission = cc. TA, where, T=839-94 k, A=359.10 09=1° 52x1015 photons/s. m? K3 .: Rate of emission = (1-52x1015 (839.943 x 39 x 10-49 photons is = 3.58 1020 photons/