Question

Assuming that your surface temperature is 97.7 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 1.00 nm at that wavelength, from a surface area of 4.10 cm², 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.)

Answer 1

Temperature T = 97.7 F = 36.5 C

T = 309.5 K

(a)

From wein's law,

max = b / T = 2900*10^(-6) / 309.55

max = 9.37*10^(-6) m

(b)

Power P = s*A*(d)

here, s = spectral radiancy =  (2*h*c^2 / ^5) * [ 1 / (e^hc/*k*T) - 1)

by solving, s = 3.55*10^7 W/m^3

so, P =  3.55*10^7 * 4.10*10^(-4) * 1*10^(-9)

P = 1.46*10^(-7) W

(c)

E = hc /

E = 6.62*10^(-34)*3*10^8 / 9.37*10^6 = 2.13*10^(-20) J

dN / dt = P / E = 1.46*10^(-7) / 2.13*10^(-20)

dN / dy = 6.8*10^14 photons / s

(d)

spectral radiancy when = 500 nm

s = 5.6*10^(-26) W/m^3

so, P =  5.6*10^(-26) * 4.10*10^(-4) * 500*10^(-9)

P = 1.2*10^(-35) P