A 100 W incandescent light bulb converts approximately 2.5% of the electrical energy supplied to it into visible light. Assume that the average wavelength of the emitted light is λ = 530 nm, and that the light is radiated uniformily in all directions. How many photons per second, N, would enter an aperture of area A = 3 cm2 located a distance D = 6 m from the light bulb?
Energy of photon = h x c / lambda (wavelength)
Power = change in energy / change in time
Surface area of sphere = 4πr
The Attempt at a Solution
I basically used the formula above to calculate the energy of the photons being emitted:
E = 1240 eV nm / 530 nm = 2.3396 eVm
The total power emitted by the light bulb should be 2.5% of what is put in - 2.5 watts. I know that if I have a sphere of radius 6m, the surface should "pick up" all of the power emitted. Therefore, I can set up a ratio of W/m2 : 2.5 / (4π x 6) W/m2 (not sure if this is a valid reasoning, because the aperture is not necessarily curved). Since the element(aperture) I am looking at is 3 cm2 :
Power through element = 2.5 / (4π x 6) x 0.0003m2 = 9.947183943 x 10-6 W
This power should be equal to the number of photons per second (n) multiplied by the energy of one photon, simply because both quantities represent the energy per second.
9.947183943 x 10-6 W = n x (2.3396 eV x 1.602 x 10-19 J / eV)
n = 2.653970093 x 1013 photons per second
When I enter this answer (the homework is online), it is wrong. I'm pretty sure the problem lies with how I found the power through the aperture; I'm not sure what is wrong.
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