A) Estimate the amount of energy in a photon with a visible light wave- length o

Question

A) Estimate the amount of energy in a photon with a visible light wave- length of 5.5 · 107 m.

b) A 100 Watt lightbulb consumes 100 Joules per second of power. Sup- pose that all of that power were converted into photons. If so, estimate the number of photons leaving the lightbulb per second. Assume that the average wavelength of light emitted by the lightbulb is the same as the wave- length which is given in part a).

c) Suppose that the 100 Watt lightbulb from part b) is surrounded by a spherical light shade with a radius of 0.2 meters. Estimate the flux of photons through that light shade.

d) Estimate the temperature of the filament of the lightbulb, assuming that the average wavelength is close to the wavelength of peak emission.

Explanation / Answer

Given

wavelength of the light is lambda = 5.5*10^-7 m

we know that energy of photon is E = h*nue

where nue is frequency nue = c/lambda , c is speed of light  

a) E = h*c/lambda

E = (6.626*10^-34*3*10^8)/(5.5*10^-7) J

E = 3.614182*10^-19 J

b) 100 w bulb consumes 100 J of energy per sec

100 J = N*h*nue  

N = 100 J /(3.614182*10^-19 J)

N = 2.7669*10^20 photons

c) area of the sphere is A = 4pi*r^2 = 4pi*0.2^2

the flux of the photons from the sphere i s

flux = N /A = 2.7669*10^20 / (0.5026548245744) = 5.50*10^20 photons/m^2

d)

weins law Lambda_m*T = constant

T = constant / lambda

T = 2.898*10^-3 /(5.5*10^-7) k

T = 5269 k

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