How to Determine the amount of photons, difficult problem?

Question

How many photons are emitted every 0.260 s by a 139.0 W sodium lamp if the wavelength of sodium light is 1240 nm? Planck’s constant is 6.63 × 10−34 J • s and the speed of light is 3 × 108 m/s. Answer in units of photons.

Daversauce · Accepted Answer

I'll try to outline the problem for you so you can lead yourself to the answer.

A Watt is a Joule/Second, so by telling you a time interval and wattage, they are specifying the amount of joules, which is an amount of energy, where E = 139W*.26S = ___ Joules

We'll assume for simplicity that all photons have the wavelength 1240nm (on average this is true so its fine). We can figure the amount of energy per photon by E = hc/lambda = joules/photon. Actually this may come out in electron volts depending on your choices for the constants, but you can convert easily enough.

Now you know the energy per photon and the total amount of energy being produced, solve for the # of photons required to produce said energy.

Let&#39;slearntothink · Answer

Assuming that all energy given to the lamp is converted to photons of the given wavelength only and not to any other form required number, 'n' of photons is given by

n = (139.0*0.260)/[(6.63*10^-34)*(3*10^8)/1240*10^-9)] = [(139.0*0.260*1240)/[6.63*3]10^17 or 
n = 2.25*10^20

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How to Determine the amount of photons, difficult problem?

2 Answers