Photons per second?

Question

If an FM radio station is emitting 81.7 kW in its 82.6-MHz radio wave, how many photons is it emitting each second?

Answer 1

Power = energy/sec
each photon carries E = h v
where v= frequency = 82.6*10^6 Hz
if (n) photons are emitted/sec
then energy emiited/sec = n h v Joule/sec
this is power
P = 81.7*10^3 watt = n h v Joule/sec
n = no of photon/s = P/hv = 81.7*10^3 / 6.6*10^-34*82.6*10^6
n = 81.7*10^31 / 6.6*82.6
n = 1.498*10^30 photons/sec

Answer 2

Power = (total energy) / time

The problem says the power is 81.7 kW and the time is 1 second, so:

(1): 81.7 kW = (total energy) / (1 sec)

The total energy is:

(2): total energy = (energy per photon) × (total photons)

energy per photon is given by:

(3): energy per phton = hν

where "h" is Planck's constant and "ν" is the photon's frequency (which is 82.6 MHz)

Combine equations (1), (2) and (3), and solve for "total photons".