Calculate How Many Photons Produced

Question

The energy is 5,500,000 J

frequency is 824 Megahertz

wavelength of 36.4 m

Answer 1

E = 5,500,000 J

f = 824 MHz = 824,000,000 sec^-1 = 8.24x10⁸sec^-1

λ = 36.4 m

There appears to be an error in the data provided. The product of wavelenght x frequency should equal the speed of light (~3x10⁸ m/sec). In this problem, this is not the case:

8.24x10⁸ sec-1 x 36.4 m = 299.9x10⁸ m/sec = 3x10¹⁰ m/sec (not 3x10⁸ m/sec)

Find the energy of 1 photon from the frequency or the wavelength

I will use the frequency but you should get the same answer whether you use f or λ

E = hf = 6.626x10^-34 Jsec x 8.24x10⁸sec^-1 = 5.46x10^-25 J / photon

Number of photons = 5,500,000 J x 1 photon / 5.46x10^-25 J = 5.5x10⁶ J x 1 photon / 5.46x10^-25 J = 1x10^-19 photons