Question

An AM radio station broadcasts an electromagnetic wave with a frequency of 916 kHz, whereas an FM station broadcasts an electromagnetic wave with a frequency of 91.8 MHz. How many AM photons are needed to have a total energy equal to that of one FM photon?

Answer 1

Photons are not AM or FM, what a strange idea.

However, I can compare the energy of photons at the two frequencies.

Energy equivalent to an EM photon
E = hf, where h = Plank's constant 6.626e-34 Js
E = hc/λ (alternate form)
E is the energy of the particle in Joules
f is frequency in Hertz, λ is wavelength in meters
c is speed of light in m/s

for the first
E = hf = h(916e3)
for the second
E = hf = h(91.8e6)

and the ratio of the two is
Ratio = h(91.8e6) / h(916e3) = 100