Answer to Question #137229 in Mechanics | Relativity for Jessica

Question

An AM radio station broadcasts an electromagnetic wave with a frequency of 743 kHz, whereas an FM station broadcasts an electromagnetic wave with a frequency of 92.1 MHz. How many AM photons are needed to have a total energy equal to that of one FM photon?

Answer 1

Since the energy of a photon is defined as $E=\nu\times h$ , where $\nu$ is the wave frequency and $h$ is Planck's constant, to find the number of AM photons are needed to have a total energy equal to the energy of one FM photon, you need to find the ratio of energies of the FM to AM photon-photons:

$K=\frac { \nu_{FM}\times h }{ \nu_{AM}\times h }$ $=\frac{ \nu_{FM}}{ \nu_{AM}}=$ $\frac{ 92.1\times 10^6}{743\times 10^3}\approx123.96$ , as the number of integer it is necessary $124$ of the photon.