Question

Radio Waves If your favorite FM radio station broadcasts at a frequency of 104.5 MHz, what is the wavelength of the station’s signal in meters? What is the energy of a photon of the station’s electromagnetic signal?

Answer 1

Answer:

The wavelength of the station’s signal is 2.9 meters

The energy of a photon of the station’s electromagnetic signal is $6.9\times10^{-26}J$

Explanation:

Wavelength $\lambda$ is inversely proprtional to frequency (f) and directly proportional to velocity of the wave (v).

$\lambda=\frac{v}{f}$ (1)

But electromagnetic waves as radio signals travel at speed of light so using this on (1):

$\lambda=\frac{c}{f}=\frac{3.0\times10^{8}}{104.5\times10^{6}}\approx2.9\,m$

Albert Einstein discovered that energy of electromagnetic waves was quantized in small discrete packages of energy called photons with energy:

$E=hf=(6.6\times10^{-34})(104.5\times10^{6})\approx6.9\times10^{-26}J$

with h the Planck's constant.