Question

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?

Solution

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ν\nu = 104.5 MHz\mathrm{MHz} ×\times 106HzMHz\dfrac{10^6\text{Hz}}{\text{MHz}} = 1.045 ×\times 108^8 Hz\mathrm{Hz}

As per. wave equation of motion:-

v=λtv=λ×ν\begin{align*} &v = \dfrac{\lambda}{t}\\ &v = \lambda \times \nu \end{align*}

where vv represents velocity, tt represents time and ν\nu represents frequency that is reciprocal of time

Now putting value of vv = 3$\times1010^{8}$ ms1\mathrm{ms^{-1}} and ν\nu = 1.045$\times1010^{8}$ s1\mathrm{s^{-1}}, we get λ\lambda = 2.871 m\mathrm{m}

Now, as per Planck-Einstein equation

Ephoton=hν\begin{equation} E_{photon} = h\nu \end{equation}

where EE is energy of photon, hh refers to Planck's constant and ν\nu refers to frequency

Now putting value of hh = 6.626$\times1010^{-{34}}$ Js\mathrm{Js} and ν\nu = 1.045$\times1010^{8}$ s1\mathrm{s^{-1}}, we get EphotonE_{photon} = 6.924$\times1010^{{-26}}$ J\mathrm{J}

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