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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$\nu$ = 104.5 $\mathrm{MHz}$ $\times$ $\dfrac{10^6\text{Hz}}{\text{MHz}}$ = 1.045 $\times$ 10$^8$ $\mathrm{Hz}$

As per. wave equation of motion:-

\begin{align*} &v = \dfrac{\lambda}{t}\\ &v = \lambda \times \nu \end{align*}

where $v$ represents velocity, $t$ represents time and $\nu$ represents frequency that is reciprocal of time

Now putting value of $v$ = 3$\times$10$^{8}$ $\mathrm{ms^{-1}}$ and $\nu$ = 1.045$\times$10$^{8}$ $\mathrm{s^{-1}}$, we get $\lambda$ = 2.871 $\mathrm{m}$

Now, as per Planck-Einstein equation

$\begin{equation} E_{photon} = h\nu \end{equation}$

where $E$ is energy of photon, $h$ refers to Planck's constant and $\nu$ refers to frequency

Now putting value of $h$ = 6.626$\times$10$^{-{34}}$ $\mathrm{Js}$ and $\nu$ = 1.045$\times$10$^{8}$ $\mathrm{s^{-1}}$, we get $E_{photon}$ = 6.924$\times$10$^{{-26}}$ $\mathrm{J}$

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