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# Calculate the wave length for several examples of sinusoidal electromagnetic radiation: radio, $1000 \mathrm{kHz}, \lambda=?$ television, $100 \mathrm{MHz}, \lambda=?$ red light, $4.3 \times 10^{14} \mathrm{Hz}, \lambda=?$ blue light, $7.5 \times 10^{14} \mathrm{Hz}, \lambda=?$ (Note for comparison that an atomic diameter is about $1 \times \left.10^{-10} \mathrm{m} .\right)$

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The wavelength is determined by $\lambda = \frac{v}{\nu}$. So given the frequency of the $\textbf{radio}$ waves, $\nu = 1000$ kHz, and being the speed of the electromagnetic wave $v=3\cdot 10^8 m/s$ we have

$$$\lambda = \frac{3\cdot 10^8 m/s}{1000 \cdot 10^3 \, Hz} = 300 \,m$$$

For $\textbf{television}$ we have $\nu = 100$ MHz, thus

$$$\lambda = \frac{3\cdot 10^8 m/s}{100 \cdot 10^6 \, Hz} = 3 \,m$$$

For $\textbf{red light}$ the frequency is $\nu = 4.3 \cdot 10^{14} Hz$. So the wavelength is

$$$\lambda = \frac{3 \cdot 10^8 \, m/s}{4.3 \cdot 10^{14} \, Hz} = 697.6 \cdot 10^{-9} \,m$$$

Finally, for the $\textbf{blue light}$ the frequency is $\nu = 7.5 \cdot 10^{14} \, Hz$, so the wave length is

$$$\lambda = \frac{3 \cdot 10^8 \, m/s}{7.5\cdot 10^{14} \, Hz }= 400 \cdot 10^{-9} \, m$$$

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