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Calculate the wave length for several examples of sinusoidal electromagnetic radiation: radio, 1000kHz,λ=?1000 \mathrm{kHz}, \lambda=? television, 100MHz,λ=?100 \mathrm{MHz}, \lambda=? red light, 4.3×1014Hz,λ=?4.3 \times 10^{14} \mathrm{Hz}, \lambda=? blue light, 7.5×1014Hz,λ=?7.5 \times 10^{14} \mathrm{Hz}, \lambda=? (Note for comparison that an atomic diameter is about 1×1010m.)1 \times \left.10^{-10} \mathrm{m} .\right)

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Answered 2 years ago
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The wavelength is determined by λ=vν\lambda = \frac{v}{\nu}. So given the frequency of the radio\textbf{radio} waves, ν=1000\nu = 1000 kHz, and being the speed of the electromagnetic wave v=3108m/sv=3\cdot 10^8 m/s we have

λ=3108m/s1000103Hz=300m\begin{equation} \lambda = \frac{3\cdot 10^8 m/s}{1000 \cdot 10^3 \, Hz} = 300 \,m \end{equation}

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

λ=3108m/s100106Hz=3m\begin{equation} \lambda = \frac{3\cdot 10^8 m/s}{100 \cdot 10^6 \, Hz} = 3 \,m \end{equation}

For red light\textbf{red light} the frequency is ν=4.31014Hz\nu = 4.3 \cdot 10^{14} Hz. So the wavelength is

λ=3108m/s4.31014Hz=697.6109m\begin{equation} \lambda = \frac{3 \cdot 10^8 \, m/s}{4.3 \cdot 10^{14} \, Hz} = 697.6 \cdot 10^{-9} \,m \end{equation}

Finally, for the blue light\textbf{blue light} the frequency is ν=7.51014Hz\nu = 7.5 \cdot 10^{14} \, Hz, so the wave length is

λ=3108m/s7.51014Hz=400109m\begin{equation} \lambda = \frac{3 \cdot 10^8 \, m/s}{7.5\cdot 10^{14} \, Hz }= 400 \cdot 10^{-9} \, m \end{equation}

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