Calculate the wave length for several examples of sinusoidal electromagnetic radiation:

radio,$\mathbf{1000}\mathbf{}\mathit{k}\mathit{H}\mathit{z}\mathbf{,}\mathbf{}\mathit{\lambda }\mathbf{=}\mathbf{}\mathbf{?}$

television,$\mathbf{100}\mathbf{}\mathit{M}\mathit{H}\mathit{z}\mathbf{,}\mathbf{}\mathit{\lambda }\mathbf{=}\mathbf{}\mathbf{?}$

red light,$\mathbf{4}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{14}}\mathbf{}\mathit{H}\mathit{z}\mathbf{,}\mathbf{}\mathit{\lambda }\mathbf{=}\mathbf{}\mathbf{?}$

blue light,$\mathbf{7}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{14}}\mathbf{}\mathit{H}\mathit{z}\mathbf{,}\mathbf{}\mathit{\lambda }\mathbf{=}\mathbf{}\mathbf{?}$

(Note for comparison that an atomic diameter is about $\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathit{m}\mathbf{,}$).

Frequency of the radio,$f=1000\text{kHz}$

Frequency of the television,$f=100\text{MHz}$

Frequency of the red light,$f=4.3\times {10}^{14}\text{Hz}$

Frequency of the blue light,$f=7.5\times {10}^{14}\text{Hz}$

The wavelength of the frequency and speed of the light is defined as the ratio of the light of the speed and frequency.

$\mathit{\lambda }\mathbf{=}\frac{\mathbf{v}}{\mathbf{f}}$ …(i)

Here,$\mathit{\nu }$ is the speed of the light.

Calculate the wavelength of the radio.

Substitute$1000\text{kHz}$ for f and$3\times {10}^{8}m/s$ for$\nu$ into equation (i).

$$\begin{gathered} \lambda =\frac{3\times {10}^{8}m/s}{1000\times {10}^3\text{Hz}} \\ =\frac{3\times {10}^{8}m/s}{{10}^{6}1/s} \\ =3\times {10}^2\text{m} \\ =300\text{m} \end{gathered}$$

Therefore, the wavelength of the radio is $300\text{m}$.

Calculate the wavelength of the television.

Substitute $100\text{MHzforf}$and $3\times {10}^{8}m/sfor\nu$into equation (i).

$$\begin{gathered} d\lambda =\frac{3\times {10}^{8}m/s}{100\times {10}^6\text{Hz}} \\ =\frac{3\times {10}^{8}m/s}{{10}^{8}1/s} \\ =3\text{m} \end{gathered}$$

Therefore, the wavelength of the television is $3m$.

Calculate the wavelength of the red light.

Substitute $4.3\times {10}^{14}\text{Hzforf}$and $3\times {10}^{8}m/sfor\nu$into equation (i).

$$\begin{gathered} \lambda =\frac{3\times {10}^{8}m/s}{\text{4.3}\times {\text{10}}^{14}\text{Hz}} \\ =\frac{3\times {10}^{-6}m/s}{\text{4.3}1/s} \\ =0.6976\times {10}^{-6}\text{m} \\ =697.6\text{nm} \end{gathered}$$

Therefore, the wavelength of the red light is $697.6nm$.

Calculate the wavelength of the red light.

Substitute $7.5\times {10}^{14}\text{Hzforf}$and $3\times {10}^{8}m/sfor\nu$into equation (i).

$$\begin{gathered} \lambda =\frac{3\times {10}^{8}m/s}{7.5\times {\text{10}}^{14}\text{Hz}} \\ =\frac{3\times {10}^{-6}m/s}{7.51/s} \\ =0.4\times {10}^{-6}\text{m} \\ =400\text{nm} \end{gathered}$$

Therefore, the wavelength of the blue light is $400nm$.

Hence the wavelength of the radio, television, red light, and blue light are $300m,3m,697.6nm,and400nm$respectively.