Example 6.1: Determining the Frequency and Wavelength of Radiation
A sodium streetlight gives off yellow light that has a wavelength of
589 nm. What is the frequency of this light?
Solution
\(λ_{\mathrm{\ce{Na}}}\) \(= 589\ \mathrm{nm}\)
\(ν_{\mathrm{\ce{Na}}}\) = ?
We can rearrange the equation
\(c_{\mathrm{0}} = λ \cdot ν\) to solve for the frequency:
\(ν = \dfrac{c_{\mathrm{0}}}{λ}\)
\(ν_{\mathrm{\ce{Na}}}\) \(= \dfrac{c_{\mathrm{0}}}{λ_{\mathrm{\ce{Na}}}}\)
\(\ \ \ =\dfrac{2.998\times 10^{8}\ \frac{\mathrm{m}}{\mathrm{s}}}{589\ \mathrm{nm}}\)
\(\ \ \ =5.090\times 10^{14}\frac{1}{\mathrm{s}}\)
\(ν_{\mathrm{\ce{Na}}}\) \(= 5.090\times 10^{14}\frac{1}{\mathrm{s}}\)
\(\ \ \ =5.090\times 10^{5}\ \mathrm{GHz}\)