Question 6.1: Neon lights emit an orange-red colored glow. This light has ......
Neon lights emit an orange-red colored glow. This light has a wavelength of 670 nm. What is the frequency of this light?
Strategy We know that wavelength and frequency are related through Equation 6.1. In using this equation, we will need to be careful of units. Because the wavelength is given in nanometers, we will convert it to meters so that it is consistent with the meters per second in the speed of light.
c = λ × ν (6.1)
670\;\mathrm{nm}\times{\frac{1\;\mathrm{m}}{1\times10^{9}\,\mathrm{nm}}}=6.7\times10^{-7}\,\mathrm{m}
We know that c = λν, so, rearranging, ν = \frac cλ. Then we simply substitute the values for the speed of light and the wavelength in the equation:
\nu=\frac{2.998\times10^{8}\,\mathrm{m\;s}^{-1}}{6.7\times10^{-7}\,\mathrm{m}}=4.5\times10^{14}{\mathrm{\ s}}^{-1}
Analyze Your Answer It is difficult to have a physical intuition about something like the frequency of light. But with some practice we can develop an idea of the expected order of magnitude. First, notice that to find the frequency, we took a large number (the speed of light) and divided it by a small number (the wavelength). So we should expect a very large numerical answer. It is also handy to become familiar with the typical magnitudes of some quantities. A glance at Figure 6.6, for example, will show us that the frequency of visible light is on the order of 10^{14}\ s^{−1}, so our answer seems plausible. These kinds of checks can be very handy because the most common errors in problems like this involve mishandling of units, leading to results that can be off by several orders of magnitude.
Check Your Understanding When trace amounts of xenon gas are added to neon lights, the color becomes blue-green. If the wavelength of this light is 480 nm, what is the frequency?
