What is the frequency of a photon that has an energy of 2.52 times 10 to the negative 19 joules? Use a value of 6.63 times 10 to the negative 34 joule-seconds for the Planck constant. Give your answer in scientific notation to two decimal places.
To relate the frequency of a photon to its energy, we use the formula 𝐸, the energy of a photon, is equal to ℎ, the Planck constant, times 𝑓, the photon’s frequency. Now, we are given a value for the energy of the photon and also a value for the Planck constant. So what we need to do is rearrange this formula to solve for frequency. We can do this by dividing both sides by the Planck constant. On the right-hand side, Planck constant divided by Planck constant is just one. So we’re left with frequency. And on the left-hand side, we have energy divided by the Planck constant.
All that we need to do now is substitute values into our formula. We have 2.52 times 10 to the negative 19 joules divided by 6.63 times 10 to the negative 34 joule-seconds. The numbers work out to 3.8009 and several more decimal places times 10 to the 14th. And for the units, we have joules divided by joule-seconds. Joules divided by joules is just one, so we’re left with one over seconds, which is the same as the unit hertz. At this point, we know that we’re on the right track because our units are hertz or inverse seconds. And hertz are a unit of frequency, which is what we are looking for.
The last thing we need to do is round our answer to two decimal places. Rounding 3.800 et cetera to two decimal places gives us a frequency of 3.80 times 10 to the 14 hertz. As it happens, this frequency corresponds to a wavelength of about 789 nanometers, which is right near the border between visible red light and invisible infrared light.