WEBVTT
00:00:02.710 --> 00:00:09.560
What is the frequency of a photon that has an energy of 2.52 times 10 to the negative 19 joules?
00:00:10.030 --> 00:00:15.280
Use a value of 6.63 times 10 to the negative 34 joule-seconds for the Planck constant.
00:00:15.750 --> 00:00:19.170
Give your answer in scientific notation to two decimal places.
00:00:19.500 --> 00:00:29.990
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.
00:00:30.410 --> 00:00:35.110
Now, we are given a value for the energy of the photon and also a value for the Planck constant.
00:00:35.690 --> 00:00:39.690
So what we need to do is rearrange this formula to solve for frequency.
00:00:40.050 --> 00:00:42.990
We can do this by dividing both sides by the Planck constant.
00:00:43.230 --> 00:00:47.100
On the right-hand side, Planck constant divided by Planck constant is just one.
00:00:47.330 --> 00:00:48.720
So we’re left with frequency.
00:00:49.190 --> 00:00:52.960
And on the left-hand side, we have energy divided by the Planck constant.
00:00:53.430 --> 00:00:57.070
All that we need to do now is substitute values into our formula.
00:00:57.510 --> 00:01:06.020
We have 2.52 times 10 to the negative 19 joules divided by 6.63 times 10 to the negative 34 joule-seconds.
00:01:06.280 --> 00:01:12.430
The numbers work out to 3.8009 and several more decimal places times 10 to the 14th.
00:01:13.190 --> 00:01:16.960
And for the units, we have joules divided by joule-seconds.
00:01:17.260 --> 00:01:24.170
Joules divided by joules is just one, so we’re left with one over seconds, which is the same as the unit hertz.
00:01:24.720 --> 00:01:29.920
At this point, we know that we’re on the right track because our units are hertz or inverse seconds.
00:01:30.150 --> 00:01:33.590
And hertz are a unit of frequency, which is what we are looking for.
00:01:34.050 --> 00:01:37.970
The last thing we need to do is round our answer to two decimal places.
00:01:38.210 --> 00:01:46.450
Rounding 3.800 et cetera to two decimal places gives us a frequency of 3.80 times 10 to the 14 hertz.
00:01:46.940 --> 00:01:57.360
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.