In this video, we're going to focus on a few problems that ask to find the wavelength and the frequency of a photon. So let's start with this one. Calculate the wavelength of a photon that has a frequency of 2.5 times 10 to the 12 hertz. So what equation do we need? Perhaps you've seen this one.
C is equal to lambda times nu. Now C is the speed of light. Lambda represents the wavelength in meters. And nu is the frequency in hertz.
So the wavelength is going to be the speed of light divided by the frequency. The speed of light, you need to know it, it's 3 times 10 to the 8 meters per second. The frequency is 2.5 times 10 to the 12 hertz, which is the same as seconds to the minus 1, or 1 over. a second. So basically we just need to divide these two numbers.
And so you should get 1.2 times 10 to the negative 4 meters. And so that's all you need to do in order to get the answer. Now sometimes you may need to convert it to a different unit, because this number is pretty small.
So let's convert it to micrometers. How can we convert meters to micrometers? What is the value of 1 micrometer?
Micro represents 10 to the minus 6, so 1 micrometer is 10... to the negative 6 meters. You can take this number and move it to the top by changing the exponent from negative 6 to positive 6. So this is equivalent to 1.2 times 10 to the minus 4 multiplied by 10 to the positive 6. And when you multiply by a common base, you need to add the exponent. So negative 4 plus 6 is 2. So the answer is 1.2 times 10 to the 2 micrometers. Now 10 squared is 100, and 100 times 1.2 is 120. So the wavelength you could say is 120 micrometers.
So if you have a multiple choice test, your answer may be in meters, or it could be in a different unit, micrometers. So you might have some conversions with these problems as well. Just be ready for that. Now let's move on to number two.
What is the frequency of a photon that has a wavelength of 1.5 times 10 to the negative 8 meters? So go ahead and try that problem. So starting with this equation, we need to solve for the frequency. So nu is equal to the speed of light divided by the wavelength. The speed of light is going to be the same.
It's 3 times 10 to the 8 meters per second. And when using this formula, the wavelength has to be in meters, which it's already in meters. So now we just got to divide these two things.
So 3 divided by 1.5 is 2. Now what's 10 to the 8 divided by 10 to the negative 8? When you divide by a common base, you need to subtract the exponents. So you take the top exponent, which is positive 8, and subtract it by the bottom one, which is negative 8. 8 minus negative 8 is the same as 8 plus 8, so that's 16. So the answer is 2 times 10 to the 16 hertz. So that's the frequency of this photon. And you can type it in to make sure that we do indeed have the right answer, which it is that answer.
Now what about number three? What is the frequency of a photon that has a wavelength of 350 nanometers? So let's use the same formula.
The frequency is the speed of light divided by the wavelength. But this time, the wavelength is not in meters. It's in nanometers, which means we need to convert it to meters.
So how do we go about doing that? It turns out that all you need to do is replace nanometers with 10 to the minus 9 meters. And it's going to work out.
If you want to write it out, here's what you can do. Start with what you're given. And know that 1 nanometer is equivalent to 10 to the minus 9 meters. So these units will cancel.
And all you have is 350 times 10 to the minus 9. So you just got to replace this with 10 to the minus 9 meters. And the speed of light is not going to change. In a vacuum, it's constant. However, when light passes through a different material, let's say water or through diamond, the speed of light does change. It decreases.
But in pure empty space in the vacuum, it's 3 times 10 to the 8 meters per second. So the frequency is going to be 8.57. times 10 to the 14 hertz, or seconds to the minus 1. So this is the answer for this problem. Number 4. Determine the wavelength of a photon that has a frequency of 95 megahertz. So to calculate the wavelength, we know it's the speed of light divided by the frequency.
Now let's convert megahertz into hertz. So what is the value of mega? A megahertz is basically a million hertz.
Mega represents 10 to the 6. So what we have now is 95 times 10 to the 6 hertz. So that's the frequency. So now that we changed a unit, we can plug it in to the equation.
So let's go ahead and divide these two numbers. So you should get 3.16 meters. So that's the wavelength of a photon with that frequency. Now here's a question for you.
What happens to the wavelength of a photon as the frequency increases? So we know that wavelength is the speed of light divided by the frequency. Notice that the frequency is in the bottom of the equation, which means it's inversely related to the wavelength. So as the frequency increases, the wavelength decreases, and vice versa.
So as the wavelength increases, the frequency decreases. So these two are always going to be inversely related to each other. And so that's all you need to know about photons and the relationship between wavelength and frequency.
When one goes up, the other goes down. Now what if you're given the energy of a photon? How can you calculate the frequency? The equation that relates the energy of a photon to the frequency is this equation. The energy of the photon is basically the product of Planck's constant, represented by the symbol H, multiplied by the frequency.
Now the value of Planck's constant is 6.626 times 10 to the negative 34 joules times seconds. So if you wish to calculate the frequency, it's simply the energy of the photon divided by Planck's constant. So it's going to be 3.5.
times 10 to the minus 18 joules divided by 6.626 times 10 to the negative 34 joules times seconds. So as you can see the unit joules will cancel leaving the unit 1 over seconds which is equivalent to the hertz. So let's divide these two numbers.
So the frequency is going to be 5.28 times 10 to 15 Hertz. And so that's how you can calculate the frequency of a photon, given its energy. Now this is going to be the last problem.
Determine the wavelength of a photon with an energy of 4.3 times 10 to the negative 19 joules. So what we're going to do in this problem is just like before we're going to calculate the frequency first. And once we have the frequency then we're going to calculate the wavelength.
So the frequency is going to be the energy divided by Planck's constant. So it's 4.3 times 10 to the negative 19 joules divided by 6.626 times 10 to the minus 34. So for the frequency, you should get 6.49 times 10 to the 14 hertz. So now that we have the frequency, let's go ahead and calculate the wavelength. Now we know that the wavelength is going to be the speed of light divided by the frequency. So that's 3 times 10 to the 8 meters per second divided by 6.49 times 10 to the 14 hertz.
So you should get 4.62 times 10 to the negative 7 meters. Now let's go ahead and convert this to nanometers. So keep in mind, 1 nanometer is equivalent to 10 to the minus 9 meters.
So I'm going to take this and move it to the top. So then it becomes 4.62 times 10 to the minus 7. times 10 to the positive 9. And negative 7 plus 9 is 2, so it's 4.62 times 10 to the 2 nanometers. And we know 10 squared is 100, so 100 times 4.62 is 462 nanometers.
So that's the wavelength in nanometers. This is the answer.