Electromagnetic waves produced by X-ray machines typically have a frequency of approximately 3.5×1016Hz3.5\times10^{16}Hz3.5×1016Hz . What is the wave number of these waves?

7.33 × 1 0 8 m − 1 7.33\times10^8m^{-1} 7.33 × 1 0 8 m − 1

Electromagnetic waves produced by X-ray machines typically have a frequency of approximately 3.5 × 1 0 16 H z 3.5\times10^{16}Hz 3.5 × 1 0 16 Hz . What is the wave number of these waves?

Welcome back, everyone. Hopefully, you had a chance to try this practice problem on your own. This pract problem tells us that electromagnetic waves produced by an X-ray machine typically have a frequency of about 3.5 times 10 to the 16, and we're asked to figure out what's the wave number of these types of waves. Alright? So remember that the wave number, remember, is the variable k inside of your, wave function equations, and there's a couple of different equations that tell us what k is. The more natural one, the one that we saw from mechanical waves, is that it's 2 pi over lambda, the wavelength. But you can also relate k to the frequency and angular frequency using this equation over here. K is related to f, and it's also related to angular frequency. Those three things are all equal to each other, so you can use whichever 2 of the equations that you are looking for or whatever, right, that you have. Alright. So then how do we figure out what k is? Well, I actually wanna show you that there's really just two ways to figure out what k is. You could use the first equation k equals 2 pi over lambda, but notice how this problem gives us the frequency. Now remember, we can always convert frequency to lambda wavelength by using the equation v equals, lambda times frequency. So what we could do is or this also is equal to c equals lambda times frequency. So what you could do is divide over the frequency, c e c over f is equal to lambda, and you'd plug in some numbers and you would take whatever you get for that number and you would plug it into the k equation, and that would give you the right answer. What I wanna show you is that there's also a more direct way to figure out k by using the second equation that we have here. So we can also use that omega is equal to 2 pi frequency, which is equal to c times k. Notice how we have this frequency and we're looking for k, so we basically can just sort of ignore this part of the equation over here and just look at these last two things that are equal to each other. So we have those numbers and c is just a constant, so all we do is just divide c over to the other side. And what you're going to see here is that 2 pi frequency divided by c is equal to k. Now we just have to plug in some numbers. Right? This is gonna be times 3.5 times 10 to the 16, and then we divide this by 3 times 10 to the 8 meters per second. If you go ahead and work this all out, what you should get is 7.23, sorry, 7.33 times 10 to the 8th. Now remember, the wave number actually doesn't have units. It's sort of just a number. It's a unitless number. So you can just leave this as 7.33 times 10 to the 8th, and this would be your final answer. Alright, folks. Now what I want you to do is pause the video, and if you want to go ahead and work this out, figure out c over frequency, take that number and plug this into your k, and you should get the exact same number. Anyway, folks, that's it for this one. Let me know if you have any questions.