The Electromagnetic Spectrum - Online Tutor, Practice Problems & Exam Prep

The electromagnetic spectrum is a continuum of electromagnetic waves characterized by varying wavelengths and frequencies. It includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Wavelength and frequency are inversely proportional, meaning longer wavelengths correspond to lower frequencies and energy. The equation for wave speed is $c=\lambda \times f$, where c is the speed of light. Understanding these concepts is crucial for grasping the properties and applications of different types of electromagnetic radiation.

The Electromagnetic Spectrum

How's it going, everyone? So in this video, I want to talk about the electromagnetic spectrum. This is something that you've probably seen before in other science classes going all the way back to grade school, so I'm going to go ahead and fly right through it. Now we know that electromagnetic waves, just like all kinds of waves, have wavelength and frequency. And if you sort of plot this out on a number line because there's no limit to how large and small those frequencies can get, you end up with a spectrum. And so this electromagnetic spectrum is what we call a continuum. This is just a number line that goes off to infinity in both directions. It's a continuum of electromagnetic waves, otherwise known as light, and it contains all possible wavelengths and frequencies. Now, different wavelengths and frequencies have very different properties in the universe. For example, visible light is like all the colors of the rainbow that you'd see, which is very different from an x-ray that you would get at the doctor's office or something like that. So based on their properties, scientists have labeled certain portions or bands of the spectrum based on sort of like these ranges of wavelengths. And these definitions are very arbitrary. In some textbooks, you might see different numbers. Basically, there's no really set rule or set number in which something becomes an x-ray or something like that. Alright? So I'm just going to go ahead and sort of fly right through this. You know, if you got your long radio waves on the left and your radio waves, this is where you would have your FM and AM stations like on a home or car radio or something like that. We've got microwaves like you would, you know, heat up your food in a microwave at home. We've got infrared radiation, which is otherwise known as thermal or heat radiation. Whenever you feel heat, you're actually feeling an infrared electromagnetic wave. And then over here, we've got this visible light portion. And if you sort of blow it up, what you're going to see is you're going to see all the colors of the rainbow here. So all the colors of the universe that we see are actually just really in a narrow band of 350 nanometers along the electromagnetic spectrum, and that's all there is to it. Moving forward, we've also got ultraviolet rays. These are responsible for giving you sunburns on a really sunny day. We've got x-rays like we talked about that you would get at the doctor's office. We've also got very powerful gamma rays that we see flying throughout space and the universe, and we also use them to treat cancers and things like that. Alright? So, there's actually a memory tool that we sort of come up here to help you sort of remember, each of the names here. And it's that large, rude Martians invented very unusual x-ray gadgets. So you can kind of just memorize that, and each one of those letters here corresponds to the sort of band that it's talking about. Right? So, it's a memory tool that'll help you sort of, like, remember each of the bands. Alright? Now there's a couple of conceptual things that you'll need to know, about the wavelengths, frequencies, and energy along the electromagnetic spectrum. So we can see here on the left side is on the left side the wavelengths of these waves are very long and the wavelengths over here for gamma rays are very short. So we can say here is that on the left side for long radio waves, you're going to have longer wavelengths. Then on the right side, you're going to have shorter wavelengths. Now one of the things that we already know is that wavelength and frequency are inversely proportional. So in other words, wavelength is inversely proportional to the frequency. So if you have a longer wavelength, then you're going to have a lower frequency because it's fewer cycles per second. And then that means that we're going to have higher frequencies on the right side. Now one of the things that we're going to talk about a little bit later on, but I can tell you is that frequency is also related to energy. We're going to see that energy, the energy of light, is proportional to the frequency. So if you have lower frequency on the left, then you have lower energy, and then you have higher energy on the right side. There's actually a really easy way to remember all of this information. One thing you can remember is that the l's, all are on the left side. So left side starts with l, and that's where l's are. So large radio waves have longer wavelengths, lower frequency, and lower energy, and they're all on the left side. So everything with l is on the left side. Alright? And then, everything else is on the right side. Alright. So the last thing I want to say here is that because, is that remember that all waves obey a mathematical relationship that the speed is equal to wavelength times frequency. Now light is a wave and light always moves at the same speed which we've talked about which is the speed of light c. So that means we can actually just write our new equation, which is that c is equal to lambda times frequency. And to show you how this works, I'm actually going to we're just going to jump right into a problem over here. Alright? So we have human beings continuously emit electromagnetic radiation or waves, of approximately 9 micrometers. So this is actually giving us a wavelength over here. Now the first thing we want to do is we want to calculate the frequency of these electromagnetic waves. So that's going to be f. Well, we have this new relationship over here, this new equation. It's going to be pretty straightforward. We have c=λ⋅f. So that means that we can just move the wavelength or sorry lambda over. So that means c/λ=f. So this is going to be \(3 \times 10^8\) meters per second, and this is going to be divided by the wavelength over here. Now remember that 9 micrometers, micro means \(\times 10^{-6}\). So this is going to be \(9 \times 10^{-6}\). Alright? Now if you go ahead and work this out, what you're going to get is you're going to get a frequency of \(3.33 \times 10^{13}\), and that's going to be whoops. And that's going to be in Hertz. Alright? So that's your final answer. That's how you use this equation. It's very straightforward. And we're going to move on to the next part here, which is which band of the electromagnetic spectrum do these waves belong to? Now this is something we actually could have figured out already because we already have the wavelength, so we could have gone up there to the electromagnetic spectrum and find out where it sits. But now that we know the frequency, it's going to be a little bit easier. So this is what I calculated the frequency to be, \(10^{13}\). And if you look at the frequency line, what you'll see is that \(10^{14}\) is going to be pretty much squarely in the infrared. So this number here would actually sort of sit probably somewhere over here on the frequency spectrum, and so that means that these types of waves actually belong to the infrared radiation spectrum or infrared part of the electromagnetic spectrum. Anyway, folks, so that's your final answer. Let me know if you have any questions, and I'll see you in the next video.

A standard cell phone transmits electromagnetic waves with a frequency of $1.90\times10^9Hz$ . Calculate the wavelength of these electromagnetic waves (in cm).

• A. 15.8 cm
• B. $5.70\times10^{15}cm$
• C. 0.158 cm
• D. 0.0633 cm

Here’s what students ask on this topic:

What is the electromagnetic spectrum?

The electromagnetic spectrum is a continuum of electromagnetic waves characterized by varying wavelengths and frequencies. It includes different types of radiation such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. These waves travel at the speed of light and differ in their wavelengths and frequencies. Longer wavelengths correspond to lower frequencies and lower energy, while shorter wavelengths correspond to higher frequencies and higher energy. The spectrum is essential for understanding the properties and applications of different types of electromagnetic radiation.

How are wavelength and frequency related in the electromagnetic spectrum?

Wavelength and frequency in the electromagnetic spectrum are inversely proportional. This means that as the wavelength (λ) increases, the frequency (f) decreases, and vice versa. The relationship is given by the equation:

$c=\lambda \times f$

where c is the speed of light (approximately 3 × 10⁸ meters per second). This equation shows that the product of wavelength and frequency is always equal to the speed of light.

What are the different types of electromagnetic waves?

The electromagnetic spectrum includes several types of waves, each with distinct properties and applications. These are:

• Radio waves: Used in communication systems like AM and FM radio.
• Microwaves: Used in microwave ovens and radar technology.
• Infrared: Felt as heat and used in thermal imaging.
• Visible light: The range of wavelengths visible to the human eye.
• Ultraviolet: Causes sunburn and is used in sterilization.
• X-rays: Used in medical imaging.
• Gamma rays: Emitted by radioactive materials and used in cancer treatment.

How do you calculate the frequency of an electromagnetic wave?

To calculate the frequency (f) of an electromagnetic wave, you can use the equation:

$f=\frac{c}{\lambda }$

where c is the speed of light (approximately 3 × 10⁸ meters per second) and λ is the wavelength. For example, if the wavelength is 9 micrometers (9 × 10^-6 meters), the frequency would be:

$f=\frac{\mathrm{3\; \times \; 10⁸}}{\mathrm{9\; \times \; 10^-6}}=\mathrm{3.33\; \times \; 10¹³}Hz$

What is the relationship between frequency and energy in the electromagnetic spectrum?

In the electromagnetic spectrum, the energy (E) of a wave is directly proportional to its frequency (f). This relationship is given by the equation:

$E=h\times f$

where h is Planck's constant (approximately 6.626 × 10^-34 Joule seconds). Higher frequency waves, such as X-rays and gamma rays, have higher energy, while lower frequency waves, like radio waves, have lower energy. This principle is crucial for understanding the different effects and applications of various types of electromagnetic radiation.