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## Physics library

### Course: Physics library>Unit 14

Lesson 1: Introduction to electromagnetic waves

# Light: Electromagnetic waves, the electromagnetic spectrum and photons

Properties of electromagnetic radiation and photons

## Introduction to electromagnetic waves

Electromagnetic radiation is one of the many ways that energy travels through space. The heat from a burning fire, the light from the sun, the X-rays used by your doctor, as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation. While these forms of energy might seem quite different from one another, they are related in that they all exhibit wavelike properties.
If you’ve ever gone swimming in the ocean, you are already familiar with waves. Waves are simply disturbances in a particular physical medium or a field, resulting in a vibration or oscillation. The swell of a wave in the ocean, and the subsequent dip that follows, is simply a vibration or oscillation of the water at the ocean’s surface. Electromagnetic waves are similar, but they are also distinct in that they actually consist of 2 waves oscillating perpendicular to one another. One of the waves is an oscillating magnetic field; the other is an oscillating electric field. This can be visualized as follows:
While it’s good to have a basic understanding of what electromagnetic radiation is, most chemists are less interested in the physics behind this type of energy, and are far more interested in how these waves interact with matter. More specifically, chemists study how different forms of electromagnetic radiation interact with atoms and molecules. From these interactions, a chemist can get information about a molecule’s structure, as well as the types of chemical bonds it contains. Before we talk about that, however, it’s necessary to talk a little bit more about the physical properties of light waves.

## Basic properties of waves: Amplitude, wavelength, and frequency

As you might already know, a wave has a trough (lowest point) and a crest (highest point). The vertical distance between the tip of a crest and the wave’s central axis is known as its amplitude. This is the property associated with the brightness, or intensity, of the wave. The horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave. These lengths can be visualized as follows:
Keep in mind that some waves (including electromagnetic waves) also oscillate in space, and therefore they are oscillating at a given position as time passes. The quantity known as the wave’s frequency refers to the number of full wavelengths that pass by a given point in space every second; the SI unit for frequency is Hertz left parenthesis, start text, H, z, end text, right parenthesis, which is equivalent to “per seconds” left parenthesiswritten as start fraction, 1, divided by, start text, s, end text, end fraction or start text, s, end text, start superscript, minus, 1, end superscript, right parenthesis. As you might imagine, wavelength and frequency are inversely proportional: that is, the shorter the wavelength, the higher the frequency, and vice versa. This relationship is given by the following equation:
c, equals, lambda, \nu
where lambda (the Greek lambda) is the wavelength (in meters, start text, m, end text) and \nu (the Greek nu) is the frequency (in Hertz, start text, H, z, end text). Their product is the constant c, the speed of light, which is equal to 3, point, 00, times, 10, start superscript, 8, end superscript, start text, space, m, slash, s, end text. This relationship reflects an important fact: all electromagnetic radiation, regardless of wavelength or frequency, travels at the speed of light.
To illustrate the relationship between frequency and wavelength, let’s consider an example.

## Example: Calculating the wavelength of a light wave

A particular wave of electromagnetic radiation has a frequency of 1, point, 5, times, 10, start superscript, 14, end superscript, start text, space, H, z, end text.
What is the wavelength of this wave?
We can start with our equation that relates frequency, wavelength, and the speed of light.
c, equals, lambda, \nu
Next, we rearrange the equation to solve for wavelength.
lambda, equals, start fraction, c, divided by, \nu, end fraction
Lastly, we plug in our given values and solve.
lambda, equals, start fraction, 3, point, 00, times, 10, start superscript, 8, end superscript, start fraction, start text, m, end text, divided by, start cancel, start text, s, end text, end cancel, end fraction, divided by, 1, point, 5, times, 10, start superscript, 14, end superscript, start fraction, 1, divided by, start cancel, start text, space, s, end text, end cancel, end fraction, end fraction, equals, 2, point, 00, times, 10, start superscript, minus, 6, end superscript, start text, space, m, end text
Concept check: What would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of 10?

## Period

The last quantity we will consider is the period of a wave. A wave’s period is the length of time it takes for one wavelength to pass by a given point in space. Mathematically, the period (T) is simply the reciprocal of the wave’s frequency (f):
T, equals, start fraction, 1, divided by, f, end fraction
The units of period are seconds (start text, s, end text).
Now that we have an understanding of some basic properties of waves, we’ll look at the different types of electromagnetic radiation.

## The electromagnetic spectrum

Electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies; this classification is known as the electromagnetic spectrum. The following table shows us this spectrum, which consists of all the types of electromagnetic radiation that exist in our universe.
As we can see, the visible spectrum—that is, light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist. To the right of the visible spectrum, we find the types of energy that are lower in frequency (and thus longer in wavelength) than visible light. These types of energy include infrared (IR) rays (heat waves given off by thermal bodies), microwaves, and radio waves. These types of radiation surround us constantly, and are not harmful, because their frequencies are so low. As we will see in the section, “the photon,” lower frequency waves are lower in energy, and thus are not dangerous to our health.
To the left of the visible spectrum, we have ultraviolet (UV) rays, X-rays, and gamma rays. These types of radiation are harmful to living organisms, due to their extremely high frequencies (and thus, high energies). It is for this reason that we wear suntan lotion at the beach (to block the UV rays from the sun) and why an X-ray technician will place a lead shield over us, in order to prevent the X-rays from penetrating anything other than the area of our body being imaged. Gamma rays, being the highest in frequency and energy, are the most damaging. Luckily though, our atmosphere absorbs gamma rays from outer space, thereby protecting us from harm.
Next, we will talk about the relationship between a wave’s frequency and its energy.

## Quantization of energy and the dual nature of light

We have already described how light travels through space as a wave. This has been well-known for quite some time; in fact, the Dutch physicist Christiaan Huygens first described the wave nature of light as far back as the late seventeenth century. For about 200 years after Huygens, physicists assumed that light waves and matter were quite distinct from one another. According to classical physics, matter was composed of particles that had mass, and whose position in space could be known; light waves, on the other hand, were considered to have zero mass, and their position in space could not be determined. Because they were considered to be in different categories, scientists did not have a good understanding of how light and matter interacted. This all changed in 1900, however, when the physicist Max Planck began studying blackbodies – bodies heated until they began to glow.
Planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics, which postulated that matter could absorb or emit any quantity of electromagnetic radiation. Planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value h, \nu, where h is Planck’s constant, 6, point, 626, times, 10, start superscript, minus, 34, end superscript, start text, space, J, end text, dot, start text, s, end text, and \nu is the frequency of the light absorbed or emitted. This was a shocking discovery, because it challenged the idea that energy was continuous, and could be transferred in any amount. The reality, which Planck discovered, is that energy is not continuous but quantized—meaning that it can only be transferred in individual “packets” (or particles) of the size h, \nu. Each of these energy packets is known as a quantum (plural: quanta).
While this might sound confusing, we are actually already very familiar with quantized systems. The money we use daily, for example, is quantized. For instance, when you go into a store, you will not see anything on sale for a price of one dollar and two and a half cents left parenthesis, dollar sign, 1, point, 025, right parenthesis. This is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this. Just as we cannot pay the cashier at the store half of a cent, energy cannot be transferred in anything less than a single quantum. We can think of quanta as being like “pennies” of electromagnetic energy—the smallest possible units by which such energy can be transferred.
Planck’s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave. In actuality, light seemed to have both wavelike and particle-like properties.

## The photon

Planck’s discoveries paved the way for the discovery of the photon. A photon is the elementary particle, or quantum, of light. As we will soon see, photons can be absorbed or emitted by atoms and molecules. When a photon is absorbed, its energy is transferred to that atom or molecule. Because energy is quantized, the photon’s entire energy is transferred (remember that we cannot transfer fractions of quanta, which are the smallest possible individual “energy packets”). The reverse of this process is also true. When an atom or molecule loses energy, it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule. This change in energy is directly proportional to the frequency of photon emitted or absorbed. This relationship is given by Planck’s famous equation:
E, equals, h, \nu
where E is the energy of the photon absorbed or emitted (given in Joules, start text, J, end text), \nu is frequency of the photon (given in Hertz, start text, H, z, end text), and h is Planck’s constant, 6, point, 626, times, 10, start superscript, minus, 34, end superscript, start text, space, J, end text, dot, start text, s, end text.

## Example: Calculating the energy of a photon

A photon has a frequency of 2, point, 0, times, 10, start superscript, 24, end superscript, start text, space, H, z, end text.
What is the energy of this photon?
First, we can apply Planck's equation.
E, equals, h, \nu
Next, we plug in our given value for the frequency, as well as the value for Planck's constant, h, and solve.
E, equals, left parenthesis, 6, point, 626, times, 10, start superscript, minus, 34, end superscript, start text, space, J, end text, dot, start cancel, start text, s, end text, end cancel, right parenthesis, times, left parenthesis, 2, point, 0, times, 10, start superscript, 24, end superscript, start cancel, start text, space, s, end text, start superscript, minus, 1, end superscript, end cancel, right parenthesis, equals, 1, point, 3, times, 10, start superscript, minus, 9, end superscript, start text, space, J, end text
Concept check: The wavelength of orange light is about 590, minus, 635, start text, space, n, m, end text, and the wavelength of green light is about 520, minus, 560, start text, space, n, m, end text. Which color of light is more energetic, orange or green?
(Hint: Keep in mind what you have already learned about the relationship between wavelength and frequency.)

## Conclusion

Electromagnetic radiation can be described by its amplitude (brightness), wavelength, frequency, and period. By the equation E, equals, h, \nu, we have seen how the frequency of a light wave is proportional to its energy. At the beginning of the twentieth century, the discovery that energy is quantized led to the revelation that light is not only a wave, but can also be described as a collection of particles known as photons. Photons carry discrete amounts of energy called quanta. This energy can be transferred to atoms and molecules when photons are absorbed. Atoms and molecules can also lose energy by emitting photons.

## Want to join the conversation?

• Does light have different speeds depending on the medium (e.g. air, water, etc) it is in? If it does, does it change wavelength, frequency, or both? When the speed decreases, does the light has less energy? Does light traveling through air, then water, then air again, has the same speed as it does in the beginning and in the end? •   The speed of light can change.
The highest ever recorded is 299 792 458 m / s.
In 1998, Danish physicist Lene Vestergaard Hau led a combined team from Harvard University and the Rowland Institute for Science which succeeded in slowing a beam of light to about 17 meters per second, and researchers at UC Berkeley slowed the speed of light traveling through a semiconductor to 9.7 kilometers per second in 2004.
Hau later succeeded in stopping light completely, and developed methods by which it can be stopped and later restarted.
• So do different kinds of lightbulbs give off different spectrums? • Where do we find a photon in an atom? • Any kind of Electro-Magnetic wave travels in small energy packets called photons. In the visible range of light these are called photons and in the invisible range, i.e Infrared, UV and others the energy are called quanta. When a electron gains a certain amount of energy then it jumps to a higher energy orbit unless it has absorbed so much energy that its ejected, it again comes back to its original orbit after losing the energy i.e emitting it in form of Electro-magnetic Radiation. That is called emission spectrum.
• from where photon is emmited or absorbed? •  Photons can be absorbed by electrons. These will increase in energy and jump energy levels. Afterward, the same electron can emit the photon to jump down energy levels.
• Why do things travel in waves and not in a straight line ?
simply if I throw a ball , it doesnt make a wave. So why do electrons make waves ? • actually, you thrown ball does make a wave. its just that the wavelength is so small, you could not observe or measure it

DeBroglie said:
Wavelength = h/p h/mv = (approx) 6 x 10>-34 / (0.01 kg x 20m/s) = (roughly) 3 x 10>-33 m

a nucleus of an atom is about 10>-15 so, the wavelength of your thrwon ball is verrrrry small

:)

ok??
• So the only thing I'm having trouble with is the relationship between a photon's frequency and a light wave's frequency. Is this correct?:

If you take the "frequency of a light wave" and multiply it by "6.626*10tothe-34" you get the frequency of a photon of that light wave? • First you cannot treat the energy of a classical light wave the same way as the energy of a photon.
The energy of a photon is E = hf.
The energy of a light wave is proportional to the square of the amplitude of oscillation of the electromagnetic wave.
These are two completely different models of light, classical vs quantum mechanical.
• I am confused: is wave the energy itself or the disturbance in electromagnetic field caused by energy (like throwing a stone into a pond and wave forms) • How do you sole for wavelength? • Planck's equation for energy of an electromagnetic waves depends on only one factor - frequency or wavelength. Shouldn't amplitude, in some way, be directly related to energy? (I'm saying this after a comparison to sound .. sound is 'louder' when it has a large amplitude or a comparison the energy lost in a resistor in an AC circuit which equal to ((Vrms^2)*t)/R here Vrms is directly related to Vpeak which is the amplitude of the voltage signal. The energy is a directly related to the voltage's amplitude (square relationship) in an AC circuit , same as energy stored in a capacitor ..). All of this could be so wrong.. please correct me. • it might be too late but ill try to answer.
as per my understanding, a photon's energy is dependent only on its wavelength, that's what quantum mechanics tells us. photons do not have a "real" discernable amplitude. However, classical mechanics associates energy with amplitude. here's the problem though, you cannot use classical mechanics to deal with photons. we can approximate that the "amplitude" of a light wave is proportional to the number of photons hitting a particular surface per unit time. in other words, it is proportional to the intensity of the wave. this does not hold true when we consider one photon, only a system of many photons.

I am not an expert so PLEASE correct anything wrong I said :)
• What are some of the different effects that various frequencies of electromagnetic radiation have when absorbed by matter? • The different effects light has on atoms can best be understood when considering the energies of types of light. And since energy and frequency are directly proportional, the trend we describe using energy will be the same for frequency.

Higher energy light such as gamma rays, X-rays, and high energy UV light cause ionizations. They transfer enough energy to electrons so they can escape from the pull of the atom’s nucleus and turn the atom into an ion.

Low energy UV and visible light cause electron transitions. The electrons are able to move between the energy levels within the atom, but do not have enough energy to escape.

Infrared light causes molecular vibrations. The bonding atoms of a molecule vibrate back and forth like an oscillating spring.

Microwaves cause rotational motion where a molecule rotates.

Radio waves cause nuclear spin transitions which is when a proton changes its spin state.

The lower the energy the light, the less work can be done with it by the atom when it absorbs that light.

Hope that helps.