6.1 Electromagnetic Energy

Electromagnetic energy is a term used to describe all the different kinds of energies released into space by stars such as the Sun. These kinds of energies include some that you will recognize and some that will sound strange. They include

• Radio Wave
• Radar waves
• TV wavee
• Heat (infrared radiation)
• Light
• Ultraviolet Light (This is what causes Sunburns)
• X-rays (Just like the kind you get at the doctor’s office)
• Short waves
• Microwaves, like in a microwave oven
• Gamma Rays

All these waves do different things (for example, light waves make things visible to the human eye, while heat waves make molecules move and warm up, and x rays can pass through a person and land on film, allowing us to take a picture inside someone’s body) but they have some things in common.

They all travel in waves, like the waves at a beach or like sound waves, and also are made of tiny particles. Scientists are unsure of exactly how the waves and the particles relate to each other. The fact that electromagnetic radiation travels in waves lets us measure the different kind by wavelength or how long the waves are. That is one way we can tell the kinds of radiation apart from each other.

Although all kinds of electromagnetic radiation are released from the Sun, our atmosphere stops some kinds from getting to us. For example, the ozone layer stops a lot of harmful ultraviolet radiation from getting to us, and that’s why people are so concerned about the hole in it.

We humans have learned uses for a lot of different kinds of electromagnetic radiation and have learned how to make it using other kinds of energy when we need to. DS1 would not be able to communicate with Earth, for example, if it could not produce radio waves.

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms and was able to demonstrate that white light consists of the individual colors of the rainbow combined together. Newton explained his optics findings in terms of a “corpuscular” view of light, in which light was composed of streams of extremely tiny particles travelling at high speeds according to Newton’s laws of motion. Others in the seventeenth century, such as Christiaan Huygens, had shown that optical phenomena such as reflection and refraction could be equally well explained in terms of light as waves travelling at high speed through a medium called “luminiferous aether” that was thought to permeate all space. Early in the nineteenth century, Thomas Young demonstrated that light passing through narrow, closely spaced slits produced interference patterns that could not be explained in terms of Newtonian particles but could be easily explained in terms of waves. Later in the nineteenth century, after James

Clerk Maxwell developed his theory of electromagnetic radiation and showed that light was the visible part of a vast spectrum of electromagnetic waves, the particle view of light became thoroughly discredited. By the end of the nineteenth century, scientists viewed the physical universe as roughly comprising two separate domains: matter composed of particles moving according to Newton’s laws of motion, and electromagnetic radiation consisting of waves governed by Maxwell’s equations. Today, these domains are referred to as classical mechanics and classical electrodynamics (or classical electromagnetism). Although there were a few physical phenomena that could not be explained within this framework, scientists at that time were so confident of the overall soundness of this framework that they viewed these aberrations as puzzling paradoxes that would ultimately be resolved somehow within this framework. As we shall see, these paradoxes led to a contemporary framework that intimately connects particles and waves at a fundamental level called wave-particle duality, which has superseded the classical view.

Electromagnetic Energy

Energy

Energy travels through space or material. This is obvious when you stand near a fire and feel its warmth or when you pick up the handle of a metal pot even though the handle is not sitting directly on the hot stove. Invisible energy waves can travel through air, glass, and even the vacuum of outer space. These waves have electrical and magnetic properties, so they are called electromagnetic waves. The transfer of energy from one object to another through electromagnetic waves is known as radiation.

Different wavelengths of energy create different types of electromagnetic waves (Figure below).

Figure-6.1: The electromagnetic spectrum; short wavelengths are the fastest with the highest energy

Ref: common.wikimedia.org/

Speed of all Electromagnetic Spectrum Waves (c) = 3.0 x 10⁸ m/s = speed of light.

c (m/s)  =  ν x λ = speed of light or speed of all electromagnetic spectrum waves

ν (Hz) = c / λ = frequency

λ (m) = c / ν = wavelength

Note that the unit Hz = 1/s (inverse of the seconds)

Figure 6.2 Relationship between Frequency, Wavelength & Velocity

Ref: Commons.wikimedia.org/

Examples:

1. Violet light has a wavelength of 4.10 x 10-12 m. What is the frequency?

ν (Hz) = c / λ = frequency  =  [ 3.0 x 10⁸ m/s ]  /  [ 4.10 x 10-12 m ] = 7.31 x 10¹⁹ Hz

2. Green light has a frequency of 6.01 x 1014Hz. What is the wavelength?

λ (m) = c / ν = wavelength = [ 3.0 x 10⁸ m/s ]  /  [ 6.01 x 1014 Hz ] = 4.99 x 10 ^{– 7} m

The energy of the electromagnetic spectrum can be calculated using the formula below:

Energy (J) = h x ν

h (Planck’s Constant) = 6.626 x 10^-34J.s

ν (Hz) = c / λ = frequency

Figure 6.3 Relationship between Frequency, & Energy

Ref: Commons.wikimedia.org/

Examples:

1. Calculate the energy of a photon of radiation with a frequency of 8.5 x 10¹⁴Hz

Energy (J) = h x ν = [ 6.626 x 10^-34J.s ] x [ 8.5 x 10¹⁴Hz ] = 5.63 x 10 ^{– 19} J

2. Calculate the energy of a photon of radiation with a wavelength of 6.4 x 10^-7m

Energy (J) = h x ν = h x [ c / λ ] = [ 6.626 x 10^-34J.s ] x  [ ( 3.0 x 10⁸ m/s ) / ( 6.4 x 10^-7m ) ] = 3.1 x 10 ^-19 J

3. What is the relationship between frequency and wavelength?

1. Direct
2. Inverse

Answer: Inverse

4. What is the relationship between frequency and energy?

1. Direct
2. Inverse

Answer: Direct

Can you think of some objects that appear to radiate visible light, but actually do not? The Moon and the planets do not emit light of their own; they reflect the light of the Sun. Reflection is when light (or another wave) bounces back from a surface. Albedo is a measure of how well a surface reflects light. A surface with high albedo reflects a large percentage of light. A snow field has high albedo.

One important fact to remember is that energy cannot be created or destroyed — it can only be changed from one form to another. This is such a fundamental fact of nature that it is a law: the law of conservation of energy.

In photosynthesis, for example, plants convert solar energy into chemical energy that they can use. They do not create new energy. When energy is transformed, some nearly always becomes heat. Heat transfers between materials easily, from warmer objects to cooler ones. If no more heat is added, eventually all of a material will reach the same temperature.

Summary

• Energy travels in waves with electrical and magnetic properties and so is called electromagnetic radiation.
• The wavelengths of visible light vary from long wavelength red to short wavelength violet. Infrared and ultraviolet wavelengths continue outward at longer and shorter wavelengths.
• The law of conservation of energy states that energy cannot be created or destroyed, it can only change forms.

The Electromagnetic Spectrum

Electromagnetic waves

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.

Figure 6.4 Electromagnetic Radiation

Ref: Commons.wikimedia.org/

Figure 6.5 Wave Properties

Ref: Commons.wikimedia.org/

Figure: One-dimensional sinusoidal waves show the relationship among wavelength, frequency, and speed. The wave with the shortest wavelength has the highest frequency. Amplitude is one-half the height of the wave from peak to trough.

Reference: Chemistry 2e OpenStax.

Electromagnetic waves are invisible forms of energy that travel though the universe. However, you can “see” some of the results of this energy. The light that our eyes can see is actually part of the electromagnetic spectrum.

This visible part of the electromagnetic spectrum consists of the colors that we see in a rainbow – from reds and oranges, through blues and purples. Each of these colors actually corresponds to a different wavelength of light.

The sound we hear is a result of waves which we cannot see. Sound waves need something to travel through in order for it to move from one place to the next. Sound can travel through air because air is made of molecules.

Figure 6.6 Electromagnetic Radiation Properties

Ref: Commons.wikimedia.org/

Electromagnetic Wave

These molecules carry the sound waves by bumping into each other, like dominoes knocking each other over. Sound can travel through anything made of molecules – even water! There is no sound in space because there are no molecules there to transmit the sound waves.

Figure 6.7 Electromagnetic spectrum

Ref: Commons.wikimedia.org/

Electromagnetic waves are not like sound waves because they do not need molecules to travel. This means that electromagnetic waves can travel through air, solid objects and even space. This is how astronauts on spacewalks use radios to communicate. Radio waves are a type of electromagnetic wave.

Electricity can be static, like what holds a balloon to the wall or makes your hair stand on end. Magnetism can also be static like a refrigerator magnet. But when they change or move together, they make waves – electromagnetic waves.

Electromagnetic waves are formed when an electric field (which is shown in red arrows) couples with a magnetic field (which is shown in blue arrows). Magnetic and electric fields of an electromagnetic wave are perpendicular to each other and to the direction of the wave.

When you listen to the radio, watch TV, or cook dinner in a microwave oven, you are using electromagnetic waves. Radio waves, television waves, and microwaves are all types of electromagnetic waves. They only differ from each other in wavelength. Wavelength is the distance between one wave crest to the next.

Waves in the electromagnetic spectrum vary in size from very long radio waves the size of buildings, to very short gamma-rays smaller than the size of the nucleus of an atom. Yet their size can be related to their energy.

The smaller the wavelength the higher the energy. For example, a brick wall blocks visible light wave lengths. Smaller, more energetic, x-rays can pass through brick walls, but themselves are blocked by denser material such as lead.

While it can be said waves are “blocked” by certain materials, the correct understanding is that wave lengths of energy are “absorbed” by objects, or not. That is, wave length energy can be absorbed by certain material.

Electromagnetic Waves

Elelectromagnetic wave begins when an electrically charged particle vibrates. The Figures below shows how this happens. A vibrating charged particle causes the electric field surrounding it to vibrate as well. A vibrating electric field, in turn, creates a vibrating magnetic field. The two types of vibrating fields combine to create an electromagnetic wave.

Figure 6.8 Electromagnetic Wave Travels

Ref: Commons.wikimedia.org/

As you can see in the Figure above, the electric and magnetic fields that make up an electromagnetic wave are perpendicular (at right angles) to each other. Both fields are also perpendicular to the direction that the wave travels. Therefore, an electromagnetic wave is a transverse wave. However, unlike a mechanical transverse wave, which can only travel through matter, an electromagnetic transverse wave can travel through empty space. When waves travel through matter, they lose some energy to the matter as they pass through it. But when waves travel through space, no energy is lost. Therefore, electromagnetic waves don’t get weaker as they travel. However, the energy is “diluted” as it travels farther from its source because it spreads out over an ever-larger area.

Electromagnetic Wave Interactions

When electromagnetic waves strike matter, they may interact with it in the same ways that mechanical waves interact with matter. Electromagnetic waves may:

• reflect, or bounce back from a surface;
• refract, or bend when entering a new medium;
• diffract, or spread out around obstacles.

Electromagnetic waves may also be absorbed by matter and converted to other forms of energy. Microwaves are a familiar example. When microwaves strike food in a microwave oven, they are absorbed and converted to thermal energy, which heats the food.

Sources of Electromagnetic Waves

The most important source of electromagnetic waves on Earth is the sun. Electromagnetic waves travel from the sun to Earth across space and provide virtually all the energy that supports life on our planet. Many other sources of electromagnetic waves depend on technology. Radio waves, microwaves, and X rays are examples. We use these electromagnetic waves for communications, cooking, medicine, and many other purposes.

The Electromagnetic Spectrum

Summary

• Electromagnetic waves are waves that consist of vibrating electric and magnetic fields. They transfer energy through matter or across space. The transfer of energy by electromagnetic waves is called electromagnetic radiation.
• The electric and magnetic fields of an electromagnetic wave are areas of electric or magnetic force. The fields can exert force over objects at a distance.
• An electromagnetic wave begins when an electrically charged particle vibrates. This causes a vibrating electric field, which in turn creates a vibrating magnetic field. The two vibrating fields together form an electromagnetic wave.
• An electromagnetic wave is a transverse wave that can travel across space as well as through matter. When it travels through space, it doesn’t lose energy to a medium as a mechanical wave does.
• When electromagnetic waves strike matter, they may be reflected, refracted, or diffracted. Or they may be absorbed by matter and converted to other forms of energy.
• The most important source of electromagnetic waves on Earth is the sun. Many other sources of electromagnetic waves depend on technology.

Check This Out!

A nice simulation of electromagnetic radiation reacting with different molecules can be visible and played around it.

Black Body Radiation

All objects above the temperature of absolute zero emit electromagnetic radiation consisting of a broad range of wavelengths described by a distribution curve whose peak wavelength λ (lambda) at absolute temperature T for a “perfect radiator” known as a black body is given by Wein’s law which predicts that λ_max is inversely proportional to T.

At ordinary temperatures this radiation is entirely in the infrared region of the spectrum, but as the temperature rises above about 1000K, more energy is emitted in the visible wavelength region and the object begins to glow, first with red light, and then shifting toward the blue as the temperature is increased.

This type of radiation has two important characteristics. First, the spectrum is a continuous one, meaning that all wavelengths are emitted, although with intensities that vary smoothly with wavelength. The other curious property of black body radiation is that it is independent of the composition of the object; all that is important is the temperature.

Figure 6.9 Black Body Radiation

Ref: Commons.wikimedia.org/

Planck’s Equation                                                      

Black body radiation, like all electromagnetic radiation, must originate from oscillations of electric charges which in this case were assumed to be the electrons within the atoms of an object acting somewhat as miniature Hertzian oscillators. It was presumed that since all wavelengths seemed to be present in the continuous spectrum of a glowing body, these tiny oscillators could send or receive any portion of their total energy. However, all attempts to predict the actual shape of the emission spectrum of a glowing object on the basis of classical physical theory proved futile.

Figure 6.10 Max Planck

In 1900, the great German physicist Max Planck (who earlier in the same year had worked out an empirical formula giving the detailed shape of the black body emission spectrum) showed that the shape of the observed spectrum could be exactly predicted if the energies emitted or absorbed by each oscillator were restricted to integer values of hν, where ν (“nu”) is the frequency and h is a constant 6.626E–34 J s which we now know as Planck’s Constant. This means that the allowable energies of each oscillator are quantized. (Owing to the minute differences in frequency among the uncountable numbers of oscillators in any visible body, the spectrum appears to be continuous.) This modification of classical theory, the first use of the quantum concept, was as unprecedented as it was simple, and it set the stage for the development of modern quantum physics.

Particle Theory of Light

Photoelectric effect

Shortly after J.J. Thompson’s experiments led to the identification of the elementary charged particles we now know as electrons, it was discovered that the illumination of a metallic surface by light can cause electrons to be emitted from the surface. This phenomenon, the photoelectric effect, is studied by illuminating one of two metal plates in an evacuated tube. The kinetic energy of the photoelectrons causes them to move to the opposite electrode, thus completing the circuit and producing a measurable current. However, if an opposing potential (the retarding potential) is imposed between the two plates, the kinetic energy can be reduced to zero so that the electron current is stopped. By observing the value of the retarding potential V_r, the kinetic energy of the photoelectrons can be calculated from the electron charge e, its mass m and the frequency ν of the incident light:

This plot illustrates the photoelectric effect in metallic zinc. No photoelectrons are emitted until the frequency of the incident light reaches 10.4 ×10¹⁴ hz = 1.04 × 10¹⁵ hz. This frequency corresponds to a wavelength of

(3E8 m s^—1) / (1.04E15 s^—1) =288E-6 m

which, as the diagram indicates, falls outside the range of visible light, in the ultraviolet region of the spectrum             

Figure 6.11 Photoelectric Effect on metallic Zinc

Ref: Commons.wikimedia.org/

Figure 6.12 Photoelectric Effect

The Idea of Photon

Although the number of electrons ejected from the metal surface per second depends on the intensity of the light, as expected, the kinetic energies of these electrons (as determined by measuring the retarding potential needed to stop them) does not, and this was definitely not expected. Just as a more intense physical disturbance will produce higher energy waves on the surface of the ocean, it was supposed that a more intense light beam would confer greater energy on the photoelectrons. But what was found, to everyone’s surprise, is that the photoelectron energy is controlled by the wavelength of the light, and that there is a critical wavelength below which no photoelectrons are emitted at all.

Figure 6.13 Albert Einstein

Ref: Commons.wikimedia.org/

Albert Einstein quickly saw that if the kinetic energy of the photoelectrons depends on the wavelength of the light, then so must its energy. Further, if Planck was correct in supposing that energy must be exchanged in packets restricted to certain values, then light must similarly be organized into energy packets. But a light ray consists of electric and magnetic fields that spread out in a uniform, continuous manner; how can a continuously-varying wave front exchange energy in discrete amounts? Einstein’s answer was that the energy contained in each packet of the light must be concentrated into a tiny region of the wave front. This is tantamount to saying that light has the nature of a quantized particle whose energy is given by the product of Planck’s constant and the frequency:

Einstein’s publication of this explanation in 1905 led to the rapid acceptance of Planck’s idea of energy quantization, which had not previously attracted much support from the physics community of the time. It is interesting to note, however, that this did not make Planck happy at all. Planck, ever the conservative, had been reluctant to accept that his own quantized-energy hypothesis was much more than an artifice to explain black-body radiation; to extend it to light seemed an absurdity that would negate the well-established electromagnetic theory and would set science back to the time before Maxwell.

De Broglie Equation:

Although the photon has no rest mass, it does possess kinetic energy by virtue ot its velocity. The mass-equivalent of this energy is given by Einstein’s relation m = e/c². Combining this with Planck’s relation e = hν, the effctive mass of the photon becomes

which corresponds to a momentum m v of (h/cλ) × c = h/λ .