We can use two models to help us understand how light "truly" behaves:
light as bullets, and light as waves.
First think of light as consisting of a bunch of bullets that turn out to have a couple of remarkable properties! In the first place, all bullets of light, from ultraviolet to infrared move through a vacuum at the same speed, "the speed of light": 186,000 miles/second = 300,000 km/sec = 1 foot/nanosecond. All types of light move at this speed through a vacuum no matter how much energy they carry. We don't live in a vacuum, of course, and in air the speeds do differ a little bit, but only a VERY little bit: red light moves about 60 km/sec slower in air than it does in a vacuum, and blue light moves about 60 km/sec slower than the red light does. This is a tiny fraction of 300,000 km/sec, so forget it for now. Light, all light, moves at 300,000 km/sec. So the energy carried by the bullets of light is not determined by their speed; energy is an independent property of the bullet. The energy per bullet distinguishes the different types of light from each other: an infrared bullet carries less energy than a red bullet, which carries less than a blue bullet, which carries less than an ultraviolet bullet, and so on.
The second remarkable property of these "bullets" is that when they pass an atom there is a small chance that they will be absorbed by the atom. They will just disappear. Really. If 100 bullets of UV A-B start at the top of the atmosphere, only 66 will make it to the ground. The other 34 will have been absorbed by the atoms in the atmosphere; they will have just vanished, leaving their energy in the atoms that have absorbed them.
A truly remarkable thing about light is that you can also think of it as a wave on water! A water wave usually moves straight ahead, just like light does. A water wave also bends a little bit when it goes around obstacles. That behavior also happens with visible light, although it is hard to see. In a dark room, aim a beam of light at the edge of a razor blade and then image the blade edge on a screen. You will see that the light has NOT gone in straight lines but has in fact gone a little bit around the blade. The image of the edge of the blade is tinged in red because the red light bends more than does the blue. Radio waves offer a more common experience of this effect. Radio reception "fades out" as you drive into a tunnel instead of suddenly cutting off, because the radio waves bend a little bit into the tunnel. So light bends around obstacles much as water waves or radio waves do. The longer the wavelength of a wave on water the more it will bend; we can color the picture of light as a wave by attributing different wavelengths to the different colors: red light bends more than blue light so it has a longer wavelength, blue light is longer than ultraviolet, and so on.
These bending effects may suggest to you that the bullet picture is wrong, that light really is more like a wave in something. But all sufficiently sensitive detectors of light find that light really does come in lumps. Light is "quantized." If light was only a wave in something then we ought to detect the energy in, say, 1/7 of the wave. But we don't. The minimum amount of energy is always just the energy in the appropriate bullet.
This fact of nature has another nice consequence; it solves a problem with the wave picture. The problem is that the picture of light as a nice continuous wave turns out to imply (using a difficult line of reasoning from 19th century physics) that any warm object, even a human body, should emit an infinite amount of energy! This energy would be in wavelengths shorter than the ultraviolet, so this impossible prediction is called the "ultraviolet catastrophe." Recognizing that light comes in lumps solves that, as Max Planck discovered in 1899.
So what is light? Is it bullets, because it comes in lumps? or waves, because it bends around stuff? It is neither and both. Light is a unique aspect of nature. Our job is to learn how it behaves, and what it is going to do in any situation. Our current understanding of light, called the "quantum theory of light," or "quantum electrodynamics," predicts light to have just the strange sort of behaviors we have identified. Rather than delving into this complex branch of physics, we will instead describe the results of this theory and see how they help us understand how light of all types behaves and how it interacts with atoms.
Light can be thought of as a wave with a wavelength, or as a photon (the
proper name of the bullet) carrying energy. The relationship between the two
models of light is this:
For example, orange light with a wavelength of 620 nm corresponds to photons carrying 1240 eV-nm/620 nm = 2 eV.
Practice with the numbers.
1. What is the wavelength of a 4 eV UV-B photon?
2. What is the wavelength of a 13.6 eV photon? (This is the energy needed to ionize a hydrogen atom.)
3. What is the wavelength of a 4000 eV photon? (This is an X-ray.)
4. What is the energy of a 500 nm photon? (More photons leave the sun with approximately this wavelength than any other.)
5. What is the energy of a photon whose wavelength is the size of a hydrogen atom?
6. What is the energy of a photon whose wavelength is the size of a barium atom?
Electrons in molecules also have allowed patterns, places they are likely to be. For example, in a molecule of hydrogen, H2, there are two electrons, both likely to be found between the two nuclei. Their negative charge holds the two positive nuclei together to make the molecule. In H2O some electrons are concentrated close to the oxygen nucleus, but one pair is most likely to be found in between the O and one of the H nuclei, and another pair between the O and the other H. Again the negative charge of these localized electrons holds the molecule together. These electron arrangements are the source of the "chemical bond." The atoms in DNA are also held in place by chemical bonds; electrons stay between the atoms and hold them together because the electrons don't have an allowed pattern that permits them to slip away.
Each arrangement has a certain energy. Low energy arrangements have
electrons that are likely to be close to the nuclei, while those in which the
electrons are likely to be farther away have higher energy. If an electron changes
from a high energy arrangement to a lower energy arrangement it emits a photon
that carries away the lost energy. For example, when a hydrogen atom changes
from the 2p to the 1s arrangement, the atom loses 10.2 eV and thus emits a photon
carrying 10.2 eV.
3s,3p 1.5 eV
2s,2p 3.4 eV
10.2 eV photon emitted
1s 13.6 eV
Now we can describe how ultraviolet light is produced in a fluorescent light
bulb, and also why, in spite of this, they are safe ordinary lighting.
When a fluorescent light is turned on, electrons start racing from one end of the tube to the other. On the way they bump into atoms, often of mercury, giving them enough energy to allow the electrons to rearrange into a higher energy pattern. Electrons in the high energy pattern in mercury quickly rearrange into the lower energy pattern, losing about 4.9 eV and so emitting a 4.9 eV photon. Now our eyes are not sensitive to photons with this much energy and they are UV-C photons besides, which are very bad for our health! But the high energy photons are absorbed by atoms in the white powder that coats the inside of the bulb. This powder is a mixture of various materials that "fluoresce," that absorb the high energy photons and emit lower energy photons. Here is how they manage this trick. Between the lowest energy arrangement of electrons in the fluorescent material and the 4.9 eV pattern there are several other energy levels. When the atom rearranges it usually does not emit a 4.9 eV photon but jumps to one of the intermediate levels, losing less energy than 4.9 eV. In fact, a whole range of energies is emitted that gives the impression of "white light," although the actual distribution of colors is not the same as sunlight. Remember that "photon energy" corresponds to "color."
Click here for figure 1
Click here for figure 2
4.9 eV state visible energy photon
More About Energy
Energy is what it takes to do work, and our idea of work grows out of
everyday experiences: you do more work when you pull a heavy load than a light
load; you do more work if you pull it a long distance than a short distance. The
more work you do, the more energy you need.
Molecules do work, too. It takes energy to pull atoms from one place in a molecule into a new position, or to pull an atom out of one molecule and into another. The energy first goes into rearranging the electrons into a new pattern. In the new pattern the electrical forces are a bit different so the atoms start shifting around in response to these changed forces. (By the way, the electrical forces between atoms that result from the quantized patterns of the electrons are sometimes called "chemical forces.") Since the first step in molecular energy transactions is electron rearrangement, let's look at the amount of energy this involves in a number of typical situations.
Rearranging the electrons that form a chemical bond typically involves a
few tenths of an eV up to a few eV. For example, to rearrange the electrons in the
H2 molecule into two H atoms requires about 4.5 eV; to form the bonds in a
molecule of ATP requires about 0.3 eV. These are typical energy requirements for
many chemical reactions, all of which involve the rearranging of some outer
electrons of atoms. If the reaction goes the other way, of course the energy is
released. For example, if 2H turns into H2 then 4.5 eV are released when each
molecule is formed. In our bodies, and in yeast cells, the bonds in a molecule of
ATP are broken to release 0.3 eV of energy the cell needs to do its work.
Here are some examples involving different amounts of energy.
a) Hammering a nail, one blow: This involves lots of eV, around 10^19, but this energy is spread out through LOTS of atoms, maybe 1023 or so. Thus the energy per atom is very small, about 10-4 eV, too small to cause any chemical reaction. Instead, the atoms just shift position a little bit, their electrons remaining as they were.
b) Fire: This involves lots of different chemical reactions, but a very important one is oxygen and carbon combining to form carbon dioxide. Each time this happens 4.1 eV of energy are released. Much of this energy goes to make the molecules move faster, that is, to make the gas hot.
c) Batteries: When an atom gains or loses some of its outer electrons, its energy changes. This is called its "electromotive force" in chemistry and physics books, and is typically between 0.1 and 3 eV. For example, at the positive electrode of a lead storage battery, the lead gains two electrons and at the negative electrode it loses two electrons; the difference in energy of the two processes is just over 2 eV. (This depends a bit on the concentration of the lead ions, but that is a more advanced topic. We want to leave a little for your chemistry and physics courses to explain!)
Table 1: Energy Conversion Table
|1 eV =||1||1.4 10-23||1.7 10-26||5.9 10-23||6.2 10-20||4.6 10-^20|
|1 Cal =||7.0 1022||1||1.2 10-3||4||4200||3100|
|1 kW-hr =||5.8 1025||860||1||3400||3.6 106||2.7 106|
|1 BTU =||1.7 1022||0.25||2.9 10-4||1||1100||780|
|1 J =||1.6 1019||2.4 10-4||2.8 10-7||9.5 10-4||1||0.74|
|1 ft-lb =||2.2 1019||3.4 10-4||3.9 10-7||1.3 10-3||1.4||1|
Ordinary amounts of matter contain many eVs of energy because ordinary
amounts of matter contain so many atoms. The basic unit for number of atoms is
the "mole," or "Avogadro's number." If you have 6 1023 atoms of a substance
then you have one mole of the stuff. Since different atoms have different weights
you can measure out a mole by weighing the stuff. One gram of hydrogen
contains 6 1023 atoms of hydrogen; it is one mole of hydrogen. Four grams of
helium make up one mole of helium and so it contains 6 1023 atoms of helium; 12
grams of carbon equal one mole of carbon; and so on. If you check the atomic
weights (which are on most periodic tables) of hydrogen, helium and carbon you
will quickly get the point: whatever the atomic weight of an element is, that many
grams of the element contains one mole of atoms.
Since a chemical reaction involves around one eV per atom we should expect one mole of atoms to produce around 6 1023 eV. From the table above we see that this is about 23 Calories. Sure enough, the typical "heats of formation" studied in chemistry are in this range for simple molecules.