radiation. The speed of light is a constant. It is represented by the letter “c.”
The constant “c” is (approximately) 186,000 miles per second and it never varies (which is what makes it a “constant”). It does not matter whether light is going up or down, has a high frequency or a low frequency, a large wavelength or a small wavelength, is coming toward us or going away from us: Its velocity is always 186,000 miles per second. This fact led Albert Einstein to the theory of special relativity, as we shall see later.
It also permits us to know both the frequency and the wavelength of light if we know either one of them. This is because the product of the two is always 186,000 miles per second in empty space. The larger one of them is, the smaller the other must be. For example, if we know that by multiplying two numbers together we get 12 for an answer, and if we know that one of the numbers is 6, then we also know that the other number must be 2. If we know that one of the numbers is 3, then we know that the other number must be 4.
Similarly, the higher the frequency of a light wave, the shorter its wavelength must be; the lower the frequency of a light wave, thelonger its wavelength must be. In other words, high-frequency light has a short wavelength and low-frequency light has a long wavelength.
Now we return to Planck’s discovery. Planck discovered that the energy of a light quantum increases with frequency. The higher the frequency, the higher the energy. Energy is proportional to frequency, and Planck’s constant is the “constant of proportionality” between them. This simple relation between frequency and energy is important. It is central to quantum mechanics. The higher the frequency, the higher the energy; the lower the frequency, the lower the energy.
When we put wave mechanics and Planck’s discovery together we get this: High-frequency light, such as violet light, has a short wavelength and high energy; low-frequency light, such as red light, has a long wavelength and low energy.
This explains the photoelectric effect. Photons of violet light knock electrons loose from the atoms of a metal and send them flying away at a higher velocity than photons of red light because the photons of violet light, which is a high-frequency light, have more energy than the photons of red light, which is a low-frequency light.
This all makes sense if you overlook the fact that we are talking about particles (photons) in terms of waves (frequencies) and waves in terms of particles, which, of course, makes no sense at all.
If you feel that you understand the last few pages, congratulations! You have mastered the most difficult mathematics in the book. If not, go back and reread these pages. It is easy to dance with wavelengths and frequencies if you know how they are connected.
Waves are playful creatures that like to do dances of their own. For example, under certain conditions they bend around corners. When this happens it is called diffraction.
Imagine that we are in a helicopter hovering over the mouth of an artificial harbor. The mouth of the harbor is wide enough for two aircraft carriers to pass each other going through it. The sea is rough and the wind and waves are blowing straight into the mouth of theharbor. When we look down, this is the pattern that we see the waves making in the harbor:
The waves are stopped cleanly by the walls of the harbor except at the harbor entrance, where they continue straight forward into the harbor until they are dissipated.
Now imagine that the mouth of the harbor is so small that a rowboat scarcely can pass through it. As we look down from the helicopter, the pattern we see is quite different.
Instead of moving directly ahead into the harbor, the waves inside the harbor are spreading out from the mouth of the harbor almost as if itwere a pond and we had dropped a rock into it at that point. This is diffraction.
Why does it happen? Why does reducing the
The constant “c” is (approximately) 186,000 miles per second and it never varies (which is what makes it a “constant”). It does not matter whether light is going up or down, has a high frequency or a low frequency, a large wavelength or a small wavelength, is coming toward us or going away from us: Its velocity is always 186,000 miles per second. This fact led Albert Einstein to the theory of special relativity, as we shall see later.
It also permits us to know both the frequency and the wavelength of light if we know either one of them. This is because the product of the two is always 186,000 miles per second in empty space. The larger one of them is, the smaller the other must be. For example, if we know that by multiplying two numbers together we get 12 for an answer, and if we know that one of the numbers is 6, then we also know that the other number must be 2. If we know that one of the numbers is 3, then we know that the other number must be 4.
Similarly, the higher the frequency of a light wave, the shorter its wavelength must be; the lower the frequency of a light wave, thelonger its wavelength must be. In other words, high-frequency light has a short wavelength and low-frequency light has a long wavelength.
Now we return to Planck’s discovery. Planck discovered that the energy of a light quantum increases with frequency. The higher the frequency, the higher the energy. Energy is proportional to frequency, and Planck’s constant is the “constant of proportionality” between them. This simple relation between frequency and energy is important. It is central to quantum mechanics. The higher the frequency, the higher the energy; the lower the frequency, the lower the energy.
When we put wave mechanics and Planck’s discovery together we get this: High-frequency light, such as violet light, has a short wavelength and high energy; low-frequency light, such as red light, has a long wavelength and low energy.
This explains the photoelectric effect. Photons of violet light knock electrons loose from the atoms of a metal and send them flying away at a higher velocity than photons of red light because the photons of violet light, which is a high-frequency light, have more energy than the photons of red light, which is a low-frequency light.
This all makes sense if you overlook the fact that we are talking about particles (photons) in terms of waves (frequencies) and waves in terms of particles, which, of course, makes no sense at all.
If you feel that you understand the last few pages, congratulations! You have mastered the most difficult mathematics in the book. If not, go back and reread these pages. It is easy to dance with wavelengths and frequencies if you know how they are connected.
Waves are playful creatures that like to do dances of their own. For example, under certain conditions they bend around corners. When this happens it is called diffraction.
Imagine that we are in a helicopter hovering over the mouth of an artificial harbor. The mouth of the harbor is wide enough for two aircraft carriers to pass each other going through it. The sea is rough and the wind and waves are blowing straight into the mouth of theharbor. When we look down, this is the pattern that we see the waves making in the harbor:
The waves are stopped cleanly by the walls of the harbor except at the harbor entrance, where they continue straight forward into the harbor until they are dissipated.
Now imagine that the mouth of the harbor is so small that a rowboat scarcely can pass through it. As we look down from the helicopter, the pattern we see is quite different.
Instead of moving directly ahead into the harbor, the waves inside the harbor are spreading out from the mouth of the harbor almost as if itwere a pond and we had dropped a rock into it at that point. This is diffraction.
Why does it happen? Why does reducing the
Similar Books
