Absolutely Small - Michael D. Fayer [136]
Our experiences and the basic nature of systems that obey classical mechanics allow us to develop an intuition for the behavior of many things we see about us daily. Even a novice pool player quickly grasps that if you hit the cue ball so that it strikes the left side of another ball, that ball will take off to the right. The pool ball collision is classical, and the balls move according to the precepts of classical mechanics with well-defined trajectories. However, the world around us, which is governed by the rules of quantum mechanics, is generally beyond consideration and understanding. When it comes to phenomena that are controlled by the properties of absolutely small systems, most people are like the toddler looking at the moon. They see it, but lack understanding of what they are seeing.
UNDERSTANDING WHAT WE SEE AROUND US REQUIRES SOME KNOWLEDGE OF QUANTUM MECHANICS
Why should we care? It is possible to go through life and see the moon with no idea of what it really is. A person can get up in the morning, go to work, eat, sleep, have a family, not know what the moon is, and be perfectly happy. It is also possible to have no conception of what makes the everyday things around us have their properties. We live in a sea of physical phenomena that can toss us around like ocean waves. We may not be able to control the physical world around us, but is it reasonable to completely lack any understanding of it? Do we want to be like a toddler or, even worse, an adult with no understanding of the moon? Do we really want to have no conception of why the element in an electric stove gets hot? I believe that the world is a more interesting place when we have some appreciation for the nature of the matter that surrounds us. From biological molecules to electrical conductivity, the natural world is driven by quantum phenomena. If we are adrift in an ocean of quantum physics, then some knowledge of quantum theory increases our appreciation for the wonders of the natural world.
COLOR IS A QUANTUM PHENOMENON
After plowing through the previous chapters, you have grown from toddler to adult in your quantum thinking. Now you know what color is. Let’s go back to the first sentence in the book. Why are cherries red and blueberries blue? The question is what gives objects color and what makes one thing have a different color than another. The answer is that matter is made of atoms and molecules. In contrast to classical mechanics, where energy varies continuously, atoms and molecules have discreet energy levels. Light is also not continuous. Light comes in discreet packets called photons. A photon has a particular energy, which means it has a particular color. Because energy must be conserved, a photon can only be absorbed by the atoms and molecules that make up matter if the energy of the photon matches the energy difference between two atomic or molecular quantum energy levels. If the energy matches, the photon can be absorbed, and the system makes a transition from a lower energy level to a higher energy level. The photons that do not match energy level differences reflect from the object. So if the energy level spacing of the molecules is such that red light is absorbed, blue light will bounce off, and the object looks blue. If the energy level differences are such that blue light is absorbed, then red light bounces off, and the object looks red.
ENERGY LEVELS AND COLOR COME FROM THE WAVELIKE NATURE OF PARTICLES
To reprise the color of objects in a little more detail, we discussed the one-dimensional particle in a box problem in Chapter 8. We learned that absolutely small “particles” are not particles in the everyday classical sense. They are actually waves or wave packets that are more or less localized in space. In the particle in a box, only waves of certain shapes were allowed. In three-dimensional systems, such as the hydrogen atom discussed in Chapter 10, the shapes of the waves