MEASURING SHORT DISTANCES

In almost everything we do in physics, we are constantly confronted with the need for making measurements. But it is particularly satisfying to be able to see things of sizes normally beyond our reach and to measure them directly. When we measure any length or distance, we do it by reference to a standard so that our measurements will have the same meaning to everyone. If we measure something very large, like the distance to a star, we need large units and our standard must be scaled up to fit our needs. Now today, we're going in the opposite direction and measuring things that are extremely small. So, we're going to have to scale our standard down to fit our needs. Now here is our familiar standard of length in the metric system, the meter. These are centimeters. My finger is just about 1 cm wide or 1/100 of the meter. For something smaller still, like this lead, we can use the millimeter marks. This lead is just about 1 mm wide. But if we want to look at something smaller still, like the width of this hair, for example, we find we have no marks to guide us. We need a smaller scale with finer divisions. This little scale is called a stage micrometer. The divisions on this are very small indeed. In fact, there are 100 of them per millimeter. Even with a magnifying glass, we can't see much of these tiny lines. But this scale was made for using with a microscope. Now, the microscope has a combination of lenses in it so that we get a highly magnified image. We want to look at these lines and compare them with our other scale. Now, when we get this focused, you can see these tiny divisions very well. And we can compare this with a millimeter scale. We can just get two millimeter marks into the picture along with the other scale, and you see how many divisions there are. Now, let's use the scale to measure that hair. It fits neatly between the two large marks. That is, it covers 10 of the divisions. It's a hundredth of a centimeter wide. Using powers of 10, we say that the hair is 10 to the minus two centimeters wide. I have some lycopodium powder here, and I'm going to put some on a microscope slide. I'll blow it on because it's very fine. These tiny particles are the spores of club mosses. Now, let's use a different microscope this time because I want to show you a new kind of measuring device. The scale that you see is the image of a small one in the eyepiece. It's called an ocular scale. To find out what distance each division represents, we can compare this scale directly with the stage micrometer that we saw before. You see that 20 divisions of the ocular scale correspond to 30 divisions of the stage micrometer, or one division to one and a half of the stage micrometer, or 1.5 * 10 ^ -3 cm. This comparison of the scale with the standard scale is called calibration. If we increase magnification, which we do by changing objectives, we must recalibrate. Now, 15 divisions of the ocular scale correspond to five of the stage micrometer, or one division to 1/3, or 0.33 * 10 ^ -3 cm. Now, the lycopodium. This lycopodium spore is about nine divisions wide. Nine divisions equals 3 * 10 ^ -3 cm. So, we've come down to another order of magnitude. Here's some flour, and we can see that the particles are of varying sizes. These have been measured, and the smaller particles are of a size that give us another order of magnitude, farther down the measuring scale. These are about 10 ^ -4 cm wide. To get to the next order of magnitude, we may use specimens of bacteria. A number of these have sizes in the range of 10 to the minus 5 cm. This particular specimen is Bacillus cereus. The width is measured at 8 * 10 to the minus 5 cm, which is by no means a full factor of 10, but we know there's structure here of the order of 10 to the minus 5 cm and smaller. However, we can't see that structure under the light microscope. If we try to magnify one of these pictures, the result reveals nothing more than a larger image of the same indistinct view seen at smaller magnification. So, it isn't just magnification that matters, is it? We need more detail. What we need is a thing called resolution. We want two points that are very, very close together on an object to look like two points and not like one blurred spot. You see how light plays tricks on us. Now, you've seen that we can't get the kind of resolution that we need just by magnification. The nature of light is responsible for this. Light has certain characteristics that make it impossible to distinguish two points that are closer together than about 10 to the minus 5 cm. This microscope has as good a resolution as we can possibly get. Money won't buy a way to get better resolution with a light microscope. But, we've been talking about light that we can see, visible light. Now, you know that not all radiations are visible, but there are other kinds of radiations that have helped us and by a large factor. As long ago as the 1870s, it was known that electron streams can cause fluorescent materials to glow. A device like this was developed more than half a century ago. It's called a Crookes tube. It has an electron gun at the small end, and the electrons are propelled across the evacuated tube to cause the face of the tube to glow, just as in the television tube. We can watch it better in the dark. Now, if I put a barrier in the path of the electrons, we can see an important point. The shadow of that cross-shaped barrier is sharp and distinct. This shows that electrons travel in straight lines. Much later, it was learned that electrons can be controlled and focused, and this new knowledge led to the development of a new kind of microscope using electrons instead of light, an electron microscope. We have our camera in the laboratory at MIT, and Dr. Alan Hodge is demonstrating one of the electron microscopes used in his research. Like the Crookes tube, the electron microscope also employs an electron gun, an evacuated tube into which the specimen is inserted, and a fluorescent screen. Because the tube is evacuated, we cannot, of course, look at living specimens. When the electrons are accelerated by a high voltage, they pass through the specimen, more electrons going through thin spaces than through heavier portions, and are focused to give us a highly magnified shadow picture on the fluorescent screen. Electron microscopes are in use at many laboratories, and we've gone to Professor Chapman at Harvard for this electron micrograph of our friend the Bacillus cereus. Not only is this magnification more than 100 times greater than we obtained under the light microscope, but we get resolution, which allows us to see detail clearly. Unlike the picture made with visible light, which gives us only the outlines, the electron micrograph provides a view of structure. We can see where the cell has divided and distinguish the completed cell wall at the division. With resolution like this, we can even see virus particles. It's easy to realize how valuable a tool the electron microscope has been in medical and biological research. Dr. Robley Williams of the University of California has provided us with these micrographs. The tobacco mosaic viruses here have a width of 1.5 * 10 to the minus 6 cm, which gives us a measurement in our next smaller order of magnitude. To help us reach the next order, Dr. Hodges is preparing a crystal specimen. A device called a microtome is used, a slicing machine which cuts off minute wafers of matter. They are so small that they can't be seen except by the flashes of light they reflect. As they float on water in the container, they can be picked up and prepared as specimens for viewing. This is an edge-on view of a platinum phthalocyanine crystal. The lines show the spacing of the molecules, which are only an atom in thickness. Those stripes are only about 10 to the minus 7 cm apart. Now, when we see separate layers of molecules, we're really getting to small things. After all, a molecule is the smallest bit of a substance that still retains the identity of that substance. But molecules are made of atoms. Can we see atoms? We can calculate the average distance between atoms in a metal. And it turns out that this distance is less than a factor of 10 below the distance that we've been seeing between molecular layers. But when we come this close to seeing atoms, we find that we're reaching another limit of resolution. This is as far as we can go with electron beams. Another difficulty is that separate atoms don't cast very good shadows. So that shadow pictures, like the ones we've been seeing, don't show us very much. We need more contrast. A new idea to help us farther down the scale of seeing came from Professor Erwin Müller of Penn State University. We'll take you to his laboratory and let him show you. If you compare the smallness of an optical microscope with the large dimensions of an electron microscope, you might think that a better microscope will be much larger, but actually it is not to be at all. We have here a new microscope, a so-called field electron microscope, which consists, as you see, of a very small tube and which contains all the essential parts. To show you how it looks inside, I make a little sketch. We have a glass vessel which is evacuated and I am sketching it here. This vessel has sealed in a fine metal tip which stands opposite to a fluorescent screen, just a fluorescent screen in a television tube, for instance. And now, if you put high voltage to this thing, we get electrons streaming out from that needle and projecting an image onto that screen. Now, if you want to know how much magnification you get with this, I should explain it to you in a second sketch. Now, you imagine the tip is very highly enlarged. We have here, in fact, the very end of that needle, which has a very perfectly rounded tip. And from this end, electrons stream out always normal to the surface, and they stream to the right distant fluorescent screen, which I simply sketch here. And now, the magnification, capital M, is determined by the distance from the tip center to the screen, which I call R, and the ratio of this distance to the tip radius, which I call small r. And now, we have a tip radius, let's say, of 5 cm and a screen radius a screen distance of 5 cm, and the tip radius is only 10 to the minus 6 cm, which is very small. You cannot measure directly, and this gives a magnification of 500,000 diameters. From Dr. Müller's film records, let's first compare the thin needle under a light microscope with the point of an ordinary pin, which looms like the nose of a rocket. Actually, the tip of the fine needle cannot be seen. The picture shows only the larger midsection. Now, in this picture taken with an electron microscope, the tip is not only visible, but large enough for us to measure. Since the magnification is known, it's easy to calculate the actual radius. You'll remember that the needle is sealed into the tube, pointed toward the face of the tube. As the voltage is applied, electrons stream out. The screen begins to glow, and a pattern appears. The screen is bright where many electrons hit. This pattern is symmetrical because the tip has a regular crystalline structure. Although the lateral resolution is no better than that of the electron microscope, we get improved contrast because the electrons come directly from the tip surface. Now, suppose we add something to the tip surface such as a few phthalocyanine molecules. This is a model of one in which each ball represents an atom. The structure is well known. The molecule is thin and flat, only one atom thick. And you can note the four-fold symmetry of the face. When some of these are added to the tip surface, the molecules appear and disappear as they turn and the four-leaf clover appearance is noticeable. When the temperature of the tip is raised, they quickly boil away. Now, we see molecules, groups of atoms, but not individual atoms. At this point, the field emission microscope is at its theoretical limit of resolution. So, Dr. Müller went a step further seeking better resolution. He gave up using electrons and developed the field ion microscope using positive ions instead, repelled from a positive needle. A positive ion is an atom from which an electron has been stripped. Now, ions cannot be pulled from the needle tip as electrons were, so they must be introduced in some other way. Helium atoms are fired against the tip, lose their electrons, thus becoming positive ions, and are repelled in straight lines to form an image on the screen. In this new device, the needle tip is mounted in a separate structure, and the tube is operated vertically. The pictures enable Dr. Müller to study the arrangement of atoms in crystals, and permit him to record changes that occur when materials are added or taken away. We are looking at atoms. The bright spots are individual atoms in a platinum crystal. The symmetry here illustrates the regularity that exists even in such minute pieces of matter. The image of each atom we see is formed by at least 10,000 helium ions reaching the screen per second. Here's a picture formed by a tungsten needle, showing the regular crystalline structure of tungsten. Since it is known that the atoms in tungsten are arranged in cubes like this, Dr. Müller has been able to construct this model of the whole tungsten needle tip using cork balls for atoms. The field strength is greatest at the edges of these flat faces, and the helium ions that come from these atoms are the ones that make the picture. At low temperatures, the atomic surfaces of the tip appear immobile. But if we raise the temperature, the image on the screen comes to life. These pictures are composed of a series of still photographs. They are, of course, time-lapse photographs, so that what we see is not the true speed of the reaction. Surface atoms on the needle are torn off, first from the tip, then back along the planes and layers. For the first time, we can see and study reactions between atoms. By measuring the distance between atoms on the image, and using the known magnification, we find that the atomic spacing agrees with previous theoretical calculations. These distances are of the order of 10 to the minus 8 cm. We have come far down the scale of measurement that we began with the standard meter stick. This last range of distance has been so recently reached that few, even in the scientific world, have seen it.