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c20 - 198 Chapter 20 THE ATOM ©2004 2008 2011 Mark E Noble...

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Unformatted text preview: 198 Chapter 20 THE ATOM ©2004, 2008, 2011 Mark E. Noble Stop and pause. We are changing directions. We are changing directions in a big way. 20.1 Welcome You have kept pace for nineteen chapters, covering various portions of the Grand Puzzle. We've touched on all sorts of things so far. We started with atoms and elements, we went to molecules and compounds, we covered reactions and stoichiometry, we dove into the aqueous world, we expanded into gases, and then we got into energy. Much of that jumped around a bit but I explained that purpose in the beginning of Chapter 1. “ I am going to introduce sections and work with them. I may partially build the section and then move to another. This may seem scattered, but with time I will bring these sections together. In the earlier chapters, I will refer to fuller explanations in the later chapters. If you want to, you can look ahead for more. In the later chapters, I will tie back to the earlier chapters. If you're rusty, go back to those pages and refresh. Sometimes, you will need to go back and read a portion. This approach is not idle repetition. These are the links which will hopefully thread the various sections together. You must understand this process. Nature does not work in isolated bits and pieces. Nature is inherently interconnected. All pieces are part of the Grand Puzzle. 9’ With this Chapter we launch a major undertaking, since we now start tying things together. We return to the beginning, to the atom, but now in far greater detail. We will develop this picture for all things monatomic. This much will take us through Chapter 24. Then we will bond these pieces to form molecules and all things polyatomic. That will take us through Chapter 33. Monatomic and polyatomic units make up the microscopic world. Beginning in Chapter 34, we jump to the bigger part, the macroscopic world, and we look at how molecules interact with each other to give bulk properties including the very phases of matter. The next jump after that is how different compounds interact with each other in mixtures. This massive sequence is a study of matter as you know it. Keep in mind where we are at, what we are doing and where we are going. YOU ARE HERE 1 Chapter: 20 21 22 23 24 25 26 27 28 29 3O 31 32 33 34 35 36 37 38 39 4O 41 42 43 \——-W————-—I \_—,—_.4 w—l W monatomics polyatomics phases mixtures For now, we are going back to the world of the atom. And our primary emphasis is the electron. Why? Chapter 2: “ For the most part, CHEMISTRY INVOLVES ELECTRONS. Not protons. Not neutrons. (Unless you're nuking things.) ELECTRONS DO CHEMISTRY! This will be a recurring theme throughout the entire course. This makes electrons a primary focus in our coverage. We need to know three key pieces of information regarding electrons. We need to know how many there are. We need to know their locations within the atom. We need to know their energies. Beginning in this Chapter, we will see how many electrons there are. Locations and energies are more complicated; we begin those details in Chapter 20. 9’ As promised, here we are. By now, we can determine how many electrons there are in a chemical unit, but we still need to know locations and energies. This material is often referred to as "atomic structure", but this does not touch at all upon the structure of the nucleus. It's really the structure of the electrons in the atom. You might also see the term "electronic structure“, which is a better term. Now, I must warn you. We will be treading on strange turf. Outside chemistry or physics, most people do not encounter this. It is difficult to comprehend because it is so contrary to our normal expectations and experiences. There are many strange things to be found among the family of atoms. "They're creepy and they're kooky. Mysterious and spooky." And what‘s worse, they‘re real. Chapter 20: The Atom 199 Welcome to the quantum realm. 20.2 Basics and background Before we embark into the quantum realm, you must be reasonably prepared. You can be prepared, but you can never be certain. Much of our modern understanding of the atom was developed in the early 1900's. For hundreds of years prior to that, classical laws of motion prevailed. Those laws arose from and dealt with the macroscopic world, the world we are used to seeing. Those laws covered the trajectory ofa ball and other normal objects. (Those laws also covered gas phase molecules, as described in Chapter 17.) When it came time to apply these laws of physics to the behavior of the electron in the atom, they were a flop. The old laws failed to describe the motion of the electron whirling around the nucleus. Do electrons violate the laws of physics? No, they merely violated the laws of physics as known at that time. Nature had other laws, laws that apply to the quantum realm, and it took a while to realize this. Within the grip of the atom, those are the laws which the electron obeys. Now don't get this picture wrong. These two sets of laws are not totally separated. There is overlap. It is simply easier for us to think about the classical laws for normal objects and the quantum laws for electrons in atoms. Part of developing the picture ofthe quantum realm requires light and other forms of electromagnetic radiation, so I will provide some basics here. There is much to be seen. I mean that literally. Your vision depends on it. Electromagnetic (EM) radiation encompasses the visible (vis) light which you see and light which you don't see, such as ultraviolet (UV), infrared (IR), radiofrequencies (rf), microwaves, etc. It is common to describe EM radiation as waves, so we need to summarize some terminology about waves to the extent that we need to deal with it now. If you've studied waves in classes before, then you'll be familiar with these basics. (Sine and cosine functions, sin x and cos X, are common examples of waves.) 0 Wavelength: the wavelength is the distance between two equivalent A points in a wave. The two points can be maxima, minima, or whatever, as I—I long as they are equivalent. Wavelength is designated by lower case, Greek lambda, A. The units are normal length units such as m, cm, nm, A etc. Be sure you know your numerical prefix symbols. We will be doing some of the odd ones such as nano, pico, giga, etc. Go back and review it these (Chapter 1) if necessary. 0 Frequency: the frequency is the number of wave cycles per second. It gets the symbol of lower case, Greek nu, v. The "number of wave cycles" is just a number and it does not carry a unit, but "per second" is written "per 5" or just 5". In older days and other uses such as electrical things, they would call this cps for cycles per second. Nowadays, they call it a hertz, Hz; thus, Hz = cps = 5". Like many units, Hz's can also take a prefix: for example, there are kHz (103 Hz) and MHz (106 Hz). 0 Velocity: the velocity is the speed and direction of the wavefront, or simply how fast the wave is moving through space. Arithmetically, it is equal to wavelength times frequency, A x v. The velocity for EM radiation is what we commonly call the speed of light. The speed of all forms of EM radiation is the same and constant through a vacuum, regardless of whether it's vis, UV, IR or whatever. (Light is slower going through air, water, glass, plastic, etc., but we won't worry about that here.) This speed gets the symbol c (not to be confused with specific heat capacity which also uses c) and the value is 3.00 x 108 m/s. (I'm rounding it to three sigfigs for convenience.) c = Av = 3.00 x 108 m/s That's three hundred million meters per second, or 186,000 miles per second. That's fast. Real fast. THIS RELATIONSHIP IS TRUE FOR ALL EM RADIATION. Same speed for everybody, but different combinations of)» and v. Since c is fixed, then A and v are reciprocally related: as one goes up, the other must go down so that c stays the same. 0 Amplitude: the amplitude is the height of the wave at some point. For a simple wave such as a sine or cosine wave, it's the height above (positive amplitude) or below (negative amplitude) its axis. An amplitude can be measured at any point along the wave. 200 Chapter 20: The Atom 0 Node: a node is a point of the wave with zero amplitude. Although it has zero amplitude, a node is still a part of the wave and the wave still exists at that node. OK, that covers the wave terms which we need. Let's get more into EM radiation and EM waves. Let me bring in the word, "spectrum". (The plural is "spectra", not spectrums. Latin again.) A spectrum is a range of EM radiation. You can talk about the entire EM spectrum which covers everything, or you can talk about one range in particular. For example, the visible spectrum of EM radiation is the part displayed by a rainbow. It's the range of colors as detected by human eyeballs. The entire range of EM radiation is immense, spanning a million—billion—fold in terms of A and v, although they all move at the same c. Nature designed human eyeballs to sense EM radiation within a tiny stretch of wavelengths from about 390 to 720 nm. All of color is there, in that tiny stretch which we call the visible (vis) region. Different wavelengths in that stretch correspond to different colors or different shades of color. Put all the wavelengths together and you perceive white light but, as Roy G Biv would tell you, spread out the wavelengths and you get the rainbow. Since colors are spread by wavelength, they are also spread by frequency. For example, consider EM radiation with a wavelength of 390. nm: calculate the frequency of this radiation. In order to do this, we take the equation from above and then re—arrange and plug-and—chug. C = Av = 3.00 x 108 m/s 8 v = i = M = 7.69 x 10145-1 OR 7.69 x 1014Hz A 390. x 10'9 m Look at how I did the denominator: I just inserted 10‘9 m for nanometer, nm; that's an easy way of handling these units. Notice also how Hz can substitute for s". The final result tells us that EM radiation of 390. nm wavelength has a frequency of 7.69 x 1014 Hz. By the way, if you were hit in the eyes with this radiation, then you would perceive this as the color violet. Let's go to the other end of vis, to 720. nm. Do the same calculation. You get 4.17 X 1014 Hz for the frequency. If you were blasted in the eyes by EM waves of A = 720. nm, which has v = 4.17 x 1014 Hz, then you would perceive red. Notice that red has a longer wavelength but a smaller frequency than violet. This is a simple illustration of the inverse relationship between A and v. In between 390 and 720 nm lie the rest of color. red . . . orange . . . yellow . . . green . . . blue . . . violet A 720 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 nm v 4.17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.69 x 1014 Hz The colors are not evenly spaced by A or v, but the progression is in the above sequence. Like I said, the visible spectrum is a tiny fraction of the whole picture. At wavelengths longer than 720 nm, we enter the infrared (IR) region of EM radiation. IR waves extend from 720 nm out to about 1 mm. I say "about" because the borders are not rigorously nor uniformly defined. IR is a huge range just by itself, which is perhaps easier to see ifI rephrase it as 720 nm to 1,000,000 nm. Humans cannot "see" this with their eyes, but our skin can detect some of it as the warmth ofa fire nearby. Some critters can see or sense better than humans in this range. Although we can't see IR with our eyes, we use devices that operate in this region, such as IR film, night-vision devices, heat sensors, etc. Just past the IR range is the microwave range, whose wavelengths extend from 1 mm out to approximately 0.1 — 1 m or so. Microwave ovens operate here, with a frequency of 2.45 GHz. When you cook your food, you're actually blasting it with EM radiation of 2.45 GHz frequency. This corresponds to a wavelength of 8 A = i = M = 0.122m OR 12.2cm v 2.45 x 109 5‘1 At longer wavelengths than microwave, we enter the radiofrequency (rf) range. The rf range gets into all sorts of stuff such as TV, FM, AM, CB, remote control devices, etc. That's what those symbols, MHz and kHz, mean on your radio tuner. Go look next time. Let's say you listen to an FM station at 95.0: that's 95.0 MHz and that means the station broadcasts using EM waves with a frequency of 95.0 x 106 Hz. Chapter 20: The Atom 201 A lot of electronic communications occur in the rf region although, in more recent years, some devices such as cell phones have extended into the microwave range. Notice as we've been going along through the different EM regions that the wavelengths increased while the frequencies decreased. Keep this inverse relationship in mind. It's important. For what we want to do right now, these EM regions with long wavelengths and low frequencies are not of primary concern. We must go back and return to visible, which is where EM radiation can take on important chemical consequence. Furthermore, we need to continue our survey beyond visible in the other direction toward shorter wavelengths and higher frequencies. This is where more and more things can happen. Starting from the shortest visible wavelength of 390 nm, let's trek to even shorter wavelength, into the ultraviolet (UV). The UV range extends from 390 nm down to about 10 nm. UV light is also invisible to the human eyeball. This is unfortunate, since UV is more harmful than vis and we are therefore not aware of it when we are in danger. By the way, this is the reason for the warnings during solar eclipses: do not stare directly into the sun or you can be permanently blinded. The reason is that you can be unknowingly taking in far more UV than your retina can safely handle. You also suntan with UV, and you should be aware of the hazards of suntanning under any conditions. "Black lights" also use UV; they are called "black light" since the UV light cannot be seen, although many of these do show some violet from the visible. Continuing to shorter wavelengths and higher frequencies, we reach X-rays whose range reaches to about 0.01 nm or 10 pm. X-rays are even stronger and more deadly than UV, although they do find important medical use. Even this is not the end, since beyond X-rays lie gamma rays, y, the strongest, most powerful, and deadliest of all EM radiation. You don't normally run into y unless you're nuking things or you're in outer space. The atmosphere pretty much protects surface—dwellers from the gamma rays which come from the sun or from other extra—terrestrial sources. This completes our survey of EM radiation. From deadly gamma to the wimpy radio range, all have the same c and all differ only in their specific A and v combination. We have traversed a range of ~1015 or so in wavelength and frequency. This is a massive, massive range covering a massive, massive range of energies, as we shall see. Before that, however, we must introduce another type of wave and a bit of terminology to go with it. 20.3 Stand and wave. Light waves are traveling waves. This means that the wave moves from one place to another. You are familiar with other traveling waves also, such as the ripples in a pond. On the other hand, you are also familiar with some kinds of waves which do not travel. These are called standing waves or stationary waves. These go through wave motions but the motions are confined to a fixed region. Common examples include a stretched rubber band or various stringed instruments such as a guitar or violin. The band or string is held taut between two end points. When plucked, it undergoes wave motion, but all motion is confined to that region in space as defined by the ends. The string's vibrations are within a fixed, stationary region relative to the end points. Since stationary, these waves don‘t have velocity but they still have wavelength, frequency, amplitude and nodes. Let's look at a few examples of standing waves. We can imagine these to be plucked strings whose ends are fixed at some distance "a". If A you grab the string in the middle and let it go, you get a wave as shown at right, vibrating from one extreme position (solid line) to the other extreme (dashed line). This wave is the easiest to do and it's the simplest wave ................... which is possible. At left, I show another possible wave. It can vibrate within the a region shown. This wave is composed of one full waveform. (One full waveform corresponds to a region of both positive and negative amplitudes.) In this case, one full wavelength exists between the fixed points, and we can write A = a. For our first wave, above right, we only had a half-waveform; thus, one half-wavelength exists between the fixed points, and (1/2)A = a or A = 2a. Check out the nodes: the one at above right has two nodes while the one at above left has three nodes. Since the end points are fixed and cannot move, then these are always two of the nodes. 202 Chapter 20: The Atom Let's go one step more complicated and add another half—waveform to the picture, at left. Now we have three half-waveforms which span the distance a, so (3/2)A = a or A = 2/3 a. This wave has four nodes. We could continue this, adding half-waveforms as we go, but hopefully you're starting to get the picture. I am doing these examples to illustrate a a very important point about stationary waves as they compare to traveling waves. Although traveling waves (such as EM) can be any wavelength whatsoever, this is not true for stationary string waves. There are restrictions due to the fixed end points. Although we can construct string waves from m-waveforms, we can't do just any fraction of a waveform; if we tried, then there would be a violation of the boundary condition imposed ' by the end points. I show this at right: it's an attempt to use a three— quarter waveform, but it fails. Yes, it is indeed a three—quarter waveform, but it fails because one end does not connect to the fixed end point. This string wave cannot exist. a Let me summarize these observations. A stationary, string wave can be constructed using some multiple of half-waves; no other variation is possible. We can derive a mathematical expression for this. First, notice how the first three examples above can be written. one half—wave tw_o half-waves three half-waves 1xlA=a gxlA=a 3x3A=a 2 2 2 We can generalize this as follows. We'll let n be any whole—number, positive integer. Since only some multiple of half—waves is allowed for our string, we can write this limitation as nxlA=a 2 which re-arranges to 31 n A: Now, remember: a is a fixed distance; it is a constant for any given set of end points. On the other hand, n is a restricted variable. It can vary but it is restricted, in this case, to positive whole numbers. Nothing else is allowed. With these restrictions in mind, this equation defines every wavelength which is possible for our string wave. So what does string have to do with an electron? Our discussion here of a string wave introduces two essential concepts to prepare you for your venture into the quantum realm. It introduces the notion of the stationary (standing) wave, which we shall come back to later. It also introduces you to the notion that mathematical equations and their variables can have restrictions on the value which they can be. This restriction to specific values, which are not continuous, is called "quantization". The verb is "quantize", which means to restrict to such types of values. For our vibrating string, we say that "the wavelength is quantized". Given the equation for A above, we can further say that "the wavelength is quantized by n", since n contains the restriction for a whole number. Quantization is extremely important in the quantum realm, but don't be confused by it. The notion is actually known to you, even if the term is no...
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