132 A NATURAL APPROACH TO CHEMISTRY. What are atoms? What are their properties? Why are atoms important in chemistry?

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1 What are atoms? What are their properties? Why are atoms important in chemistry? What would happen if you took a piece of aluminum foil and tore it in half again and again? Then, when that piece of aluminum became too small to hold, imagine that you could keep cutting it in half again and again. Keep thinking of smaller and smaller pieces of aluminum. Could you keep cutting forever, or do you reach a limit that is the smallest possible piece of aluminum? The answer to this question has far-reaching consequences. Either there is a smallest piece, which means the aluminum is made from tiny particles (atoms), or the aluminum is one smooth substance that can be cut in half forever. Over time, starting with the ancient Greeks, scientists struggled with this question, each building upon the work of others. Today we know that everything is made from atoms: There is a smallest piece of aluminum. Our modern view of the atom is the culmination of 2,500 years of scientific thinking and experimentation. Our understanding of the properties of the atom has led to major chemical discoveries that have improved our lives from medicine to energy. 132 A NATURAL APPROACH TO CHEMISTRY

2 Light, color, atoms, and electrons When you pass high-voltage electricity through a gas, it can light up. This is how a neon sign works. In the lab we use glass tubes filled with gas in a high-voltage power supply. Different elements give off noticeably different colors of light. The most interesting thing happens when you observe this light through a special lens called a diffraction grating. You may know that pure white light is really an equal mixture of all colors together. The light from a gas discharge tube is also a mixture of colors. A diffraction grating separates the light into its component colors. To the eye, the light from nitrogen gas looks purple and helium looks pink. However, through the diffraction grating, the purple and pink are not so simple! Instead of a single color, the diffraction grating shows us that the light is really many colors. Each color shows up as a vertical line in what chemists call a line spectrum. Do you notice how nitrogen and helium are different? Each element has its own unique line spectrum. In fact, the unique patterns of spectral lines are often called the fingerprints of the elements. How are these line spectra different? Do the line spectra remind you of a barcode used at the checkout counter of a store? It is a good analogy! Line spectra contain information about the structure of each element just as barcodes contain information about product numbers. Compare the line spectra of helium, nitrogen, and oxygen. What differences do you see? What similarities do you see? There are areas of the rainbow in which no color is emitted (black). Nitrogen and oxygen have more lines than helium. All three spectra are noticeably different. Some of the lines are thicker than others. The number of spectral lines is related to the number of electrons in each atom. Helium has two electrons and nitrogen has seven electrons. Could it be that nitrogen has more spectral lines because it has more electrons? In this chapter we will learn how to categorize atoms according to their electron structures in a table called the periodic table, which is the major reference document of chemistry. A NATURAL APPROACH TO CHEMISTRY 133

3 Section 5.1 The Atom Has a Structure 5.1 The Atom Has a Structure Elements and compounds In the previous chapters, we learned that ordinary matter is made of atoms of the 92 naturally occurring elements. These atoms usually form compounds, such as salt (NaCl) or sodium bicarbonate (NaHCO 3 ). Compounds explain how we get millions of types of matter from 92 elements, but 92 is still a relatively large number. Are the 92 different types of atoms (i.e., the elements) made of even smaller things? The answer is yes. Atoms are made from smaller particles called protons, neutrons, and electrons How can three particles explain the universe? Each element is a unique type of atom This is an extraordinary fact! How can the incredible variety of matter in the universe come from only three particles? Think about making all the words in the dictionary with only three letters or all the paintings in the world with only three colors. It may seem incredible, but it is true nonetheless. The atoms of all 92 elements (and more) are created from three basic particles: electrons, protons, and neutrons. The beautiful variety of nature arises from how the three particles come together in rich and complex ways. Before we delve into the depths of the atom, let s review what we know. There are 92 naturally occurring elements, plus 20 to 30 other elements that have been created in a laboratory. Each element represents a unique type of atom. For example, all oxygen atoms are similar to each other but different from carbon atoms or hydrogen atoms. 134 A NATURAL APPROACH TO CHEMISTRY

4 The beginning of atomic theory Democritus ( BC): the beginning of atomic theory John Dalton ( ) - first modern atomic theory Cathode rays J.J. Thomson ( ) - the discovery of the electron Democritus ( BC) was an ancient Greek philosopher who proposed the idea that you can t divide something in half forever. He argued that eventually you must reach the smallest indivisible part. He called this smallest piece of matter an atom. Democritus correctly deduced the existence of atoms, but he could go no further in discovering any of their properties. For the next 2,000 years atomism was an interesting idea, but there was no good scientific evidence to support its truth or falsehood. In 1808, John Dalton, an English school teacher, put together many ideas in his four postulates of the atomic theory. Dalton s four postulates were a brilliant synthesis based on what little evidence there was at that time. They remain true today. 1. All elements are made of tiny indivisible particles called atoms. 2. All atoms of the same element are alike but different from atoms of every other element. 3. Chemical reactions rearrange atoms but do not create, destroy, or convert atoms from one element to another. 4. Compounds are made from combining atoms in simple whole number ratios. In the mid 1800s it was discovered that high voltage made a glow in a sealed glass tube from which most of the air had been pumped out. In 1870, William Crookes invented a tube in which virtually all of the gas was removed. Now, the glow inside the tube disappeared, but the glass at one end of the tube was glowing. Some kind of invisible ray was being emitted from the cathode end of the tube and striking the glass at the other end. These rays were called cathode rays, and a great debate occurred over their nature. Were they another kind of light? Were they a stream of particles? Thomson High voltage electricity creating cathode rays inside a Crookes tube Cathode rays deflected away from negative plate and toward positive plate In 1897, J. J. Thomson was finally able to resolve the debate. His experiments showed that cathode rays were deflected toward a positively charged plate and away from a negatively charged plate. Thomson deduced that cathode rays must be negative. He also found that they could be deflected by magnetic fields. No ordinary ray of light would behave this way. He tried using different metals or starting with the tube filled with different gases. None of those factors mattered. He always got the same cathode rays, and they always were deflected in the same way. A NATURAL APPROACH TO CHEMISTRY 135

5 Section 5.1 The Atom Has a Structure The discovery of the nucleus Cathode rays are electrons The atom must have a structure inside Ernest Rutherford: the gold foil experiment Thomson s discovery stunned the scientific world. Cathode rays were made of a stream of particles 2,000 times lighter than the lightest known atom (H)! How could there be a particle smaller than an atom? Because Thomson always got the same cathode rays regardless of which metals he used for the electrodes in his Crookes tube, he named the new particle an electron, and he proposed that electrons were inside all atoms. If electrons were inside atoms, then atoms could not be the most elementary particles of matter. Furthermore, electrons were negative and atoms were neutral, so there had to also be something positive inside atoms to cancel out the charge of the electrons. The search was on to discover the structure inside the atom. In 1910, Ernest Rutherford designed and carried out the crucial experiments that provided the answer. Marie and Pierre Curie had discovered that uranium was radioactive and released energetic alpha particles at high velocity. Alpha particles were positively charged and had a mass about 8,000 times that of an electron. Rutherford devised an experiment to shoot alpha particles through a thin gold foil and observe what happened as they collided with gold atoms. He expected Rutherford most of the alpha particles to be deflected a little as they crashed through the gold atoms. Rutherford s discovery of the atomic nucleus Rutherford s results were completely unexpected. Although most of the alpha particles went straight through the gold foil with no deflection at all and a few were deflected slightly off their original path, about 1 of every 20,000 reversed direction, bouncing back from the foil! Rutherford determined that atoms have nearly all their mass concentrated in a very tiny, very dense, positively charged nucleus. This was his reasoning: 1. The deflected alpha particles were repelled by something with a similar charge, so the nucleus must be positively charged. 2. Very few alpha particles were deflected, so it must be rare for one to come close to a nucleus. This meant the nucleus had to be tiny, about 1/10,000 the diameter of the atom. 3. The alpha particles were travelling at such high velocity that only something with significant mass could deflect them. 136 A NATURAL APPROACH TO CHEMISTRY

6 The interior of an atom The big ideas The nucleus The three most important ideas in this chapter are these: 1. Atoms are made of neutrons, protons, and electrons. The number of protons and electrons is always equal. 2. The number of protons determines the element. All atoms of hydrogen have one proton, all atoms of helium have two, lithium has three, and so on. 3. Most of the properties of atoms are determined by their electrons. Atoms interact with each other via their electrons. Of course, there are many interesting details! Electrons are quirky particles and they behave in very strange ways, but that is what makes chemistry so interesting. Neutrons and protons make up the nucleus. The nucleus is at the center of the atom. There are no electrons in the nucleus, only protons and neutrons. The nucleus is extremely small, even compared to an atom. If the atom were the size of your classroom, the nucleus would be the size of a single grain of sand in the center of the room! Particle Mass (kg) Charge (C) Relative mass Relative charge Proton , Neutron ,837 0 Electron Mass of protons, neutrons, and electrons Mass and the nucleus Look at the masses of the three particles. The masses are very small. The mass of a single electron in kilograms has 30 zeros between the decimal point and the first nonzero digit. More important are the relative masses. The proton and neutron are much more massive than the electron. The protons and neutrons have essentially all the mass of the atom. Most of an atom s mass is concentrated in the nucleus. The number of electrons and protons is the same, but electrons contribute very little mass. For example, a carbon atom has six protons, six electrons and six neutrons. Of the carbon atom s mass, 99.97% is in the nucleus and only 0.03% is electrons. nucleus: the tiny dense core of an atom that contains all the protons and neutrons, measuring about 1/10,000 the diameter of the atom. A NATURAL APPROACH TO CHEMISTRY 137

7 Section 5.1 The Atom Has a Structure Atomic number and atomic mass The atomic number Neutrons act like glue Isotopes The atomic number of each element is the number of protons in its nucleus. All atoms of the same element have the same number of protons in the nucleus. For example, every atom of helium has two protons in its nucleus. Every atom of carbon has six protons in its nucleus. The periodic table arranges the elements in increasing atomic number. Atomic number one is hydrogen with one proton. Atomic number 92 is uranium with 92 protons. All protons have positive electric charge. That means they repel each other. So how does the nucleus stay together? The answer is neutrons. Think about neutrons as glue particles that help the nucleus stay together. Every element heavier than helium has at least as many neutrons as protons in its nucleus. All atoms of the same element have the same number of protons in the nucleus. However, they do not necessarily have the same number of neutrons. Three different isotopes of carbon are found on Earth. Isotopes are atoms of the same element that have different numbers of neutrons in the nucleus. The mass number Atomic mass unit (amu) The most common isotope of carbon is carbon-12, written as 12 C. A nucleus of 12 C contains six protons (making it carbon) and six neutrons. The superscript 12 before the symbol C tells you the mass number of the nucleus. The mass number is the total number of protons plus neutrons. The two other isotopes of carbon are carbon-13 ( 13 C) and carbon-14 ( 14 C). These isotopes are carbon because they have six protons in the nucleus, but 13 C has seven neutrons and 14 C has eight neutrons. Because the mass of a proton is tiny by normal standards, scientists use atomic mass units (amu). One amu is kg, or slightly less than the mass of a proton. atomic number: the number of protons in the nucleus, unique to each element. isotopes: atoms or elements that have the same number of protons in the nucleus, but different number of neutrons. mass number: the total number of protons and neutrons in a nucleus. atomic mass unit (amu): a mass unit equivalent to kg. 138 A NATURAL APPROACH TO CHEMISTRY

8 Average atomic mass The average atomic mass may not be a whole number Elements in nature contain a mix of isotopes Let s examine the element lithium. Lithium has two isotopes that are found in nature. Lithium-6 has three protons and three neutrons. Lithium-7 has three protons and four neutrons. The periodic table lists the atomic mass of lithium as How is that possible? Do lithium atoms have 0.94 neutrons? It is not possible to split a proton or a neutron in ordinary matter. Lithium atoms have either six or seven whole neutrons. The reason the atomic mass is 6.94 is that, on average, 94 out of 100 atoms of lithium are 7 Li and 6 out of 100 are 6 Li. The average atomic mass is 6.94 because of the mixture of isotopes. No lithium atom has a mass of 6.94 amu. Radioactivity Not all isotopes exist in nature. For example, suppose scientists create a nucleus with three protons and five neutrons. This would have an atomic number of 3, making it lithium. The mass number would be 8. Lithium-8 is unstable and quickly decays into two atoms of helium instead! When an atomic nucleus decays or gives off energy, the process is called radioactivity. It means that the nucleus undergoes a spontaneous change called decay, often turning one element into a different element. How many neutrons are in the nucleus of neon-21 ( 21 Ne)? Asked: Number of neutrons Given: Mass number (21) and element (neon) Relationships: The mass number is the number of protons plus neutrons, number of protons = atomic number Solve: From the periodic table we find the atomic number of neon is 10. So, there are 10 protons in the nucleus: = 11 neutrons. Answer: There are 11 neutrons in a nucleus of neon-21. radioactivity: a process by which the nucleus of an atom spontaneously changes itself by emitting particles or energy. decay: the process during which a nucleus undergoes spontaneous change. A NATURAL APPROACH TO CHEMISTRY 139

9 Section 5.1 The Atom Has a Structure The electron cloud The electron cloud Drawing electrons Electron orbit Electrons determine the size of atoms Compared to protons and neutrons, electrons are much lighter. This has the effect of making the electron much faster, with a much wider range than either protons or neutrons. Because electrons are so fast and light, scientists call the region outside the nucleus the electron cloud. Think about a swarm of bees buzzing in a cloud around a beehive. It is not easy to precisely locate any one bee, but you can easily see that, on average, the bees are confined to a cloud of a certain size around the hive. On average, electrons are confined to a similar cloud around the nucleus. Electrons are not really particles in the same way a dust particle is a particle. Although electrons have a definite mass, they do not have a definite size. The matter in an electron spreads out over a relatively large volume within an atom. In early drawings of atoms, scientists represented electrons like tiny planets in an orbit around the nucleus of the atom. Today we draw atoms with a tiny hard nucleus surrounded by a wispy electron cloud. The size of an atom is really the size of its electron cloud. When we talk about the size of atoms, what we really mean is how close atoms get to each other. Unless the atoms are chemically bonded together, the electron cloud of one atom does not normally overlap the electron cloud of another. Except for mass, virtually every property of atoms is determined by electrons, including size and chemical bonding The electrons determine virtually everything about how one atom interacts with another. For this reason, most of chemistry will be concerned with electrons and their unusual organization within atoms. The nucleus is buried deep inside, contributing mass, but not much else, as far as chemistry is concerned. orbit: the imaginary path of an electron around the nucleus of an atom. 140 A NATURAL APPROACH TO CHEMISTRY

10 Electric charge Comparing charge and mass Positive and negative The charges of the three particles Charge is a difficult idea to grasp, so let s start by comparing mass and gravity with electric charge. Mass is a fundamental property of matter. Any two objects that have mass attract each other through a force called gravity. Mass is the property that determines an object s response to the force of gravity. The more mass there is, the stronger the force of gravity. Electric charge is another fundamental property of matter. However, unlike mass, there are two kinds of charge: positive and negative. Like gravity, there is a force that acts on electric charge called the electromagnetic force. Unlike gravity, however, the electromagnetic force can attract or repel. The electric charge on a proton is what scientists define to be positive. The charge on an electron is defined as negative. Neutrons are neutral and have zero charge. That means that two protons repel each other, and so do two electrons. Protons and electrons attract each other. Neutrons feel no electromagnetic forces from either protons or electrons. A complete atom has a charge of zero because the charge of the proton is exactly equal but opposite to the charge of the electron Complete atoms have zero net charge The charges on the electron and the proton are exactly equal and opposite. If you put a proton and an electron together, the total effective charge is zero. For this reason, the charge on a complete atom is always zero because a complete atom contains the same number of protons as electrons. For example, the positive charge from six protons in a carbon nucleus is exactly cancelled by the six electrons in the electron cloud. A NATURAL APPROACH TO CHEMISTRY 141

11 Section 5.1 The Atom Has a Structure Forces in the atom Why an atom stays together Forces in the nucleus Electrons are both attracted and repelled The attractive electromagnetic force between protons in the nucleus and electrons is what holds an atom together. The electromagnetic force between electrons is also what creates chemical bonds between atoms, as we shall see. In fact, almost all of the chemistry we learn is driven by the electromagnetic force. There is a force in the nucleus that is even stronger than the electromagnetic force, but it does not affect chemistry directly. It is called the strong nuclear force and it attracts protons to protons, neutrons to neutrons, and protons and neutrons to each other. If there are enough neutrons in the nucleus, the attractive strong nuclear force can overcome the repulsive electromagnetic force between protons. This is the reason most elements have equal numbers or slightly more neutrons than protons in the nucleus. Let s think about the electron cloud in an atom like carbon. Electrons have energy, so they cannot just fall in to the nucleus, but they must be constantly in motion. Each of carbon s six electrons is attracted to the nucleus, but each is also repelled by all the other electrons! The combination of energy with attraction and repulsion is one reason behind the peculiar behavior of electrons in an atom. Electrons are responsible for the chemical bonds between atoms. When a water molecule forms, the oxygen atom shares electrons with two hydrogen atoms. Each shared electron is a chemical bond. The molecule has its bent shape because eight of the ten electrons in a water molecule repel each other in four pairs. Two pairs are shared with hydrogen atoms and two pairs are not shared. 142 A NATURAL APPROACH TO CHEMISTRY

12 Ions All matter contains charge Neutral matter has equal positive and negative charge Ions Ionic compounds The fact that everything is made from atoms and atoms are made from electrically charged particles means that everything, including you, is just a big bundle of electric charge. This fact becomes more obvious in the winter when you scuff your feet across a carpet and get shocked by touching a metal doorknob. Static electricity and lightning are examples of how we are made of, and are surrounded by, electrically charged particles. If the numbers of electrons and protons in an atom are not equal, the atom will have an overall charge. Let s consider sodium as an example. Sodium has an atomic number of 11, so that means all sodium atoms have 11 protons. Each proton has a positive charge of +1. If these same atoms have 11 electrons, each with a 1 charge, then the 11 charge from the electrons exactly cancels out the +11 charge from the protons, and the atom is neutral. However, if there were only 10 electrons, then the total charge from the electrons would be 10 while the charge from the protons would be +11. That means there is one proton that is not being cancelled out by an electron. This gives the atom an overall charge of +1. Charged atoms are called ions. Whenever the numbers of protons and electrons are not equal, an overall positive or negative charge will occur, and an ion will be formed. Ions can be single atoms or small molecules with an overall charge. Positive and negative ions attract each other, just as protons and electrons do. The ionic compounds we introduced in Chapter 4 are examples. Sodium ions (Na + ) have one less electron and are attracted to chloride ions (Cl ), which have one extra electron. The overall compound, sodium chloride (NaCl), is electrically neutral because there are equal numbers of sodium and chloride ions. ion: an atom or a small molecule with an overall positive or negative charge as a result of an imbalance of protons and electrons. A NATURAL APPROACH TO CHEMISTRY 143

13 Section 5.2 The Quantum Atom 5.2 The Quantum Atom Why is it that the noble gases do not react? Elements just before or just after the noble gases are very reactive Some findings of quantum theory How do the chemical properties of the elements arise from the structure of atoms? We have seen that electrons are the components in atoms that are near the surface and interact with other atoms. Why is it that the noble gases (helium, neon, argon, and krypton) do not react with other elements or among themselves? Note that these elements have 2, 10, 18, and 36 electrons, respectively. The elements hydrogen, fluorine, chlorine and bromine have 1, 9, 17, and 35 electrons. They have one fewer electron than their respective noble gas group. These elements tend to form negative ions; they accept electrons from other atoms. The elements with one more electron than the noble gas group are lithium, sodium, potassium and rubidium with 3, 11, 19 and 37 electrons, respectively. These elements tend to form positive ions; they donate electrons to other atoms. The basic understanding of the electronic structure in the atom started around 1920 with a new theory called quantum theory. Championed by Niels Bohr, quantum theory provided a completely new way to look at things on the scale of atoms. Quantum theory finally gave us a way to understand why and how the elements make the bonds that they do. Quantum theory makes the following statements about matter and energy on the scale of atoms, and particularly about electrons in atoms. 1. On the scale of atoms, a particle of matter such as an electron is not solid but is smeared out into a wave over a region of space. 2. When electrons are confined in an atom, their wave properties force them into a pattern that minimizes their energy. 3. Each unique place in the pattern is called a quantum state, and each can hold one single electron. 4. Electrons are always found to be in one quantum state or another and are not found between states. 5. No two electrons can be in the same quantum state at the same time. Don t worry if these statements seem quite strange. Quantum theory is accurate, but not intuitive. quantum theory: a theory of physics and chemistry that accurately describes the universe on very small scales, such as the inside of an atom. quantum state: a specific combination of values of variables such as energy and position that is allowed by quantum theory. 144 A NATURAL APPROACH TO CHEMISTRY

14 Waves and particles Our intuition is often wrong in the quantum world The most basic idea of quantum theory is that our intuitive notion of a particle cannot be applied to the tiny world of the atom. To most of us, a particle is a tiny speck of matter that has a definite size, mass, and position, like a tiny ball. A ball-like particle can be either here or there, but it cannot be in two places at the same time. The quantum theory tells us this intuition is wrong when things are as small as an atom. In the quantum world, a particle is not like a tiny ball at all. Instead, the mass, size, and even the location is spread out into a wave. Heisenberg s uncertainty principle Frequency The fact that particles are smeared out into waves can be explained by Heisenberg s uncertainty principle. In 1927 Werner Heisenberg proposed that it is not possible to know certain parameters of a particle, such as its position and velocity, accurately at quantum scales. The better you determine one by experiment, the more you perturb the other and thereby increase its uncertainty. The quantum world is a world of statistics and probability, instead of exact certainty. The oscillations of a wave have frequency and wavelength. The frequency is the number of times per unit of time that any point on the wave goes back and forth. A light wave has a very high frequency, times per second or more! A water wave might oscillate one or two times per second. Wavelength When a wave moves through space, the successive peaks (or valleys) are separated by a distance called the wavelength. The wavelength is the same from one peak to the next. Like the frequency, it is a characteristic of a particular wave. The wavelength of light is very small, only 10 8 m or so. frequency: the rate at which an oscillation repeats; one hertz (Hz) is a frequency of one oscillation per second. wavelength: the distance (separation) between any two successive peaks (or valleys) of a wave. A NATURAL APPROACH TO CHEMISTRY 145

15 Section 5.2 The Quantum Atom Planck s constant Wave energy increases with frequency A photon is the smallest quantity of light energy Planck s constant Waves in water carry energy, as anyone who has seen waves from a storm crashing on a beach can vividly remember. The same is true of light waves and particle waves, such as electrons. You might intuitively think that the faster something oscillates, the more energy it has. You would be right! The energy carried by a wave is proportional to how fast it oscillates, or its frequency. High frequency means faster oscillation and more energy. Before quantum theory, the ideas of particle and wave were distinct. Light was a wave, and an electron was a particle. Today we know that an electron is also a matter wave, and light waves come in tiny bundles of energy called photons. A photon is like a particle because it has a definite energy and moves with a certain speed and direction. However, a photon has no mass, just pure energy. You don t see light as a stream of photons for the same reason you don t see individual atoms. A small 3 W flashlight beam emits photons per second! The scale at which the granular nature of matter and energy becomes evident is determined by Planck s constant. Planck s constant has the symbol h and a value of joule-seconds (J s). The energy and wavelength of both electrons and photons are calculated from Planck s constant. The connection among atoms, light, and electrons In his 1924 Ph.D. thesis, Louis de Broglie proposed that the wavelength of a particle is inversely proportional to the square root of its mass and energy. The de Broglie wavelength of an electron is very small. If the electron had the same energy as green light ( J), its de Broglie wavelength would be m. This is the same size as an atom, which explains the close connection between light and the behavior of electrons in atoms. Planck s constant (h): the scale of energy at which quantum effects must be considered, equal to joule-seconds (J s). photon: the smallest possible quantity (or quanta) of light. 146 A NATURAL APPROACH TO CHEMISTRY

16 Electrons in the quantum atom The wavelength of an electron in an atom Waves versus balls Most of the properties of the elements are caused by what happens to the wavelength of an electron when it is bound up inside an atom. To help understand this, consider a ball bouncing around in a box. At any instant, there is only one ball at one particular place in the box. When the ball hits the walls of the box, it bounces off it. A wave reflects when it hits a wall, just like a ball in a box. However, waves are very different from balls. A ball is only in one place, but a wave can occupy all the space in the box. So can its reflection! One ball plus one ball is two balls, but one wave plus another wave can add up to zero. If one wave is up when the other is down, then they cancel each other out! When averaged over time, the only waves that survive in a box are the ones whose wavelength fits the size of the box. All the others interfere with their own reflections and average out to zero. The atom is a box for electrons The key idea of the quantum atom Now replace the box with an atom and let the wave be an electron. Electrons are boxed inside atoms by the attraction from the positive nucleus. The walls of the box are soft to an electron because the electron never hits a hard surface, but it needs more and more energy to get farther away from the nucleus. Given a limited amount of energy, an electron is confined to be within a certain distance from the nucleus. This confinement acts just like a soft-walled box. Here is the main idea of the quantum atom. The wavelength of the electron must be a multiple of the size of the atom. If it is not, then the electron wave cancels with its own reflections over time. The diagram shows three allowed electron waves and two that are not allowed. To be stable inside an atom, an electron must have one of the allowed wavelengths that exactly fits the size of the atom. The elements differ because the size of the atom depends on the strength of the attraction from the nucleus, which depends on the atomic number. A NATURAL APPROACH TO CHEMISTRY 147

17 Section 5.2 The Quantum Atom Quantum states Consequences of restricting the electron wavelength What does it mean to say that an electron can only have a wavelength that matches the size of an atom? The most important consequence comes from the relationship between wavelength and energy. If you know the energy of an electron, then you also know its wavelength. Conversely, if the wavelength of the electron is fixed, you also fix its energy as well. Electrons inside atoms can only have specific energies that match the wavelengths they are allowed to have. Quantization Real quantum states Multiple states can have the same wavelength The restriction of energies to specific discrete values is called quantization. This is one of the most important consequences of quantum theory. An electron trapped inside an atom cannot have any value of energy. The electron can have only those specific values of energy that correspond to the allowed wavelengths. We now have a way to define a quantum state. A quantum state is one of the allowed wavelengths in an atom. Because of the connection between wavelength and energy, each quantum state has a specific energy. This is the key idea of the quantum atom. The details of real quantum states inside an atom are complicated for these reasons: Atoms are three dimensional, not simple boxes. Besides charge and mass, electrons have a purely quantum property called spin. Electrons repel each other, so in atoms with more than one electron, the size and shape of the box depend on both the nucleus and the other electrons in the atom. For example, because the electron wave can be aligned along any of the three coordinate axes (x, y, or z), there are three different quantum states that have the same wavelength, and therefore the same energy. This is a threedimensional effect. 148 A NATURAL APPROACH TO CHEMISTRY

18 Orbitals The origin of s, p, d, and f Orbitals The allowed quantum states are grouped in a peculiar, yet historically interesting way. When scientists first started using spectroscopy to explore the elements, they noticed that the spectra of the metals (Li, Na, and K) had four characteristic groups of spectral lines. They named the groups sharp, principal, diffuse and fundamental, but they had no real idea what caused the differences among the four groups. Today we know each group is associated with a quantum state in a particular shape. In deference to history, the four types of shapes are known by the letters s, p, d, and f. Orbitals are groups of quantum states that have similar shapes in space. To understand what these shapes look like, consider the single electron in a hydrogen atom. With no other electrons to repel it, this electron has an equal chance to be at any angular position around the nucleus. Hydrogen s lone electron is in an s orbital. The s orbitals are spherically symmetric, and each one can hold two electrons. Why some orbitals have strange shapes Orbitals create 3-dimensional molecules Carbon has six electrons. With this many electrons, repulsion between electrons changes the shape of the electron cloud. The p orbitals are shaped like dumbbells along each of the three coordinate axes. The three p orbitals can hold six electrons all together. The d orbitals are more elaborately shaped and can hold a total of 10 electrons. The three-dimensional shape of the orbitals represents the real three-dimensional shape of the electron cloud. The orbital shapes are directly responsible for the three-dimensional shapes of molecules. Methane (CH 4 ) is tetrahedral because of the way the s and p orbitals form chemical bonds between carbon and hydrogen. orbital: group of quantum states that have similar spatial shapes, labeled s, p, d, and f. A NATURAL APPROACH TO CHEMISTRY 149

19 Section 5.2 The Quantum Atom Energy levels The quantum states are grouped into energy levels Since several quantum states have the same energy, the states are grouped into energy levels. The diagram below shows how the quantum states are arranged in the first five energy levels. There is an even number of quantum states because they occur in spin-up/ spin-down pairs. The first energy level has two quantum states. The second and third energy levels have eight quantum states. The fourth and fifth levels have 18 states each. The Pauli exclusion principle Hund s rule Electrons confined to the same atom obey a quantum rule called the Pauli exclusion principle. The Pauli exclusion principle states that two electrons in the same atom may never be in the same quantum state. Electrons fill quantum states from the lowest energy to the highest. Lithium, with three electrons, cannot have all three in the first energy level because there are only two quantum states (spin-up and spin-down). The third electron has to go into the second energy level. Electron-electron repulsion forces affect the way electrons are distributed in orbitals. According to Hund s rule, electrons with the same-spin must occupy a different equal-energy orbital, before additional electrons with opposite spins can occupy the same orbitals. Here we see how the electrons of N and O are distributed in orbitals. energy level: the set of quantum states for an electron in an atom that have approximately the same energy. Pauli exclusion principle: principle that states that two electrons in the same atom may never be in the same quantum state. 150 A NATURAL APPROACH TO CHEMISTRY

20 The periodic table Rows correspond to energy levels The second row The third row Energy levels correspond to bonding properties The rows of the periodic table correspond directly to the energy levels for electrons. The first energy level has two quantum states. Atomic hydrogen (H) has one electron, and atomic helium (He) has two electrons. These two elements are the only ones in the top row of the periodic table because there are only two quantum states in the first energy level. The next element, lithium (Li), has three electrons. Lithium begins the second row because the third electron goes into the second energy level. The second energy level has eight quantum states and there are eight elements in the second row of the periodic table, ending with neon. Neon (Ne) has 10 electrons, which exactly fill all the quantum states in the first and second levels. Sodium (Na) has 11 electrons, and it starts the third row because the 11th electron goes into the third energy level. The third row ends with the noble gas, argon, which has 18 electrons. Eighteen electrons completely fill the third energy level. If you compare the energy level diagram with the periodic table, you find that all the noble gases have completely filled energy levels. All the elements that tend to form negative ions (F, Cl, and Br) have one electron less than a full energy level. All the alkali metals that tend to form positive ions (Li, Na, and K) have one electron more than a full energy level. This is a strong clue that the energy levels are crucial to the chemical properties of the elements. A NATURAL APPROACH TO CHEMISTRY 151

21 Section 5.3 Electron Configurations 5.3 Electron Configurations Organization of the energy levels All the elements share a common organization for how the quantum states are grouped into energy levels. Because each element has a different nuclear charge, the actual energies of each level are unique to each element. However, the overall pattern is the same for all the elements and determines the organization of the periodic table. Electrons fill up lowest energy orbitals first Every proton in the nucleus of an atom will attract one electron. Each of those electrons must exist in one of the quantum states in the diagram. Like a ball rolling downhill, each electron settles into the lowest unoccupied quantum state. Electrons settle into the lowest unfilled quantum states How the first few elements fill the energy levels Beginning the second row Ending the second row The first (and lowest) energy level holds two electrons. Hydrogen has one electron, so it belongs in the first energy level. Helium has two electrons, and they completely fill the first energy level. Lithium has three electrons. Two of lithium s electrons go into the first energy level. The Pauli exclusion principle forbids lithium s third electron from occupying either of the occupied states on the first energy level. The third one has to go into the second energy level. Fluorine has nine electrons. They fill all but the last quantum state on the second energy level. Neon has 10 electrons, which completely fill the first and second energy levels. 152 A NATURAL APPROACH TO CHEMISTRY

22 Electron configuration The principal quantum number The principal quantum number (or quantum number) defines certain properties of the quantum states. The diagram below shows the first four quantum numbers and the quantum states associated with each. The quantum states are further divided into the orbital types s, p, d, and f. The key at the right shows how the quantum states fall into energy levels. Note that the energy level is not the same as the quantum number! Electron configuration The electron configuration is a quick way to describe how electrons in an atom are distributed among the orbitals. The first number is the principal quantum number. The letter identifies the orbital, and the superscript is the number of electrons in that orbital. Quantum number 1 contains only a single s orbital which can hold two electrons. Quantum number 2 can hold up to two s electrons and six p electrons for a total of eight. Element Number of electrons Electron Configuration Description of electron locations Hydrogen 1 1s1 One electron at the 1s level. Helium 2 1s2 Two electrons at the 1s level Lithium 3 1s 2 2s1 Two electrons at the 1s level and one electron Beryllium 4 1s 2 2s Boron 5 1s 2 2s 2 2p at the 2s level 2 Two electrons at the 1s level and two electrons at the 2s level 1 Two electrons at the 1s level, two electrons at the 2s level, and one electron at the 2p level electron configuration: a description of which orbitals contain electrons for a particular atom. principal quantum number: a number that specifies the quantum state and is related to the energy level of the electron. A NATURAL APPROACH TO CHEMISTRY 153

23 Section 5.3 Electron Configurations Finding the electron configuration The table is arranged according to the structure of the atoms and orbitals Here is the complete list of orbitals and the filling order for all of the currently discovered elements: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p This order tells a chemist exactly how the electrons are structured in an atom. It may seem somewhat random, but using the periodic table as your guide, there is a way to remember the orbital filling order. This is because the structure of the periodic table is actually based on the structure of the atoms. By understanding the connection between the orbitals and the periodic table, we learn about both the structure of the atom and its connection to chemical and physical properties. First, let s look at how the periodic table would be laid out if we didn t place the rare earth elements below the table. Finding the electron configurations To find an electron configuration, start with the number of electrons (the atomic number). Use the chart below to find the largest number of electrons that is still less than the configuration you are trying to find. Subtract that number from the number of electrons you have, and the remainder is the superscript on the unfilled orbital. For noble gases, the chart will give you the exact electron configuration. Write the electron configuration for silicon (atomic number 14). Solve: There are 14 electrons. The chart shows that 12 electrons fill up to 3s 2. Therefore, the remaining 2 electrons must go into a 3p orbital, making the electron configuration 1s 2 2s 2 2p 6 3s 2 3p A NATURAL APPROACH TO CHEMISTRY

24 5.4 Light and Spectroscopy Visible light The spectrum of visible light Energy and color Light is a form of electromagnetic energy that comes mainly from electrons in atoms. If you are reading this book under a fluorescent light, then you are seeing the energy levels in the atom right now! In fact, we see when the light that enters our eyes is absorbed by electrons in molecules at the back of our eyes. When these molecules absorb light, the cells that contain them send electrical signals to your brain and you see. The different colors of light come from the energies of different photons. Red is the lowest energy photon that humans can see. The highest visible energy is violet. All the colors between red and violet form the visible spectrum. A spectrum is a representation of the different energies present in light. Since energy depends on frequency and wavelength, the colors of light also depend on frequency and wavelength. The spectrum often specifies wavelength on the x axis. One nanometer (nm) is 10 9 meters. White light is a mixture of colors The white light from a lamp is actually a mixture of many different colors and energies. White light from the Sun is not truly white. You can split white light into a spectrum of colors by using a prism. A device that splits light into its spectrum is called a spectrometer. These instruments provided one of the first and best clues to unraveling the mystery of the structure of the atom. spectrum: a representation of a sample of light into its component energies or colors, in the form of a picture, a graph, or a table of data. spectrometer: a device that measures the spectrum of light. A NATURAL APPROACH TO CHEMISTRY 155

25 Section 5.4 Light and Spectroscopy The electromagnetic spectrum There are many types of light Energy and frequency The light that we can see (visible light) is really only a small subset of a much larger spectrum of electromagnetic energy. The full electromagnetic spectrum includes lower energies (radio and microwaves) and higher energies (ultraviolet and x rays). Many scientists use the word light loosely to mean the entire electromagnetic spectrum. This includes radio waves, microwaves, x rays, and even gamma rays. Radio waves Microwaves Infrared Visible light Ultraviolet X-rays Gamma rays The energy of a photon depends on its frequency and wavelength according to the Planck relationship E = hν. The Greek symbol ν (pronounced nu ) is used to represent frequency in hertz (Hz). Because photon energies tend to be small (10 18 J), scientists define the electron volt (ev) as J. Electron volts are also about the size of energy changes in an atom. For example, the difference between the second and third energy levels in hydrogen is 1.89 ev. electromagnetic spectrum: the complete range of electromagnetic waves, including visible light. electron volt: a unit of energy equal to J. 156 A NATURAL APPROACH TO CHEMISTRY

26 The speed of light The speed of a wave is its frequency times its wavelength The speed of light c is a constant Photons and other waves move one wavelength with each oscillation. Since the number of oscillations per second is the frequency, and one wavelength is the distance the wave advances, the speed of a wave is its frequency multiplied by its wavelength. This relation-ship allows us to calculate the frequency if we know the wavelength and vice versa. Photons move very fast at a speed of m/s, or 186,000 miles per second! This is the ultimate speed limit in our universe. Nothing can move faster than light. The speed of light is so important it has its own special symbol, a lowercase letter c. The speed of light in a vacuum is a constant. That means it is the same for all frequencies and wavelengths. In chemistry, the speed of light is very useful for converting between frequency and wavelength. If you know the wavelength of light, then you can calculate its frequency from the speed of light. The wavelength of red laser light is 652 nm. What is its frequency? How much energy does a photon of this light have in electron volts? Asked: Frequency and energy Given: λ = m Relationships: c = λν, E = hν Solve: c m/s c = λν therefore ν = -- = λ = = /s s m E = hν = ( ev s) ( /s) = 1.9 ev Answer: Since 1 Hz=1/s, the frequency is Hz and the energy is 1.9 ev. speed of light (c): a constant speed at which all electromagnetic radiation travels through a vacuum, including visible light; the speed of light in a vacuum is 299,792,458 m/s or approximately m/s. A NATURAL APPROACH TO CHEMISTRY 157

27 Section 5.4 Light and Spectroscopy Interactions between light and matter Experimenting with excited electrons Light from an incandescent light bulb shows a continuous spectrum of colors. This tells us that the atoms that produced the light can absorb and release any amount of energy. Light from pure hydrogen does something completely different. Instead of a continuous rainbow, we see a few very specific colors and nothing but darkness in between. The spectrum tells us there are energy levels The spectrum from hydrogen tells us that hydrogen atoms can only absorb and emit light of very specific energies. It is like viewing the inner workings of a hydrogen atom. The fact that the spectrum shows discrete colors tells us that electrons in the hydrogen atom can only have discrete energies. Interactions between matter and light As a wave of light moves through matter, any electrons inside atoms oscillate in response to the wave. On the atomic scale, two kinds of interactions can occur: absorption or nothing. If a photon is absorbed, another photon with the same energy may be reemitted. The scattering of light is actually a two-step process of absorption and reemission. Electrons can get excited Which of the two interactions occurs depends on how the energy of the photon compares to the energy levels in the atom. If the photon energy matches a difference in the atom s energy levels, the photon may be absorbed. If not, the photon typically passes right through. If a photon passes through, we say that atom is transparent to that light. 158 A NATURAL APPROACH TO CHEMISTRY

28 Spectroscopy Different elements have different energy levels Quantum theory tells us that any electron confined to a small space, like an atom, results in energy levels. The specific energy levels depend on the strength of the force between the nucleus and the electrons. This depends on the number of protons in the nucleus, and on the number of other electrons in the atom that might be shielding the attractive force from the nucleus. For this reason, the energy levels are different and unique for each element. Each element has unique energy levels Every element and compound has a unique spectrum Emission and absorption spectra Spectroscopy Atoms both emit and absorb light at the energies corresponding to their energy levels. If white light is passed through a sample of matter, some light will be absorbed by the atoms in the sample. Not all light will be absorbed. Only colors corresponding to specific energy levels are strongly absorbed, resulting in dark lines in a continuous spectrum. This is called an absorption spectrum. Can you see the similarities between the absorption spectrum and emission spectrum? If the energy levels of electrons are different for different elements, then the light emitted from each element must also be unique. In fact, each element emits a characteristic spectrum. Chemists refer to the emission spectrum as the fingerprint of an element. Chemistry laboratories identify elements and compounds by their spectra. Using spectra to analyze substances is called spectroscopy. Spectroscopy can tell you what elements produced the light being observed. Spectroscopy is a tool to find out what distant stars are made of, identifying unknown compounds at a crime scene, and even discovering forgeries. Right now, satellites are searching for water on Mars and astronomers are studying the composition of distant stars and galaxies by using spectroscopy. Even the makeup of our own atmosphere and global scale environmental research is done via satellites using spectroscopy. spectroscopy: the science of analyzing matter using electromagnetic emission or absorption spectra. A NATURAL APPROACH TO CHEMISTRY 159