Early Atomic Theories and the Origins of Quantum Theory (PDF)

3.1 early atomic theories and the origins of Quantum theory What is matter made of? People have wondered about the answer to this question for...

3.1 early atomic theories and the origins of Quantum theory What is matter made of? People have wondered about the answer to this question for thousands of years. Around 460 BCE, the Greek philosopher Democritus specu- lated that matter is composed of elementary particles called atoms. However, it was not until thousands of years later, after collecting a lot of evidence and developing very complex technology, that scientists were able to state with some certainty that matter is composed of atoms. Recently, something very exciting happened. For the first time, scientists are able to “see” individual atoms through a special microscope, called a scanning tunnelling microscope (STM). The STM passes an extremely fine, electrically charged needle over the surface of an object. Changes in the current through the needle indicate changes in the distance between the surface and the needle. These changes indi- Figure 1 STM image of atoms on the cate the “bumps” of atoms and the “valleys” between them. An STM image of the surface surface of graphite (a form of carbon) of graphite shows an orderly arrangement of carbon atoms (Figure 1). WEB LINK Early Developments in Atomic Structure To understand chemistry, it helps to be able to visualize matter at the atomic level. Before the invention of the STM, scientists speculated that matter consisted of individual atoms. When Democritus first suggested the existence of atoms, his ideas were based on intu- ition and reason, not experimentation. For the following 20 centuries, no convincing experimental evidence was available to support the existence of atoms. As new tools to experiment with matter were developed, our understanding of the structure of matter grew. In the late 1700s, French chemist Antoine Lavoisier and others used experimenta- tion to gather the first accurate quantitative measurements of chemical reactions. These measurements were made possible by the invention of instruments that could precisely measure mass and volume. Based on the results of these experiments, John Dalton (1766–1844) proposed the first modern atomic theory: elements consist of atoms, which cannot be created, destroyed, or divided, and atoms of the same element have identical size, mass, and other properties. Dalton’s theory, although simple, has stood the test of time extremely well. In the past 200 years, a great deal of experimental evidence has accu- mulated to support atomic theory. Discovering the Electron Figure 2 The English physicist The experiments by the English physicist J.J. Thomson (Figure 2) were the first to J.J. Thomson (1856–1940) studied provide evidence for the existence of the electron, a negatively charged subatomic electrical discharges in partially evacuated particle. In his experiments, Thomson applied high voltage to a partially evacuated tubes called cathode ray tubes. tube with a metal electrode at each end. He observed that a ray was produced that electron a negatively charged subatomic started from the negative electrode, or cathode. As a result of these observations, he particle called his tube a cathode ray tube (Figure 3(a)). WEB LINK source of applied electric electric () stream of negatively potential field charged particles () metal () electrode () partially evacuated metal glass tube electrode (a) (b) Figure 3 (a) A cathode ray tube under high voltage produces a visible ray. (b) A cathode ray is deflected away from the negative pole in an applied electric field, which is consistent with the ray being composed of a stream of negatively charged particles (electrons). 134 Chapter 3 Atoms NEL  Thomson also observed that the negative pole of an applied electric field repelled the ray (Figure 3(b)). He explained these observations by hypothesizing that the ray was composed of a stream of negatively charged particles, which we now know to be electrons. By measuring the deflection of the beam of electrons in a magnetic field, Thomson was able to determine the charge-to-mass ratio of an electron, using the formula e 5 21.76 3 108 C/g m where e represents the charge on the electron in coulombs (C), and m represents the electron mass in grams (g). One of Thomson’s goals in his cathode ray tube experiments was to understand the structure of the atom. He reasoned that since electrons could be produced from elec- trodes made of various metals, all atoms must contain electrons. Since atoms are electri- cally neutral, Thomson further reasoned that atoms must also contain a positive charge. Thomson postulated that an atom consists of a diffuse cloud of positive charge with nega- tively charged electrons embedded randomly in it. This model is sometimes called the “blueberry muffin model”; the electrons are analogous to negatively charged blueberries dispersed in a positively charged muffin (Figure 4). spherical cloud of positive charge electrons (a) (b) Figure 4 (a) According to Thomson’s model, electrons are randomly embedded in a cloud of positive charge. (b) Thomson’s model of an atom is sometimes called the “blueberry muffin model.” In the model, electrons are represented by the blueberries. In 1909, scientist Robert Millikan conducted experiments at the University of Chicago in which he used charged oil drops to determine the charge of an electron. Using the apparatus shown in Figure 5, Millikan discovered that the fall of charged oil droplets due to gravity could be halted by adjusting the voltage across two charged plates. He was able to calculate the charge on the oil drop from the voltage and the mass of the oil drop. Using this value and the charge-to-mass ratio determined by Thomson, Millikan calculated the mass of an electron to be 9.11 3 10–31 kg. atomizer to produce oil droplets oil spray () microscope X-rays produce charges on the () oil drops electrically charged plates (a) (b) Figure 5 (a) A schematic representation of the apparatus Millikan used to determine the charge of an electron. (b) Robert Millikan using his apparatus NEL 3.1 Early Atomic Theories and the Origins of Quantum Theory 135  Exploring radioactivity In the late nineteenth century, scientists discovered that certain elements emit high levels of energy. In 1896, French scientist Henri Becquerel found that, in the absence of light, a piece of mineral containing uranium produces an image on a photographic plate. He attributed this phenomenon to uranium atoms spontaneously emitting radioactivity the spontaneous decay or radiation: energy, particles, or waves that travel through space or substances. disintegration of the nucleus of an atom Elements that emit radiation are said to be radioactive. Today we know that radioactivity is the spontaneous decay of the nucleus of an atom. This idea was first proposed by Ernest Rutherford (Figure 6). Rutherford showed that radioactivity resulted from the disintegration of atoms. He also discov- ered the alpha particle and named the beta particle and the gamma ray (Table 1). Table 1 Characteristics of Three Types of Radioactive Emissions Alpha particle Beta particle Gamma ray Symbol a or 42a or 42He  or 2 or e  Atomic mass (u) 4 1 0 2000 Charge 12 21 0 Speed slow fast very fast (speed of light) Figure 6 Ernest Rutherford (1871–1937) Ionizing ability high medium none did much of the early work characterizing radioactivity at McGill Penetrating power low medium high University in Montréal, Québec. He Stopped by paper aluminum lead received the Nobel Prize in Chemistry in 1908. rutherford’s Model of the Atom In 1911, Rutherford carried out a series of experiments to look for evidence in support of Thomson’s “blueberry muffin model” of the atom. Rutherford devised experiments in which positively charged alpha particles were fired at a thin sheet of gold foil. He hypoth- esized that if Thomson’s model was accurate, the massive alpha particles should break through the thin foil like bullets through paper, with only minor deflections (Figure 7). some alpha particles most particles are scattered pass straight through the foil source of beam of alpha particles alpha particles screen to detect thin scattered alpha particles gold foil Figure 7 Rutherford’s experimental design for the alpha particle bombardment of gold foil The results of the experiments were very different from what Rutherford had anticipated. Although most of the alpha particles passed straight through the gold foil, some were deflected at various angles while others were reflected back toward the source, never reaching the detector. Rutherford realized that these experimental results did not support Thomson’s model of the atom (Figure 8(a)). The only possible explanation was that the observed deflection of alpha particles was caused by a concentrated positive charge at the centre of the atom. Rutherford predicted that the positive charge at the centre of the atom must contain most of the atomic mass, which would account for the deflection 136 Chapter 3 Atoms NEL of the massive alpha particles. Rutherford also reasoned that since most of the alpha particles passed directly through the foil, the atom must be made up of mostly empty space, and the positive centre must be small in volume relative to the atom (Figure 8(b)). The deflected alpha particles must have travelled close to the positively charged centres of the atoms and, since like charges repel, changed paths. The alpha particles that bounced back must have made a direct hit on the much more massive positively charged centres. electrons scattered diffuse throughout positive – charge – – – – – – – – – + – – – – – – – – – – (a) (b) Figure 8 (a) Rutherford predicted that the alpha particles would pass right through the gold foil if Thomson’s model was correct. (b) The actual results of Rutherford’s experiments revealed that the atom is mostly open space with a small, positively charged centre that contains the bulk of the atomic mass. Rutherford concluded that these results could be explained only in terms of an atom with a nucleus: a dense, positively charged atomic centre. He proposed that elec- nucleus the dense centre of an atom with trons move around the nucleus at a relatively far distance, similar to planets orbiting a positive charge the Sun. Rutherford later named the positive charges in the nucleus protons. proton a positively charged subatomic Scientist James Chadwick worked with Rutherford to determine the masses of the particle nuclei of different elements. In these experiments, he found that the observed masses of the nuclei were not the same as the sum of the masses of the protons. Chadwick concluded that a nucleus must contain not only positively charged protons, but also neutral (uncharged) particles called neutrons. neutron an electrically neutral subatomic particle Atoms and Isotopes An atom can be described as consisting of a tiny nucleus with a diameter of about 10–15 m and electrons that move around the nucleus at an average distance of about 10–10 m. The nucleus is very small compared to the overall size of the atom: if an atom were the size of a sports stadium, the nucleus would be about the size of a ball bearing (Figure 9). However, nuclear material is so dense that a ball bearing–sized piece would have a mass of 226 million tonnes! The nucleus of an atom contains protons, which have a positive charge equal in magnitude to the negative charge of an electron, and neutrons, which have virtually the same mass as a proton but no charge. Table 2 summarizes the masses and charges of the electron, proton, and neutron. Figure 9 If the atomic nucleus were the size of this ball bearing, a typical atom Table 2 The Mass and Charge of the Electron, Proton, and Neutron would be the size of this stadium. Particle Mass (kg) Charge* electron (e 2) 9.109 3 10231 21 proton (p1) 1.673 3 10227 11 neutron (n0) 1.675 3 10227 none *The magnitude of the charge of the electron and the proton is 1.60 3 10219 C. NEL 3.1 Early Atomic Theories and the Origins of Quantum Theory 137  If all atoms are composed of these same particles, why do different atoms have dif- ferent chemical properties? The answer lies in the number of electrons in each atom. An electrically neutral atom has the same number of electrons as protons. Electrons constitute nearly all of the volume of an atom, but an insignificant amount of its mass. Electrons of different atoms interact when atoms combine to form molecules. The number of electrons in an atom and their arrangement determine the chemical behaviour of the atom. Neutral atoms of different elements have unique numbers of protons and electrons and, therefore, different chemical properties. What makes the atoms of a certain element radioactive? You know that a neutral atom by definition has an equal number of protons and electrons in its nucleus. isotopes atoms with the same number of However, the number of neutrons in a neutral atom can differ. Two atoms with the protons but different numbers of neutrons same number of protons but different numbers of neutrons are called isotopes. atomic number (Z ) the number of The nucleus of each carbon isotope in Figure 10 has the same atomic number (Z ) protons in a nucleus which is the number of protons. However, each nucleus has a different mass number mass number (A ) the total number of (A ) which is the total number of protons and neutrons. The symbols for these two protons and neutrons in a nucleus isotopes are written as 126C and 146C. Notice that the atomic number is written as a subscript and the mass number is written as a superscript. These carbon isotopes can also be written as carbon-12 or C-12, and carbon-14 or C-14. Isotopes have almost identical chemical properties because they have the same number of electrons and protons. In nature, most elements contain mixtures of isotopes. In addition to occur- ring in nature, radioisotopes can be synthesized from certain elements. nucleus nucleus 6 protons 6 protons 6 neutrons 8 neutrons 6 electrons 6 electrons 12 14 6C 6C (a) (b) Figure 10 (a) Carbon-12 contains 6 protons and 6 neutrons. (b) Carbon-14 is an isotope of carbon that has 8 neutrons. Recall that Henri Becquerel observed the spontaneous emission of radiation by uranium. When the nuclei of isotopes are unstable, as is the case for some ura- radioisotope an isotope that emits nium isotopes, they are radioactive and are called radioisotopes. A radioisotope is radioactive gamma rays and/or subatomic an isotope with an unstable nucleus, meaning that the nucleus decays and emits particles (for example, alpha and/or beta radioactive gamma rays and/or subatomic particles. Scientists and engineers use particles) the radiation emitted by radioisotopes in many applications, including carbon dating, nuclear energy, and medicine. For example, carbon-14 is used in archaeo- logical dating. The Nature of Matter and Energy During the first half of the twentieth century, scientists realized that the results of several key experiments were not consistent with the classical theories of physics developed by Isaac Newton and other scientists. To account for the observed behaviour of light and atoms, physicists developed a radical new idea called quantum theory. This new physics provided many surprises, but it also more accurately explains the behaviour of light and matter. WEB LINK 138 Chapter 3 Atoms NEL Classical Theories of Light Light, or light energy, is electromagnetic radiation. Visible light is the portion of this spectrum that can be seen by the human eye. The nature and properties of light have been debated for centuries. Around 300 BCE, Greek philosophers proposed that light existed as a stream of particles. In the seventeenth century, Dutch scientist Christiaan Huygens conducted investigations that led him to theorize that light is a wave. Not all scientists agreed with Huygens. For example, Isaac Newton believed that light was com- posed of tiny particles, which he called “corpuscles.” Investigations continued and new evidence from experiments with refraction, diffraction, and reflection provided a great deal of support for the wave hypothesis proposed by Huygens. In the mid-nineteenth century, physicist James Maxwell proposed a theory regarding the properties of magnetism, light, and electricity. Maxwell theorized that light could act on charged particles because it existed as an electromagnetic wave made of magnetic and electric fields. Over time, Maxwell’s electromagnetic wave theory gained wide acceptance and came to be the classical theory of light. According to Maxwell’s theory, light is an elec- tromagnetic wave composed of continuous wavelengths that form a spectrum (Figure 11). Electromagnetic Spectrum frequency, f (Hz) visible light 104 106 108 1010 1012 1014 1016 1018 1020 1022 1024 microwaves UV cosmic rays radio waves infrared X-rays gamma rays 104 102 1 10–2 10–4 10–6 10–8 10–10 10–12 10–14 10–16 wavelength,  (m) Figure 11 Visible light is only a very narrow band on the electromagnetic spectrum. At the end of the nineteenth century, matter and energy were considered to be distinct, and unrelated, entities. Matter was thought to be composed of particles that had mass and a specific position in space at a particular time. Light energy was con- sidered to be an electromagnetic wave that had no mass or specific position in space. However, in 1887 German physicist Heinrich Hertz was attempting to generate electromagnetic waves using induction coils, and instead, discovered the photoelectric photoelectric effect electrons are effect, in which light shining on a metal surface causes the emission of electrons from emitted by matter that absorbs energy the metal. Hertz reported the photoelectric effect, but did not attempt to explain it. from shortwave electromagnetic radiation The discovery of the photoelectric effect had a major impact on the classical theories (for example, visible or UV light) of light and matter. WEB LINK According to the classical theory of light, the intensity (brightness) of the light shining on the metal should determine the kinetic energy of the electrons emitted. Therefore, the more intense the light, the more energy the emitted electrons should have. However, Hertz’s experiments demonstrated that the frequency of the light was more important in determining the energy of the emitted electrons (Figure 12). Since the classical theory of light and matter could not explain these observations, it began to be viewed as flawed. Investigation 3.1.1 low-frequency high-frequency light light The Photoelectric Effect (page 179) e Einstein was later able to explain e the photoelectric effect through experimentation, for which he received a Nobel Prize. In this investigation, you (a) metal surface (b) metal surface will observe what Einstein observed, Figure 12 Hertz’s experiments showed that light with frequency less than a certain frequency, which ultimately led to the modern called the threshold frequency, produces no electrons (a), whereas light with frequency higher than theory of light and atoms. the threshold frequency causes electrons to be emitted from the metal (b). NEL 3.1 Early Atomic Theories and the Origins of Quantum Theory 139  Planck’s Quantum Hypothesis In 1900, German physicist Max Planck (Figure 13) was studying the spectra of the radiant energy emitted by solid bodies (called blackbodies) heated to incandescence (glowing). When a solid is heated to very high temperatures, it begins to glow, first red, then white, then blue. The changes in colour and the corresponding light spectra do not depend on the composition of the solid. The intensity of the light of different colours can be measured and plotted on a graph, to produce a curved line (or energy curve). WEB LINK Classical physics predicted that the energy curve should go up continuously Figure 13 Max Planck (1858–1947), as temperature increases: physicists thought that matter could absorb or emit any at right, is regarded as the founder of quantity of energy. However, Planck’s experiments showed that the curve reached a quantum theory. He studied the light peak and then decreased. The position of the peak correlated to the temperature and emitted by hot objects. His experiments moved toward higher light frequencies as an object became hotter. Compare the posi- led him to hypothesize that energy could tions of the peaks for a red-hot and a white-hot object in Figure 14. Now compare be gained or transferred in whole- these to the curved line that would result as predicted by the classical theory of light. number multiples. classical theory of light Intensity white hot red hot infrared visible ultraviolet low energy high energy Figure 14 A white-hot wire and a red-hot wire emit light at different colours and intensities. The light emitted does not follow the expected results of the classical theory of light. Planck accounted for the unexpected results of his heating experiments by pos- tulating that matter can gain or lose energy, E, only in whole-number multiples, according to the equation E 5 nhf where n is an integer (1, 2, 3,...), f is the frequency of the radiation and h is Planck’s constant. Planck’s constant is a constant of nature and has the value 6.63 3 10234 J # s. Planck knew that radiation was emitted as atoms vibrated back and forth (oscil- lated). He hypothesized that the energies from the oscillating atoms in the heated object were multiples of a small quantity of energy. Light was emitted in bursts of this discrete (separate and distinct) quantity of energy rather than as a continuous stream. Albert Einstein later brought Planck’s hypothesis to its logical conclusion—the light emitted by a heated solid is quantized. One burst or packet of energy is now known quantum a unit or packet of energy as a quantum of energy. (plural: quanta) A quantum is a difficult concept. It may help to imagine a quantum of energy as a unit of money. Any value of money can be understood as equal to, for example, a number of pennies, the smallest unit of money. Similarly, that same value of money can be described in terms of other units of money. For example, $2.00 is equal to 200 pennies, but it is also equal to 8 quarters or 20 dimes or 40 nickels. Quanta of light are similar to units of money in that the colours of light emitted are analogous to the value of a particular coin. Infrared light may be thought of as being analogous to a penny, red light to a nickel, blue light to a dime, and ultraviolet light to a quarter. Heating a solid until it glows in the infrared range is analogous to it emitting pen- nies of light energy. Similarly, a red-hot solid emits quantities of light energy analo- gous to nickels, a white-hot solid emits quantities of light energy analogous to dimes, 140 Chapter 3 Atoms NEL and so on. It is important to keep in mind that there are no intermediate quantities of light energy, just as there are no seven-and-a-half-cent coins. Planck’s results were a surprise to the scientific community. It was now clear that energy can occur only in discrete quanta and, therefore, a system can transfer energy only in whole quanta. Planck’s observations (for example, the bell-shaped curves shown in Figure 14) revealed that as the temperature of an object increases, more of the larger quanta and fewer of the smaller quanta of energy are emitted. Also, the colour of the light emitted by a hot object depends on the proportion of the quanta of different energies that are emitted. In this way, light energy seems to have properties similar to particles. Photons Investigation and discovery of the photoelectric effect was critical to the development of quantum theory. In 1905, Albert Einstein explained the photoelectric effect by applying Planck’s idea of a quantum of energy (Figure 15). Einstein suggested that electromag- Figure 15 Albert Einstein (1879–1955) netic radiation could be viewed as a stream of particles called photons. A photon is a received a Nobel Prize in 1921 for a paper unit of light energy. Einstein proposed that an electron was emitted from the surface of explaining the photoelectric effect in terms the metal because a photon collided with the electron. During the collision, the energy of quantum theory. of the photon transferred to the electron. Some of the transferred energy caused the photon a unit of light energy electron to break away from the atom, and the rest was converted to kinetic energy. To free an electron from the atom requires the energy from a minimum of one photon. An electron stays in place because of electrostatic forces. If a single electron absorbs a single photon with the right quantity of energy, the electron can escape the metal surface. If a photon does not have enough energy, no electrons can escape the metal no matter how many photons strike it. The kinetic energy of the ejected electrons depends on the frequency of the light used. When the frequency is below a certain level, called the threshold frequency, no electrons are ejected. Quantum theory has provided explanations for observations, namely, the photo- electric effect and blackbody radiation, that no other theory could explain. For this reason, quantum theory is one of the greatest achievements in modern science. In upcoming sections you will learn about other observations that only quantum theory has been able to explain. research This The Large Hadron Collider—A Smashing Success SKILLS Skills: Researching, Analyzing, Communicating, Defining the Issue, Defending a Decision HANDBOOK A5.1 The Large Hadron Collider (LHC) at CERN in Geneva, Switzerland, is the world’s most powerful particle accelerator (Figure 16). Scientists are using it to investigate how atomic and subatomic particles are structured. A Toroidal LHC ApparatuS (ATLAS) was built to detect the particles and energy present after protons collide. Canadian scientists, including University of Alberta professor James Pinfold, have been working on the ATLAS project alongside scientists from across the globe. 1. Research Canada’s participation in the ATLAS project. 2. Research string theory and the grand unified theory. A. Briefly outline the premises of string theory and the grand unified theory. K/u Figure 16 B. An enormous amount of money has been spent on LHC and D. Should further investments in these projects and this type of ATLAS projects. Do you think it is worth it? What are the research continue? Explain your reasoning. T/I A benefits to science and society? T/I A C. Summarize your research and choose an appropriate, interesting WEB LINK presentation format to share what you learned. T/I C A NEL 3.1 Early Atomic Theories and the Origins of Quantum Theory 141  3.1 Review Summary According to modern atomic theory, the atom has a small, dense nucleus containing protons and neutrons. Electrons reside outside the nucleus in the relatively large remaining atomic volume. The atomic number, Z, is the number of protons in an atom’s nucleus. The mass number, A, is the total number of protons and neutrons in an atom’s nucleus. Isotopes of an element have the same atomic number but different mass numbers. Radioisotopes have unstable nuclei that decay and emit radiation. According to quantum theory, electromagnetic energy is not continuous; instead, energy exists as packets or quanta, called photons. Questions 1. For each of the following atoms, identify 7. Copy Table 3 in your notebook and complete it. K/u C (a) the number of protons and neutrons in the nucleus Table 3 (b) the number of electrons present in the neutral atom for that element K/u Symbol Protons Neutrons Electrons Net charge (i) 79Br (iv) 133Cs 238 92 U 0 (ii) 81Br (v) 3H 20 20 239 12 (iii) Pu (vi) 56Fe 23 28 20 2. Write the atomic symbol (AZX) for each of the 89 39Y 0 following isotopes: K/u (a) Z 5 8; number of neutrons 5 9 35 44 36 (b) the isotope of chlorine in which A 5 37 26 33 13 (c) Z 5 27; A 5 60 13 14 10 (d) number of protons 5 26; 8. Scientists record their experimental observations number of neutrons 5 31 and conclusions in a lab book or journal. Write (e) the isotope of I with a mass number of 131 a journal entry that would reflect the results of (f) Z 5 3; number of neutrons 5 4 Rutherford’s gold foil experiment. K/u T/I C 3. For each of the following ions, indicate the number 9. According to the latest developments in nuclear of protons and electrons the ion contains: K/u theory, protons and neutrons are composed of (a) Ba21 (d) Rb1 smaller subatomic particles called quarks. Research (b) Zn21 (e) Co31 quarks and their properties K/u T/I A (c) N 32 (f) Te22 (a) How are quarks named? (b) Describe the composition of a proton, and explain 4. What is the atomic symbol of an ion with how its composition accounts for its charge. (a) 16 protons, 18 neutrons, and 18 electrons? (c) Which Canadian scientist provided some of the (b) 16 protons, 16 neutrons, and 18 electrons? K/u first supporting evidence for the existence of 5. Explain the photoelectric effect. K/u quarks and received a share of the Nobel Prize? 6. Use a series of diagrams and a few point-form notes 10. The newly updated periodic table includes pie charts to create a flow chart that summarizes the history of for each element. Each pie chart represents the atomic theory, beginning with Dalton and ending isotopes of that element found in nature, and each with Einstein. K/u C pie segment represents the abundance of that isotope in nature. Evaluate the usefulness of this new format compared to the classic table format. K/u T/I A WEB LINK 142 Chapter 3 Atoms NEL Bohr’s Model of the atom 3.2 If you have seen a fireworks display, then you have experienced a fantastic example of chemistry in action. The different colours that appear in fireworks arise when electrons in the atoms of various chemicals become excited by absorbing electrical or thermal energy, and then emit that energy at various wavelengths. This seemingly simple explanation comes from decades of work on the structure of the atom by some of the world’s most talented scientists. Limits of the rutherford Model of the Atom In the previous section you read about some of the experiments that led to the dis- covery of the electron, proton, and neutron, and to Ernest Rutherford’s model of the atom. The model of the atom proposed by Rutherford predicted that electrons move around the nucleus of the atom, much like planets orbit the Sun. This idea seemed reasonable because even though the Sun’s gravity pulls planets toward it, this pull is electron counteracted by the planets’ movement. It seemed reasonable that electrons orbiting e an atomic nucleus would behave in the same way. However, it became apparent that there was a problem with this idea. A body that is moving in an orbit is constantly changing direction, and a body that is changing e e  direction or speed is accelerating. Physicists had demonstrated that when a charged photon particle accelerates, it continuously produces electromagnetic radiation (emitted as e photons). According to classical light theory, an electron travelling in an orbit emits energy as photons and, therefore, loses energy. If an electron loses energy as it orbits, nucleus it should spiral in toward the positively charged nucleus (Figure 1). Since the electron is negatively charged and opposite charges attract, the atom would eventually col- lapse. However, this prediction is not supported by evidence. Generally, most atoms Figure 1 An electron accelerating are stable and do not appear to be collapsing. This suggests that, although electrons around the nucleus would continuously are constantly moving, they do not lose energy. Rutherford’s model, therefore, is not emit electromagnetic radiation and lose able to explain the stability of atoms. energy. Therefore, it would eventually fall into the nucleus and the atom would collapse. However, this is not consistent Atomic Spectra with real-world observations. Spectroscopy is the scientific study of spectra (plural of spectrum) in order to deter- spectroscopy the analysis of spectra to mine properties of the source of the spectra. Spectrometers and spectrophotometers determine properties of their source measure the intensity of light at different wavelengths in similar ways. Light first passes through a sample, and then is dispersed by a prism or, more commonly, a diffraction grating. The dispersed light forms a spectrum. A detector in the instrument then scans the spectrum and calculates the amount of light absorbed or transmitted at each wave- length. Figure 2 shows an early spectroscope and a more modern spectrophotometer. (a) (b) Figure 2 (a) Early spectroscopes used a candle and a gas lamp as light sources and focused light using a prism. (b) Modern spectrophotometers have a sealed area for the sample that does not allow interfering light to enter the unit, and can be adjusted to allow analysis at different wavelengths. NEL 3.2 Bohr’s Model of the Atom 143  The earliest analytical instrument invented expressly for spectroscopy was a spectroscope similar to the one shown in Figure 2(a). Robert Bunsen and Gustav Kirchhoff invented the spectroscope to use in the first spectroscopy investigations, which they conducted in 1859. They viewed and analyzed the spectra produced by emission of energy by various substances, especially elements. As with most fields of scientific study, advances in spectroscopy dovetailed with advances in technology. Investigations of light emitted from excited substances led to further developments in atomic theory. The Atomic Spectrum of the Hydrogen Atom The atomic spectrum of the hydrogen atom played an important role in advancing atomic theory. Hydrogen gas, H2(g), is a molecular element. When a high-energy spark is applied to a sample of hydrogen gas, the hydrogen molecules absorb energy, which breaks some of the H–H bonds. The resulting hydrogen atoms are excited: they contain excess energy. The excited hydrogen atoms release this excess energy by emission spectrum the spectrum of emitting light of various wavelengths. When this light is passed through a spectro- electromagnetic radiation emitted by an scope, it forms an emission spectrum. An emission spectrum is the spectrum (or pat- atom; results when an atom is returned to a tern of bright lines) seen when the electromagnetic radiation of a substance is passed lower energy state from a higher energy state through a spectrometer. continuous spectrum an emission Two types of emission spectra can be produced, depending on the nature of the spectrum that contains all the wavelengths source. A continuous spectrum contains every wavelength in a particular region of the in a specific region of the electromagnetic electromagenetic spectrum. For example, when white light passes through a prism, spectrum a continuous spectrum appears (Figure 3(a)) containing all the wavelengths of vis- line spectrum an emission spectrum ible light. In contrast, a line spectrum contains only particular wavelengths, and arises that contains only those wavelengths when excited electrons emit energy. Figure 3(b) shows the line spectrum of the characteristic of the element being studied hydrogen atom. Each coloured band corresponds to a discrete wavelength. detector arc (photographic plate) detector  slit prism (photographic plate) high VIBG Y voltage slit prism OR   continuous hydrogen gas  spectrum discharge tube electric arc; a solid light source 410 nm434 nm 486 nm 656 nm (a) (b) Figure 3 (a) A continuous spectrum contains all wavelengths of visible light (indicated by the initial letters of the colours of the rainbow). (b) The line spectrum for the hydrogen atom contains only a few discrete wavelengths. Investigation 3.2.1 The investigations of Bunsen, Kirchhoff, and other scientists in the late nineteenth Bright-Line Spectra (page 180) century revealed that each element has its own unique line spectrum. The spectra of All atoms absorb and emit the known elements were quickly catalogued. The line spectrum is like a fingerprint electromagnetic radiation. In this of a specific element. If a new spectrum was found, it provided evidence of a new investigation, you will observe the element. In fact, the elements cesium and rubidium were discovered within a year visible spectra of various substances. of the invention of spectroscopy. There are many applications of line spectra. For example, astronomers use line spectra to identify the composition of stars. 144 Chapter 3 Atoms NEL  The unique line spectrum of the hydrogen atom is significant to atomic theory because it indicates that the electron of the hydrogen atom can exist only at discrete energy levels. In other words, the energy of the electron in the hydrogen atom is quantized. This observation is consistent with Planck’s quantum theory. The par- ticular wavelengths of light emitted by the electrons of hydrogen atoms are produced by changes in energy. When excited electrons in hydrogen atoms move to a lower energy level, they emit a photon of light. This is true of excited electrons in other atoms as well. The Bohr Model of the Atom Niels Bohr was a Danish physicist who studied under J.J. Thomson at Cambridge University in the United Kingdom (Figure 4). In 1913, Bohr used the emission spectrum Figure 4 Niels Bohr (1885–1962) of the hydrogen atom to develop a quantum model for the hydrogen atom. He knew developed a quantum model for the that his model had to account for the experimental evidence provided by spectroscopy: hydrogen atom and, even though his that electrons could have only particular discrete energy levels. Bohr accounted for this model was later proved to be incorrect, Bohr was awarded the Nobel Prize in data by proposing that electrons could move only in specific orbits around the nucleus. Physics in 1922. He assigned each orbit a specific energy level, and postulated that the energy level of an orbit increased with its distance from the nucleus. When an electron gained more energy (for example, became excited), it could move into an orbit farther from the nucleus. Although Bohr’s atomic model did not explain why electrons behaved this way, it was consistent with the observed line spectrum of the hydrogen atom. Figures 5(a) and 5(b) show electron transitions in the Bohr model for the hydrogen atom. Compare these to the line spectrum of the hydrogen atom, shown in Figure 5(c). 6 6 5 5 4 4 3 3 2 2 1 Energy level 1 wavelength (a) (b) (c) Figure 5 Electron transitions in the Bohr model for the hydrogen atom. An energy-level diagram (a) and an orbit-transition diagram (b), each showing electron transitions in the Bohr model for the hydrogen atom. Both of these account for the observed line spectrum of the hydrogen atom (c). The orbits are not drawn to scale. The lines in the visible region of the spectrum correspond to transitions from higher levels to level 2. To help you envision how the orbits in Bohr’s model relate to the line spectrum of the hydrogen atom, imagine a ball sitting on a staircase. Since the ball can only be positioned on a stair, it can only ever be found at specific distances from the ground. Applying Bohr’s theory to this analogy, the higher up the staircase the ball is, the more potential energy it has. If the ball moves up the staircase (that is, to a higher energy level), it gains potential energy. If it moves down the staircase (that is, to a lower energy level), it loses potential energy. The ball in Figure 6 is moving down the staircase, so it is losing potential energy. Figure 6 The position of the ball on the stairs determines its quantity of potential energy. NEL 3.2 Bohr’s Model of the Atom 145  In the Bohr model of the atom, the electron is analogous to the ball in Figure 6 and the orbits are analogous to the different stairs. As with the ball on the stairs, electrons can only be at specific positions (energy levels or orbits) in relation to the nucleus of the atom. In Figure 7, the radius, rx, of each orbit is analogous to the height of a stair from the floor in Figure 6. The electron gains or loses potential energy by moving from one position (orbit) to another. r3 r2 r1 Figure 7 The position of an electron relative to the nucleus of an atom determines its quantity of potential energy. transition the movement of an electron The movement of an electron from one energy level to another is called a transition. from one energy level to another During a transition to a higher energy level, an electron absorbs a specific quantity of energy, such as when it is struck by a photon. During a transition to a lower energy level, an electron emits a photon of a particular quantity of energy. The lowest possible ground state the lowest energy state for energy state for an atom is called the ground state. There are no excited electrons in the an atom ground state. Successes and Failures of the Bohr Model Recall that in a Bohr-Rutherford diagram, the numbers of protons, p1, and neu- trons, n0, are noted in the nucleus. The concentric circles represent the different energy levels of electrons, and each contains a specific number of electrons. In an attempt to be consistent with observations related to the quantization of energy in atoms, Bohr’s model assumes that each energy level can hold a maximum number of electrons. For the first 18 elements in the periodic table, the Bohr model predicts that the first, second, and third orbits can contain a maximum of 2, 8, and 18 electrons, respectively, and that the lower energy levels must fill first. The corresponding Bohr–Rutherford diagrams are especially useful for the first 20 elements of the periodic table, in which atoms of all the elements are arranged according to the number of protons and electrons in a neutral atom. Beyond the 11p first 20 elements, however, Bohr–Rutherford diagrams become too cumbersome 12n0 to be useful. Bohr’s model of the atom initially appeared to be very promising for under- standing the behaviour of atoms because it appeared to be consistent with observed chemical and physical properties. For example, the energy levels Bohr calculated for the electron in the hydrogen atom were very similar to values obtained from the hydrogen atom’s emission spectrum by spectroscopy. However, the electron energies Na atom predicted by Bohr’s model were not consistent with observed data for atoms with Figure 8 Electron energies for a more than one electron (Figure 8). Scientists eventually concluded that Bohr’s model neutral sodium atom, as predicted by did not fully describe the structure of an atom. Still, the Bohr model is of great historic the Bohr–Rutherford model. Current importance because it included the quantization of energy in atoms and paved the atomic theories do not support this way for later theories. Bohr–Rutherford diagrams are so widely recognized, however, arrangement of electron energies. that it can be easy to forget that according to current theories of the atom, electrons do not actually orbit the nucleus. 146 Chapter 3 Atoms NEL  3.2 Review Summary Spectroscopy is the study of light emitted by excited sources. Spectroscopy of excited gaseous elements led to the discovery of line spectra, which are unique to specific atoms and elements. Line spectra are consistent with Planck’s quantum theory. Niels Bohr proposed a model of the atom that was consistent with experimental observations of the line spectrum of the hydrogen atom. In the Bohr model of the atom, electrons travel in circular orbits of quantized energy around the atomic nucleus. Questions 1. Explain the main weakness with the Rutherford model (b) Discuss the successes and failures of the Bohr of the atom and how Bohr addressed it. K/u model. K/u 2. Describe what happens when atoms or molecules 10. Why is the work of Bohr and Rutherford on atomic absorb light. K/u theory sometimes referred to collectively as the 3. Scientists use emission spectra to confirm the Bohr–Rutherford model? K/u presence of an element in materials. Explain why 11. (a) What part of the original Bohr model still seems this is possible. K/u to be well supported by experimental evidence? 4. Using a series of diagrams, show what happens to (b) Identify one weakness in Bohr’s atomic theory. K/u the electrons of an atom when they are excited and 12. When drawing the energy levels of an atom with one how they can produce spectra that can be viewed in electron, your friend draws the diagram shown in a spectroscope. K/u C Figure 9. Describe the line spectra that will be pro- 5. Explain why the emission spectrum of an atom or duced by an atom with this arrangement of energy molecule depends on its arrangement of electrons. K/u levels. Provide evidence that this is not an accurate 6. The emission spectrum of an element is representation of the energy levels in an atom. K/u T/I unique. K/u A 5 (a) Explain why the emission spectrum is sometimes referred to as an element’s fingerprint. 4 (b) Give a real-life example of how the emission spectrum could be used to help determine the 3 nature of an unknown chemical. (c) Would using an emission spectrum be 2 considered qualitative or quantitative analysis? Explain your answer. 1 7. In both ground-state sodium and magnesium Figure 9 atoms, the electrons are found in the first, second, and third energy levels. These electrons will jump to 13. Using a graphic organizer or a chart, higher energy levels when energy is applied, and (a) compare and contrast Thomson’s and Bohr’s then fall back down, releasing their energy and giving models of the atom off a spectrum. Why do you think the spectra for (b) compare and contrast Bohr’s and Rutherford’s sodium and magnesium are not the same? Why models of the atom K/u C might you think they would be the same? K/u T/I 14. Summarize the evolution of atomic theory, starting 8. (a) What is spectroscopy? with Thomson and ending with Bohr. Use a labelled (b) Discuss how spectroscopy was useful to the diagram or a flow chart. (You may want to add this development of early atomic theory. K/u information to your answer to Question 6 in 9. (a) Describe the Bohr model of the atom, including Section 3.1 to create a complete flow chart showing quantization and emission spectra. the development of atomic theory.) K/u C NEL 3.2 Bohr’s Model of the Atom 147  3.3 the Quantum Mechanical Model LEARNING TIP of the atom Weaknesses in theories and models provide opportunities for science to improve. It is What Is Quantum Mechanics? Classical mechanics is the branch impossible to devise a perfect theory or model the first time around. Instead, science of physics that studies the motion usually involves years and years of revisions and new discoveries. Science is constantly of macroscopic objects. Quantum changing by identifying and improving on weaknesses. The success of the Bohr atomic mechanics is the study of motion at model was important because it showed that electrons exist in discrete energy levels. the atomic level, where the laws Also, it explained experimental observations of line spectra in terms of quantum of classical mechanics do not theory. But there were weaknesses in this model that other scientists identified, which apply because particles behave paved the way for the complete development of the quantum model of the atom. like waves. By the mid-1920s, it had become apparent that the Bohr model could not explain and make predictions about multi-electron atoms. A new approach was needed. Three physicists were at the forefront of this effort: Erwin Schrödinger, Louis de Broglie, and Werner Heisenberg. The approach they developed to explain properties of matter is called quantum mechanics the application of wave mechanics or, more commonly, quantum mechanics. CAREER LINK quantum theory to explain the properties of matter, particularly electrons in atoms Schrödinger’s Standing wave Louis de Broglie, a French physicist, originated the idea that the electron, previously considered just a particle, has wave properties. Pursuing this line of reasoning, Erwin Schrödinger, an Austrian physicist, decided to approach the problem of atomic structure by focusing on the wave properties of the electron. To Schrödinger and de Broglie, an electron bound to a nucleus in an atom resembled a standing wave, so they began research on a description of the atom based on wave behaviour instead of particle behaviour. The strings on instruments such as guitars and violins are attached at both ends. When you pluck the string, it vibrates and produces a musical tone. The waves pro- duced by the plucking are standing waves. They are called “standing” because they appear to be stationary. The motions of the string are a combination of simple waves of the type shown in Figure 1. unplucked string 2 half-wavelengths 1 half-wavelength 3 half-wavelengths Figure 1 The standing waves caused by the vibration of a guitar string fastened at both ends. Each black dot represents a node (a point of zero displacement), which never moves. The black dots in Figure 1 represent the nodes, or points, of zero lateral (sideways) displacement for a given wave. Between two nodes, at the point where the amplitude of the wave is at its maximum, is the antinode. Note that there are limitations on the allowed wavelengths of the standing wave. Each end of the string is fixed, so there is always a node at each end. This means that there must be a whole number of half- wavelengths in any of the allowed motions of the string. 148 Chapter 3 Atoms NEL  Figure 2 shows how standing waves can be produced by a wave generator. Figure 2 This wave generator is set to produce standing waves that are two half-wavelengths (one wavelength) long. Mini Investigation Modelling Standing Electron waves SKILLS Skills: Performing, Observing, Analyzing, Evaluating, Communicating HANDBOOK A2.3 Schrödinger’s standing waves can be simulated with a mechanical model. A mechanical oscillator causes a loop of wire to vibrate at varying frequencies. Creating vibrations at one point along the wire causes waves throughout the remainder of the wire. This activity is like holding the edge of a stretched Slinky and moving it up and down to produce waves along it. When waves return toward the original direction, they encounter other waves: If they meet constructively, there will be an increase in amplitude. If they meet destructively, there will be a decrease in amplitude. Standing waves result in stationary nodes (no amplitude) and antinodes (at maximum amplitude). Equipment and Materials: oscillator; stand; loop of wire When unplugging the oscillator, pull on the plug, not the cord. Ask your teacher to check the attachment of the wire to the oscillator. 1. Position the oscillator on a laboratory stand. Attach the wire. Position the wire so that its loop is horizontal. 2. Turn the frequency as low as it will go. Plug in the oscillator, then turn it on. 3. Increase the frequency a little. Observe the changes in the waves on the wire. 4. Increase the frequency setting slowly until you can no longer see the nodes and antinodes. 5. Decrease the frequency slowly to the starting point. Observe the simulation in reverse order. 6. Repeat this procedure as necessary. A. Describe what the nodes and antinodes look like. K/u T/I B. Do all frequencies result in standing wave patterns? Explain. K/u T/I C. List the number of nodes and antinodes you were able to observe. K/u T/I D. How do the waves produced by the oscillator compare with waves in an atom? What are some limitations of the standing wave model of the atom? K/u T/I A NEL 3.3 The Quantum Mechanical Model of the Atom 149  Schrödinger and de Broglie took the idea of standing waves and applied it to the electron in a hydrogen atom. In their model, the electron is a circular standing wave around the nucleus (Figure 3). This circular standing wave consists of wavelengths that are multiples of whole numbers (n 5 1, 2, 3, 4,...). Only certain circular orbits have a circumference into which a whole number of wavelengths can fit. Any other orbits of the standing electron wave are not allowed because they would cause the standing wave to cancel out or collapse, that is, undergo destructive inter- ference (Figure 3(c)). This model seemed like a possible explanation for the observed quantization of the hydrogen atom: the whole-number multiples of wavelengths correspond to multiples of fixed quanta of energy that the electron can have in the hydrogen atom. However, the new question that this model raised was this: where is the electron located in the hydrogen atom? n 5 mismatch n 4 n 4 13 (a) (b) (c) Figure 3 The hydrogen electron visualized as a standing wave around the nucleus. In (a) and (b), the circumference of a particular circular orbit corresponds to a whole number of wavelengths. (c) Otherwise, destructive interference occurs. This model is consistent with the idea that only certain electron energies are allowed, because the atom is quantized. Although this idea encouraged scientists to use a wave theory, it does not mean that the electron travels in circular orbits around the nucleus. orbitals and Probability Distributions Schrödinger’s work on quantum mechanics led to his development of a mathematical equation, called the Schrödinger wave equation, that could be used to calculate elec- tron energy levels. If an electron has a definable energy, then it can be localized in orbital the region around the nucleus an orbital, which is the region around the nucleus where there is a high probability of where an electron has a high probability of finding an electron. But how can you locate something as small as an electron? being found Werner Heisenberg, who studied with Bohr, came up with a statistical approach for locating electrons. To measure the location and speed of an object, you must be able to observe it. Life-sized objects are easy to locate because you can see them. You can determine both the speed and the location of a moving car using a radar gun and a GPS unit. For atomic-sized particles and smaller, any attempt to probe them changes their position, direction of travel, or both. This idea formed the basis of Heisenberg’s uncertainty principle. Heisenberg demonstrated using mathematics that there are limits to knowing both where a subatomic particle is and its speed at a Heisenberg’s uncertainty principle the given time. According to Heisenberg’s uncertainty principle, it is therefore impossible to idea that it is impossible to know the exact simultaneously know the exact position and speed of an electron. The best we can do position and speed of an electron at a is to describe the probability of finding an electron in a specific location. given time An electron orbital is analogous to students at school moving from classroom to classroom during a scheduled break. The students are like electrons, the school is like the atom, and the classrooms are like orbitals. Someone who does not know a stu- dent’s exact schedule may be able to determine the probability of that student being in a particular classroom at a particular time, but it is not certain. Another analogy with more appropriate relative sizes is a bee in a closed stadium. You know that the bee is inside the stadium, and you can reason that it will most likely be near its nest. However, you cannot pinpoint its exact location. 150 Chapter 3 Atoms NEL  A wave function is a mathematical description of an orbital in an atom where an wave function the mathematical electron of a certain energy is likely to be found. Note that an orbital is not a Bohr probability of finding an electron in orbit—the electron is not moving around the nucleus in a circle. How, then, is the a certain region of space electron moving? The answer is surprising: we do not know. The wave function gives no information about the detailed pathway of the electron. This idea is somewhat dis- turbing. When we solve problems involving the motions of objects in the macroscopic world, we are able to predict their pathways. For example, when 2 billiard balls with known velocities collide, we can predict their motions after the collision. However, we cannot predict the electron’s motion. It is a mystery what electrons do in the atom. Quantum mechanics does not describe how an electron moves or even if it moves. It only tells us the statistical probability of finding the electron in a given location in an atom. The area or region where we are likely to find an electron is an orbital. Using wave functions, physicists have created a three-dimensional electron electron probability density the probability density, which is a plot that indicates regions around the nucleus with probability of finding an electron at a given the greatest probability of finding an electron. The electron probability density location, derived from wave equations and plot for a hydrogen electron in the ground state (lowest energy state) is spherical and used to determine the shapes of orbitals; is called the 1s orbital (Figure 4(a)). The greatest probability of finding the electron also called electron probability distribution occurs at a distance rmax from the nucleus (Figure 4(b)). This distance is the same as the distance Bohr calculated for the radius of the first circular orbit of hydrogen’s electron. Radial probability (4πr 2R 2) Distance from nucleus (r ) (a) (b) (b) Figure 4 (a) The probability distribution for the hydrogen 1s orbital in three-dimensional space. (b) The radial probability distribution is a plot of the total probability of finding the electron as a function of distance from the nucleus. LEARNING TIP Figure 5 illustrates different electron orbitals, or clouds. The electron can jump Orbitals versus Orbits to any of these orbitals if it absorbs sufficient quanta of energy. Furthermore, The table below outlines the main these orbitals overlap, rather than being distinct levels as in the Bohr model. You differences between orbitals and orbits. will learn more about electron orbitals in the next sections. WEB LINK Orbitals Orbits z 2 electrons 2n 2 electrons three two dimensions dimensions y distance from distance from nucleus varies nucleus is fixed x no set path path is elliptical or circular Figure 5 The electron probability density of various orbitals The two main ideas of the quantum mechanical model of the atom are that electrons quantum mechanical model a model can be in different orbitals by absorbing or emitting quanta of energy, and that the for the atom based on quantum theory location of electrons is given by a probability distribution. The quantum mechanical and the calculation of probabilities for the model is a radical departure from earlier atomic models because it is based on uncer- location of electrons tainty—the uncertainty of an electron’s location within the atom. According to this model, the structure of a tiny atom is much more complex than anyone would have thought possible, as you will see in the next section. NEL 3.3 The Quantum Mechanical Model of the Atom 151  3.3 Review Summary Louis de Broglie originated the idea that the electron has both particle and wave properties. The quantum (wave) mechanical model describes an electron as a standing wave. The electron can occupy a series of orbitals. Each orbital has a prescribed possible energy value and spatial distribution. The exact position of the electron and how it is moving can never both be known. This is consistent with Heisenberg’s uncertainty principle, which states that it is impossible to know both the position and the speed of a particle simultaneously. Orbitals are described as probability distributions and depicted as electron density plots. In the ground state, the single electron in a hydrogen atom resides in a low-energy orbital. The two main ideas of the quantum mechanical model of the atom are that electrons can move between orbitals by absorbing or emitting quanta of energy, and that the location of electrons is given by a probability distribution. Questions 1. Define the following terms and provide an 7. Science is divided into the arbitrary groups of expanded description: K/u biology, chemistry, and physics. K/u T/I A (a) orbital (a) Why do you think science has been so divided? (b) electron probability density (b) This section highlights one area where physics (c) quantum mechanics and chemistry overlap. Identify three more (d) wave function areas where the different groups overlap. (e) quantum mechanical model (c) Do you think it makes sense to divide up science (f) Heisenberg’s uncertainty principle into these groups? Explain your reasoning. 2. (a) Draw a concept map illustrating the important 8. When most people visualize an atom, they use the aspects of the quantum mechanical model of the Bohr–Rutherford model. K/u T/I A atom. Include a brief description of each point. (a) Why do you think this is? Include the terms “wave function,” “orbital,” (b) Do you think it is important for most people “probability density,” and “uncertainty principle.” to understand exactly how the atom functions? (b) Expand on your concept map from (a) by Explain your reasoning. including the contributions by Planck, Bohr, 9. Dr. Richard Bader and his research group at de Broglie, Schrödinger, and Heisenberg. K/u C McMaster University, Hamilton, are well known 3. Explain how an electron orbital is not the same as for their work on the structure of chemical entities. an orbit. K/u Research Bader, and determine the nature of his group’s work. Prepare a brief, general description of 4. What information about the electron cannot be how it relates to quantum mechanics. K/u T/I A determined from quantum mechanics? K/u A 10. Research Schrödinger’s wave equation, and identify the 5. Explain the value of scientists working together different mathematical symbols in it. K/u T/I and sharing information. How do you think this networking has contributed to current knowledge 11. Research the thought experiment called and understanding of major scientific principles? Schrödinger’s cat. What does this thought K/u T/I A experiment tell us about the quantum mechanical model of the atom? K/u T/I A 6. Heisenberg, de Broglie, and Schrödinger were all theoretical physicists. Explain why their work is studied in such detail in a chemistry course. K/u T/I A WEB LINK 152 Chapter 3 Atoms NEL