Chapter 7: ELECTRONS IN ATOMS AND PERIODIC PROPERTIES

Transcription

1 Chapter 7: ELECTRONS IN ATOMS AND PERIODIC PROPERTIES Problems: , , , , , , ELECTROMAGNETIC RADIATION Electromagnetic (EM) Spectrum: a continuum of the different forms of electromagnetic radiation or radiant energy (Fig. 7.1 on p. 298) The substances below are about the size of the wavelength indicated in the EM spectrum. e.g., an atom is about m in size while a CD is about 10-3 m (or 1 mm) thick. visible region: the portion of the EM spectrum that we can perceive as color For example, a "red-hot" or "white-hot" iron bar freshly removed from a high-temperature source has forms of energy in different parts of the EM spectrum red or white glow = radiation within the visible region warmth = radiation within the infrared region 7.1 WAVES OF LIGHT English chemist and physicist Michael Faraday established the basis for electromagnetism, and Scottish scientist James Clerk Maxwell expanded our understanding of electromagnetism, explaining that radiant energy consists of waves with an oscillating electric field and an oscillating magnetic field, which are perpendicular to one another. CHEM 161: Chapter 7 Notes page 1 of 26

2 Electromagnetic Radiation EM waves have the following properties: wavelength and frequency (see Fig. 7.3). wavelength ( =Greek lambda ): distance between successive peaks = distance ; generally in units of m, cm, or nm wave frequency ( =Greek nu ): number of waves passing a given point in 1 s wave = ; generally in hertz (Hz) = time cycle 1 or s s CHEM 161: Chapter 7 Notes page 2 of 26

3 speed of light The product of wavelength and frequency is equal to the speed of light in a vacuum, c= m/s, which is usually rounded to 4 s.f. c= m/s (to 4 s.f.). c length time length wave wave time Know how to convert between wavelength and frequency using the speed of light! Ex. 1 The wavelength for the electromagnetic radiation responsible for a blue sky is about 473 nm. What is the frequency of this radiation in Hz? Ex. 2 KUOW broadcasts at 94.9 MHz in Seattle. What is the wavelength (in nm) of this radio wave? THE NATURE OF MATTER CLASSICAL Descriptions of Matter John Dalton (1803) atoms are hard, indivisible, billiard-like particles atoms have distinct masses (what distinguishes on type of atom from another) all atoms of same element are the same JJ Thomson (1890s) discovered the charge-to-mass ratio of electrons atoms are divisible because electrons are only one part of the atom Ernest Rutherford (1910) shot positive alpha particles at a thin foil of gold discovery of the atomic nucleus James Maxwell (1873), Scottish scientist all forms of radiant energy consist of electromagnetic waves CHEM 161: Chapter 7 Notes page 3 of 26

4 7.3 PARTICLES OF LIGHT AND QUANTUM THEORY Transition between Classical and Quantum Theory Max Planck (1900); Blackbody Radiation heated solids to red or white heat noted matter did not emit energy in continuous bursts, but in whole-number multiples of certain well-defined quantities matter absorbs/emits energy in bundles = "quanta" (single bundle of energy= "quantum") Albert Einstein (1905); Photoelectric Effect Photoelectric Effect: Light shining on a clean metal emission of electrons only occurs when the light has a minimum threshold frequency ( ) When no electrons are emitted When electrons are emitted, more e emitted with greater intensity of light Einstein applied Planck's quantum theory to light light exists as a stream of "particles" called photons. When no electrons are emitted When electrons are emitted and produce a current CHEM 161: Chapter 7 Notes page 4 of 26

5 Energy is proportional to the frequency ( ) and wavelength ( ) of radiation, and the proportionality constant (h) is now called Planck's constant E h = h c where h = J s Ex. 1. Excited mercury atoms emit light strongly at a wavelength of 436 nm. a. What is the energy (in J) for one photon of this light? b. What is the energy (in kj/mol) for a mole of photons of this light? The Photoelectric Effect and Work Function ( ) of a Metal The work function of a metal (symbolized using the Greek letter Phi, ) is the minimum amount of energy to emit an electron from the surface of the metal. Work function: = h Ex. 2: a. The work function for sodium is J. Calculate the longest wavelength (in nm) of light that can cause an electron to be ejected from a sodium atom. b. Use the visible spectrum below to determine the color of the light. CHEM 161: Chapter 7 Notes page 5 of 26

6 7.2 ATOMIC SPECTRA 7.4 THE HYDROGEN SPECTRUM AND THE BOHR MODEL Emission Spectra: continuous or line spectra of radiation emitted by substances a heated solid (e.g. the filament in an incandescent light bulb) emits light that spreads out to give a continuous spectrum = spectrum of all wavelengths of light, like a rainbow Hydrogen Line Spectrum In contrast, when a sample of hydrogen is electrified, the resulting hydrogen emission spectrum contains only a few discrete lines: These discrete lines correspond to specific wavelengths specific energies The hydrogen atoms electrons can only emit certain energies The energy of the electrons in the atom must also be quantized. Thus, Planck s postulate that energy is quantized applies to the electrons within an atom as well. Each element has a unique line spectrum emission spectra can be used to identify unknown elements in chemical analysis the element s line spectrum is often called its "atomic fingerprint" CHEM 161: Chapter 7 Notes page 6 of 26

7 THE BOHR MODEL A Danish physicist named Niels Bohr used the results from the hydrogen emission spectrum to develop a quantum model for the hydrogen atom. Bohr Postulates: Bohr Model of the Atom 1. Energy-level Postulate An electron in a hydrogen atom may only exist in discrete (quantized), circular orbits around the nucleus "tennis ball and stairs" analogy for electrons and energy levels a ball can bounce up to or drop from one stair to another, but it can never sit halfway between two levels Each orbit has a specific energy associated with it, indicated as n=1, 2, 3,... ground state or ground level (n = 1): lowest energy state for a one-electron atom when the one electron is in the lowest energy orbit excited state: when the electron is in a higher energy orbit (n = 2,3,4,...) 2. Transitions Between Energy Levels When the atom absorbs energy, the electron can jump from a lower energy orbit to a higher energy orbit. When an electron drops from a higher energy level to a lower energy level, the atom releases energy, sometimes in the form of visible light. Note also that as n increases, the difference in energy between levels decreases. Higher energy levels are closer to one another than the lower energy levels. CHEM 161: Chapter 7 Notes page 7 of 26

8 The energy absorbed or emitted by an electron when it moves from one energy level to another can be determined using the following formula: E = J 1 1 where n final and n initial are the electron s final 2 2 and initial energy levels (or orbits) nfinal ninitial Ex. 1: Calculate the energy emitted by an electron when it drops from energy level 4 down to energy level 2. (Remember to indicate the correct sign for energy lost or gained.) Ex. 2: Calculate the wavelength (in nm) corresponding to the energy determined in Ex. 1, and indicate the color of the light emitted using the visible spectrum on page 5. wavelength = color = 7.5 ELECTRONS AS WAVES Dual Nature of the Electron Louis de Broglie (1924) If light can behave like a wave and a particle matter (like an electron) can behave like waves. If the electron behaves like a circular wave oscillating around the nucleus an electron can only have specific wavelengths to form a continuous wave. other wavelengths would cancel one another and not form a continuous wave. Topview of a standing wave Sideview of linear and circular standing waves (Images from CHEM 161: Chapter 7 Notes page 8 of 26

9 If an electron can only have specific wavelengths that electron can only have specific corresponding frequencies and energies. Thus, setting the following equations equal to one another, for matter: E = mc 2 for wave: E = hc and changing the c to any velocity, v, gives the de Broglie relation h mv This is used to determine the wavelength of any matter given its velocity and mass. Ex. 1 a. A baseball with mass kg is thrown at a velocity of 45 m/s (~101 mph); calculate the wavelength (in m) associated with the baseball s motion. b. How does the baseball s compare in size to the baseball (diameter 0.08 m)? Ex. 2 a. Calculate the wavelength (in m) of an electron also traveling at 45 m/s. (The mass of the electron is kg.) b. How does the electron s compare in size to the electron (diameter m)? Thus, although all matter can have wave properties, such properties are only significant for submicroscopic particles. The wavelength in these very small particles is about the same size or much larger than the particle, so the wave properties affect the behavior of the particle. CHEM 161: Chapter 7 Notes page 9 of 26

10 Quantum Mechanical Model In 1920s, a new discipline, quantum mechanics, was developed to describe the motion of submicroscopic particles confined to tiny regions of space. Quantum mechanics makes no attempt to specify the position of a submicroscopic particle at a given instant or to explain how the particle got there. It only gives the probability of finding submicroscopic particles. Just like video footage of a location (e.g. food court at the mall) may allow you to predict where people are likely to be but not the exact location for one person at a future time Instead we take a snapshot of the atom at different times and see where the electrons are likely to be found (See Fig on p. 325). View Bizarre Quantum Mechanics Explained animation Werner Heisenberg (1927); Heisenberg Uncertainty Principle For very small particles (e.g. an electron), it is impossible to know precisely the particle s position and its momentum (= mass velocity). We cannot know the exact motion of an electron as it moves around the nucleus. Heisenberg s Uncertainty Principle is expressed mathematically as x m v h 4 where x=uncertainty in position, m v=uncertainty in momentum, and h is Planck s constant. Example: a. Calculate the uncertainly in position for a baseball given the baseball s mass of kg and an uncertainty in velocity of 0.45 m/s (~1 mph), then compare to the size of the baseball (diameter 0.08 m). b. Calculate the uncertainly in position for an electron (mass= kg) with the same uncertainty in velocity of 0.45 m/s, then compare to the size of the electron (diameter m). Thus, the Uncertainty Principle is only relevant for very small particles, like an electron. Limitations of the Bohr Model Quantum Mechanical Model CHEM 161: Chapter 7 Notes page 10 of 26

11 Unfortunately, the Bohr Model failed for every other element with more than one proton or electron. (The multiple electron-nuclear attractions, electron-electron repulsions, and nuclear-nuclear repulsions make other atoms much more complicated than hydrogen.) Most of the energy levels split into sublevels labeled s, p, d, and f. ORBITAL ENERGY LEVELS Orbital energy levels in the hydrogen atom 3s 3p 3d Energy 2s 2p 1s Note that for hydrogen, all of the orbitals within the same principal quantum number, n, have the same energy (are degenerate). In polyelectronic atoms, the presence of more than one electron causes electron-electron repulsions that result in a change in the energies of the various sublevels within the atom. Orbital energy levels in polyelectronic atoms (every atom but hydrogen) Energy 3s 2s 3p 2p 3d 1s Note that for in polyelectronic atoms (containing more than one electron), only the orbitals within the same sublevel are degenerate. 7.6 QUANTUM NUMBERS AND ELECTRON SPIN CHEM 161: Chapter 7 Notes page 11 of 26

12 Erwin Schrödinger (1926) developed a differential equation to find the electron's wave function ( ), and the square of the wave function ( ) indicates the probability of finding the electron near a given point probability density for an electron is called the "electron cloud" or orbital each atomic orbital has a distinct shape Each orbital is identified by a set of three integers called quantum numbers. Quantum Numbers, Energy Levels, and Orbitals FOUR quantum numbers describe distribution and behavior of electrons in atoms Each wave function ( ) corresponds to a set of 3 quantum numbers and is referred to as an atomic orbital. First (or Principal) Quantum Number (n): n=1,2,3,... relates the average distance of the electron from nucleus higher n means electron is further from nucleus, in a higher-energy (less stable) orbital Second (or Angular Momentum) Quantum Number ( ): =0,, n-1 Sublevels (s, p, d, f): gives "shape" of the electron clouds associated with each orbital The limitations on n and for n=1, =0 the 1s sublevel for n=2, =0 the 2s sublevel n=2, =1 the 2p sublevel for n=3, =0 the 3s sublevel n=3, =1 the 3p sublevel n=3, =2 the 3d sublevel for n=4, =0 the 4s sublevel n=4, =1 the 4p sublevel n=4, =2 the 4d sublevel n=4, =3 the 4f sublevel Third (or Magnetic) Quantum Number (m ): m = -,,0,, indicates the number of orbitals in each sublevel =0 (s orbital): m =0 only one type of s orbital =1 (p orbitals): m =-1, 0, 1 3 types of p orbitals: p x, p y, p z =2 (d orbitals): m =-2, -1, 0, 1, 2 5 types of d orbitals: d xy, d yz, d xz, d 2, d 2 2 z =3 (f orbitals): m =-3, -2, -1, 0, 1, 2, 3 7 types of f orbitals Fourth (or Electron Spin) Quantum Number (m s ): m s = +½ and -½ This will be discussed in more detail later in the chapter. Ex. 1: What are valid values for when n=3? x y Ex. 2: What are valid values for m when n=4 and =2? Ex. 3: Check all of the following sets of quantum numbers that are valid, and for those that are CHEM 161: Chapter 7 Notes page 12 of 26

13 not valid, explain why. a. n=2, =2, m =1, and m s = +½. b. n=1, =0, m =0, and m s = +½. c. n=4, 1, m =1, and m s = ½. d. n=3, =3, m =2, and m s = ½. Note that quantum numbers allow us to determine the number of each type of orbital in each principal energy level (n value) and sublevel ( value). 7.7 THE SIZES AND SHAPES OF ATOMIC ORBITALS The images below are boundary surface representations within which there s a 90% probability of finding the electron in a given orbital. These representations show the relative size, shape, and orientation of the various orbitals. s orbitals: spherical (see Fig on p. 325) size of the orbitals increase with n since number of protons, neutron, and electrons increase with n Boundary surface representations of the 1s, 2s, and 3s orbitals showing the increase in size with n value. A cross section of the hydrogen 1s orbital probability distribution divided into thin spherical shells. p orbitals: dumbbell-shaped (see Fig on p. 327) 3 types: p x, p y, p z (where x, y, and z indicates axis on which orbital aligns) Figure (a) below shows the probability distribution for a p z orbital. Figure (b) below shows the boundary surface representations of the p orbitals. CHEM 161: Chapter 7 Notes page 13 of 26

14 d orbitals: boundary surface representations of the d orbitals (see Fig on p. 327) 5 types: d xy, d xz, d yz,, 2, d 2 d x 2 y z f orbitals: You won t be tested on f orbitals. Be able to identify a p or d orbital given its image. CHEM 161: Chapter 7 Notes page 14 of 26

15 The interesting part... Consider the figure at the right showing the electron distribution for the 2p x orbital. Note that there is a node (zero probability) at and near the origin, so the electron is never there. How can the electron be present in either of the two lobes without going through the origin? 7.8 THE PERIODIC TABLE AND FILLING THE ORBITALS OF MULTIELECTRON ATOMS Electron Configuration: Shorthand description of the arrangement of electrons by sublevel according to increasing energy Aufbau (Building-Up) Principle Electrons are distributed in orbitals of increasing energy, where the lowest energy orbitals are filled first. Once an orbital has the maximum number of electrons it can hold, it is considered filled. Remaining electrons must then be placed into the next highest energy orbital, and so on. Parking garage analogy Orbitals in order of increasing energy: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 5d < 6p REMEMBER! Each orbital can hold 2 electrons. Each s orbital can hold 2 electrons. A set of three p orbitals can hold 6 electrons. A set of five d orbitals can hold 10 electrons. A set of seven f orbitals can hold 14 electrons. Ex. 1 Li atomic number=3 3 e - electron configuration for Li: Ex. 2 Ex. 3 electron configuration for F: electron configuration for Fe: CHEM 161: Chapter 7 Notes page 15 of 26

16 Electron configurations of atoms with many electrons can become cumbersome. Abbreviated electron configurations ( noble-gas core notation): Since noble gases are at the end of each row in the Periodic Table, all of their electrons are in filled orbitals. Such electrons are called core electrons since they are more stable (less reactive) when they belong to completely filled orbitals. valence electrons: electrons that are in the outermost shell (unfilled orbitals) Noble gas electron configurations are used to abbreviate the core electrons of all elements. [He] = 1s 2 [Kr] = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 [Ne] = 1s 2 2s 2 2p 6 [Xe] = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 [Ar] = 1s 2 2s 2 2p 6 3s 2 3p 6 Writing Electron Configurations Using the Periodic Table The Periodic Table's shape actually corresponds to the filling of energy sublevels. See Fig (p. 306), to see how electrons for each element are distributed into the energy sublevels. CHEM 161: Chapter 7 Notes page 16 of 26

17 Example: Write the electron configurations for the following using Noble Gas core notation: [Fe] = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6 = [Cd] = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 = [Ni] [I] = = Exceptions to the Aufbau (Building-Up) Principle (for Cr, Mo, W, Cu, and Ag) Atoms gain extra stability with half-filled or completely filled d subshells. If we can fill or half-fill a d subshell by promoting an electron from an s orbital to a d orbital, we do so to gain the extra stability. Example: Write the electron configurations for the following using Noble Gas core notation: Transition Metal expected electron configuration actual electron configuration chromium copper silver The Fourth (or Electron Spin) Quantum Number (m s = +½ or -½), indicates if the electron in a specific orbital (indicated by the first 3 quantum # s) is spin or spin. In 1925, two graduate students in the Netherlands, Goudsmit and Uhlenbeck, found two additional electron energy states not accounted for by Schrödinger s equations. Electrons have a quantum mechanical property called spin, with two orientations: spin or. Two other scientists, Otto Stern and Walther Gerlach, observed experimental evidence of spin when they shot a beam of Ag atoms through a non-uniform magnetic field, and the field split in two. CHEM 161: Chapter 7 Notes page 17 of 26

18 ATOMIC ORBITAL DIAGRAMS electron configuration: shorthand description of an atom s electrons among sublevels atomic orbital diagram: shows the energy sublevels within an atom and the arrangement and spin ( or ) of electrons within each orbital in the sublevels Pauli Exclusion Principle: no 2 e-s in an atom can have same four quantum #s Two electrons in the same orbital must have opposite spins For example, with the helium atom, there are three ways to represent two electrons in 1s orbital (where spin is represented with the electron pointing up or down): (a) (b) (c) for He: 1s 1s 1s but the Pauli exclusion principle rules out (a) and (b) since these show two electrons in the same orbital with the same spin. Hund's Rule: the most stable arrangement of electrons in subshells has the greatest number of parallel spins i.e., distribute electrons with same spin (up or down) and do not pair electrons until each orbital in the subshell has an electron For example, if carbon s electron configuration is: 1s 2 2s 2 2p 2 carbon s orbital diagram can be shown with the sublevels further from the nucleus having higher energy and the electrons within each orbital: Energy (a) 2s 1s (b) 2s 1s (c) 2s 1s but using Hund's rule, we know (c) would be the most stable. 2p 2p 2p CHEM 161: Chapter 7 Notes page 18 of 26

19 General Rules for Assigning Electrons in Atomic Orbital Diagrams 1. First, determine the electron configuration. 2. There is only one s orbital for each level: one 1s, one 2s, one 3s, etc. There are 3 p orbitals for each p sublevel. There are 5 d orbitals for each d sublevel. 3. Each orbital can only hold 2 electrons Each s orbital can hold 2 e, the 3 p orbitals can hold 6 e, the 5 d orbitals can hold 10 e. 4. Electrons in the same orbital must have opposite spins. 5. To fill sublevels, put one electron in each orbital (with same spin) before pairing. 6. Finally, write the quantum numbers for the outermost electrons in the atom. Orbital energy levels in atoms with more than one electron (every atom but hydrogen) Energy 3s 2s 3p 2p 3d 1s Ex. 1 Use full notation to write the electron configuration then draw the atomic orbital diagram for oxygen. Ex. 2 Use core notation to write the electron configuration, then draw the atomic orbital diagram for the valence electrons in phosphorus (electrons in the outermost shell). CHEM 161: Chapter 7 Notes page 19 of 26

20 Ex. 3 Use core notation to write the electron configuration, then draw the atomic orbital diagram for the valence electrons in cobalt (electrons in the outermost shell). Ex. 4 Use core notation to write the electron configuration, then draw the atomic orbital diagram for the valence electrons in Mo (electrons in the outermost shell). 7.9 Electron Configurations of Ions Ions of the Main Group (Representative) Elements Representative elements generally form ions ie. gain or lose electrons to achieve a noble gas electron configuration Ions from representative metals are usually isoelectronic with i.e. have the same electron configuration as one of the noble gases! Electron Configurations of Cations and Anions For IONS, one must account for the loss or gain of electrons: # electrons = atomic # (charge = change in # of valence electrons) Or you can simply use the Periodic Table Find out with which element the ion is isoelectronic Move to the left for electrons lost or to the right for electrons gained write the electron configuration for that element Example 1: Fill in the blanks for the following ions: Ion Isoelectronic with what element? Electron Config. using core notation Na + I Ion P 3 Ba +2 Al +3 Ti +4 Isoelectronic with what element? Electron Config. using core notation CHEM 161: Chapter 7 Notes page 20 of 26

21 Cations from Transition Metals, Sn, Pb Transition metals lose s electrons before the d electrons when forming cations Atom Electron Configuration using core notation Ion Zn Zn +2 Electron Configuration using core notation Sn Sn +4 Cu Cu + Cd Cd +2 Ex. Write the electron configurations for the following: Fe atom: Fe +2 ion: Fe +3 ion: Example: Given the electron configurations of Fe +2 and Fe +3, predict which ion is more stable, and explain your choice PERIODIC TRENDS IN ATOMIC PROPERTIES Atomic Radius (or Size): distance from the nucleus to the outermost electrons CHEM 161: Chapter 7 Notes page 21 of 26

22 Periodic Trend for Atomic Radius ATOMIC RADIUS Increases down a group: More p +, n, and e bigger radius Decreases from left to right along a period: Electrons that lie between the nucleus and the outermost electrons shield or screen the outermost electrons, preventing them from experiencing the full charge of the nucleus. Effective nuclear charge (Z eff ) can be approximated by the following: Z eff = # of protons # of core electrons Number of p + and e increases, but electrons go into same subshell, and other valence electrons cannot shield each other from the attractive force of the nucleus. The higher the effective nuclear charge (Z eff ) smaller radius Compare atoms of aluminum and chlorine: Trend from top to bottom like a snowman Trend from left to right like a snowman that fell to the right IONIC RADIUS: distance from the nucleus to the outermost electrons in an ion An atom loses electrons to form a cation. A cation has a smaller radius than its corresponding atom. An atom gains electrons to form an anion. An anion has a larger radius than its corresponding atom. 11 p + 11 e loses 1 e 11 p + 10 e 17 p + 17 e gains 1 e 17 p + 18 e Na atom Na + ion Cl atom Cl ion Example: Order the following in terms of increasing ionic radius: I, F, Cl, P, S. < < < < smallest radius largest radius CHEM 161: Chapter 7 Notes page 22 of 26

23 7.11 IONIZATION ENERGIES (IE) First Ionization Energy: Energy necessary to remove the first electron from a neutral atom in gaseous state to form the positively charged ion. X(g) X + (g) + e Consider the following ionization energies for magnesium: Mg(g) Mg + (g) + e IE 1 = 738 kj/mol Mg + (g) Mg 2+ (g) + e IE 2 = 1451 kj/mol Thus, to completely ionize a magnesium atom requires the following: Mg(g) Mg 2+ (g) + 2 e total IE = kj/mol = 2189 kj/mol Consider the following first ionization energies for various elements: Periodic Trend for First Ionization Energy Decreases down a group: The bigger the atom, the farther away electrons are from the positively charged nucleus. Valence electrons are less strongly attracted and are more easily removed. Increases from left to right along a period: Effective nuclear charge increases from left to right across the periodic table. As the attraction between a valence electron and the nucleus increases, more energy is required to remove a valence electron from the neutral atom. CHEM 161: Chapter 7 Notes page 23 of 26

24 Variations in Successive Ionization Energies (IE) Recognize that it becomes more difficult to remove electrons from stable ions, so ionization energies increase with an increasing number of electrons removed. We can indicate first and successive ionization energies in the following way: First ionization energy = IE 1 Second ionization energy = IE 2 Third ionization energy = IE 3 Consider the following ionization energies for aluminum: Al(g) Al + (g) + e IE 1 = 580 kj/mol Al + (g) Al 2+ (g) + e IE 2 = 1815 kj/mol Al 2+ (g) Al 3+ (g) + e IE 3 = 2740 kj/mol Al 3+ (g) Al 4+ (g) + e IE 4 = 11,600 kj/mol Note the large jump between the 3 rd and 4 th IE s for aluminum. Note that removing an electron from an Al 3+ ion requires much more energy than removing an electron from a neutral Al atom or the previous ions formed. Note that Al 3+ is a stable ion (with a positive charge AND a noble gas electron configuration), so an enormous amount of energy is required to remove an electron from a stable ion and make it unstable. Consider these Ionization Energies (in kj/mol): Note that for the elements included in the table above that the largest jump in ionization energies occurs when an electron is being removed from a stable ion with a Noble gas electron configuration. CHEM 161: Chapter 7 Notes page 24 of 26

25 Ex. 1: Between which two ionization energies (e.g. IE 1 & IE 2, IE 2 & IE 3, etc.) would you expect there to be the largest jump for the following? a. Ba: Between and b. Ti: Between and Ex. 2: This 2 nd period element has a large jump between IE 5 and IE 6 : EINSTEIN S SPLIT WITH MAINSTREAM PHYSICS Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a great deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice. Einstein in a letter to Max Born, quoted from R.W. Clark, Einstein: The Life and Times. Einstein's Grand Quest for a Unified Theory (from Sept issue of Discover magazine) by Tim Folger Einstein s split with mainstream physics came at the very height of his career. In 1927, when he was 48, the world s leading physicists gathered at a conference in Brussels to debate an issue that remains contentious to this day: What does quantum mechanics have to say about reality? Einstein had won the Nobel Prize in physics for research that showed that light consists of particles of energy research that laid the groundwork for quantum mechanics. Yet he dismissed the new theory out of hand. At the conference, he clashed with the great Danish physicist Niels Bohr, launching a feud that would last until Einstein s death in Bohr championed the strange new insights emerging from quantum mechanics. He believed that any single particle be it an electron, proton, or photon never occupies a definite position unless someone measures it. Until you observe a particle, Bohr argued, it makes no sense to ask where it is: It has no concrete position and exists only as a blur of probability. Einstein scoffed at this. He believed, emphatically, in a universe that exists completely independent of human observation. All the strange properties of quantum theory are proof that the theory is flawed, he said. A better, more fundamental theory would eliminate such absurdities. Do you really believe that the moon is not there unless we are looking at it? he asked. He saw in a way more clearly than anyone else what quantum mechanics was really like, British physicist Julian Barbour says. And he said, I don t like it. In the years after the conference in Brussels, Einstein leveled one attack after another at Bohr and his followers. But for each attack Bohr had a ready riposte. Then in 1935 Einstein devised what he thought would be the fatal blow. Together with two colleagues in Princeton, Nathan Rosen and Boris Podolsky, he found what appeared to be a serious inconsistency in one of the cornerstones of quantum theory, the uncertainty principle. Formulated in 1927 by the German physicist Werner Heisenberg, the uncertainty principle puts strict limits on how accurately one can measure the position, velocity, energy, and other properties of a particle. The very act of observing a particle also disturbs it, Heisenberg argued. If a physicist measures a particle s position, for example, he will also lose information about its velocity in the process. Einstein, Podolsky, and Rosen disagreed, and they suggested a simple thought experiment to explain why: Imagine that a particle decays into two smaller particles of equal mass and that these two daughter particles fly apart in opposite directions. To conserve momentum, both particles must have identical speeds. If you measure the velocity or position of one particle, you will know the velocity or position of the other and you will know it without disturbing the second particle in any way. The second particle, in other words, can be precisely measured at all times. Einstein and his collaborators published their thought experiment in 1935, with the title Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? The paper was in many ways Einstein s swan song: Nothing he wrote for the rest of his life would match its impact. If his critique was right, quantum mechanics was inherently flawed. Bohr argued that Einstein s thought experiment was meaningless: If the second particle was never directly measured, it was pointless to talk about its properties before or after the first particle was measured. But although quantum physics eventually CHEM 161: Chapter 7 Notes page 25 of 26

26 carried the day, it wasn t until 1982, when the French physicist Alain Aspect constructed a working experiment based on Einstein s ideas, that Bohr s argument was vindicated. In 1935 Einstein was convinced that he had refuted quantum mechanics. And from then until his death 20 years later, he devoted nearly all his efforts to the search for a unified field theory. CHEM 161: Chapter 7 Notes page 26 of 26