1.    © 2009, Prentice-Hall, Inc. Chapter 6 Electronic Structure of Atoms

2.    Where are electrons (electrons distribution) ? -First question we will ask is: how are electrons distributed if we know that they interact through electromagnetic forces with nuclei and other electrons? -Second question we ask is how well could the such interaction mechanisms be described? (physical/mechanical model) © 2009, Prentice-Hall, Inc.

3.    EM radiation © 2009, Prentice-Hall, Inc.

4.    Prentice - Intelliome A. S. LLC 20054 What do you know about light : simple experiments (experiment 3)

5.    Prentice - Intelliome A. S. LLC 20055 What do you know about light : simple experiments (experiment 3)

6.    Prentice - Intelliome A. S. LLC 20056 What makes the light- the light sources Atoms can release EM light or absorb it Atoms don’t emit EM of all colors, only very specific wavelengths –in fact, the spectrum of wavelengths can be used to identify the element

7.    Prentice - Intelliome A. S. LLC 20057 Emission Spectrum

8.    Prentice - Intelliome A. S. LLC 20058 Spectra

9.    Prentice - Intelliome A. S. LLC 20059 What we know about the EM radiation: Electromagnetic Waves: check your radio, telephone or TV frequency or wavelength?

10.    Prentice - Intelliome A. S. LLC 200510 The Electromagnetic Spectrum light passed through a prism is separated into all its colors - this is called a continuous spectrum the color of the light is determined by its wavelength

11.    Prentice - Intelliome A. S. LLC 200511 Spectrum of white light Radiation composed of only one wavelength = monochromatic (one color). Radiation that spans a whole array of different wavelengths = continuous. White light = continuous spectrum of colors. Dark= no light. When light interacts with material it can be scattered, absorbed or emitted. Depending on the material, the interaction with different radiation will be different.

12.    Prentice - Intelliome A. S. LLC 200512 Types of Electromagnetic Radiation Classified by the Wavelength –Radiowaves = > 0.01 m low frequency and energy –Microwaves = 10 -4 m < < 10 -2 m –Infrared (IR) = 8 x 10 -7 < < 10 -5 m –Visible = 4 x 10 -7 < < 8 x 10 -7 m ROYGBIV –Ultraviolet (UV) = 10 -8 < < 4 x 10 - 7 m –X-rays = 10 -10 < < 10 -8 m –Gamma rays = < 10 -10 high frequency and energy

13.    Prentice - Intelliome A. S. LLC 200513 Light as well as electrons can be described through wave-like observables Waves are described by wavelength,, amplitude, A and frequency,. The speed of a wave, c, is given by its frequency multiplied by its wavelength: Velocity ( c ) = C = 2.9979 * 10 8 m/s (in vacuum)

14.    Prentice - Intelliome A. S. LLC 200514

15.    © 2009, Prentice-Hall, Inc. Waves To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. The distance between corresponding points on adjacent waves is the wavelength ( ).

16.    © 2009, Prentice-Hall, Inc. Waves The number of waves passing a given point per unit of time is the frequency ( ). For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

17.    © 2009, Prentice-Hall, Inc. Electromagnetic Radiation All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00 10 8 m/s. Therefore, c = 

18.    © 2009, Prentice-Hall, Inc. The Sources of Light For atoms and molecules one does not observe a continuous spectrum, as one gets from a white light source. Only a line spectrum of discrete wavelengths is observed.

19.    Prentice - Intelliome A. S. LLC 200519 656.3 486.1 434.1 410.2 Absorption Spectrum Emission Spectrum Absorption Spectrum Emission Spectrum

20.    © 2009, Prentice-Hall, Inc. # Note that electromagnetic structures can be very complex, this is just a simple wavelike approximation

21.    EM radiation interacting with electrons © 2009, Prentice-Hall, Inc.

22.    What is inside atom-experimental evidence

23.    A Simple Book-keeping Model of Electrons in EM radiation field drivers in Atom

24.    Experiments show that structures have well defined wavelike patterns

25.    What are electron distributions? electrons behave like wave like physical structures

26.    Interferences - Wave-like observables

27.    © 2009, Prentice-Hall, Inc. The Nature of Electron Distribution in EM fields Consequences : causal relationships between observables can explain phenomenological relations such as the one between mass and wavelength at certain conditions = h mv

28.    © 2009, Prentice-Hall, Inc. Consequence: causal relations (“uncertainty principle”) (  x) (  mv)  h4h4 For some systems h can be used, h= Planck’s constant, 6.626  10−34 J-s.

29.    Causal relationships can help: For example approximation - phenomenological relation: Electron energy+ Bonding energy = h E = h where h is Planck’s constant, 6.626  10 −34 J*s.

30.    © 2009, Prentice-Hall, Inc. How to measure electron distributions in atoms?

31.    Prentice - Intelliome A. S. LLC 200531 How to see electrons inside atoms? Can EM radiation help? In 1800s Hertz started kicking electrons with EM radiation

32.    Prentice - Intelliome A. S. LLC 200532 In 1800s Rydberg’s analysis of atomic line spectra (Na,H): *observables using h constant How to see electrons inside atoms? Can EM radiation help?

33.    © 2009, Prentice-Hall, Inc. The Electronic Structure of Atoms Experimental evidence: Electrons in an atom are seen as going from one well defined area to the other. Each of these areas (orbitals) corresponds to certain energy, so the colors we see correspond to the energies of photons that are equal to the energy difference between these orbital energies.

34.    © 2009, Prentice-Hall, Inc. The Electronic Structure of Atoms Electrons stay in well defined areas like standing waves stay in a resonance box and they do not gain or lose energy for certain time: we say they are in a certain state.

35.    © 2009, Prentice-Hall, Inc. The Electronic Structure of Atoms Energy can be absorbed or emitted: if absorbed electron will slow down to an outermost orbital, if emitted an electron will go down closer to the nucleus. The energy difference is Ei –Ef =Ephoton = h  h c/

36.    Prentice - Intelliome A. S. LLC 200536 Brings us back to the question how can we see electrons inside atoms with EM radiation. Model ? Experiment

37.    © 2009, Prentice-Hall, Inc. The Electronic Structure of Atoms The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:  E = −R H ( ) 1nf21nf2 1ni21ni2 - where R H is the Rydberg constant, 2.18  10 −18 J, and n i and n f are the initial and final energy levels of the electron.

38.    What about a mechanical model? How to describe these quantum waves? Quantum or wave mechanics and The future

39.    How to describe the mechanics of electron motion in many-electron atoms and 3 dimensions? Answer: Use any mechanics that describes what you see in experiments. If you use wave- models make sure that you accurately represent observed properties of electrons! Example: (Schroedinger wave equation) If electrons have wavelike patterns use a wave mechanics to describe it !! Also take into account 3 dimensions (x, y, z).

40.    Mechanics of electrons in atoms (probability as density)

41.    Orbits vs. Orbitals Pathways vs. Probability-Pathways Kicking “waves” is not as precise as kicking localized objects!

42.    Wave-like baseball: Here, you cannot have “straight” hits, the path of the ball has wavelike distribution and interferes with other objects, players etc.! The person catching the ball should expect “wavelike” distribution of incoming balls! The forces and interactions here are wavelike. See again our slit experiment and assume that the slit is a bat and detector is a “catcher”. This analogy requires more detailed knowledge of physics!

43.    How we describe the path of the ball ?: position (x, y, z coordinates) And how we describe the path of the electron ?: Wave-like distribution (quantum numbers n, l, m)

44.    Quantum or Wave Mechanics Angular Quantum Number, l. This quantum number depends on the value of n. The values of l begin at 0 and increase to (n - 1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f- orbitals. Magnetic Quantum Number, m l. This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. Magnetic quantum numbers give the 3D orientation of each orbital. Schrödinger’s equation and 3 quantum numbers: Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus.

45.    © 2009, Prentice-Hall, Inc. Quantum Mechanics Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. It is known as quantum or wave mechanics.

46.    © 2009, Prentice-Hall, Inc. Quantum Mechanics The wave equation is designated with a lower case Greek psi (  ). The square of the wave equation,  2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. Note:  is the solution of wave mechanical (Schrödinger) equation, so it represents a wavelak distribution- the symbol could also have been chosen

47.    © 2009, Prentice-Hall, Inc. Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. Each orbital describes a spatial distribution of electron density. An orbital is described by a set of three quantum numbers.

48.    © 2009, Prentice-Hall, Inc. Principal Quantum Number (n) The principal quantum number, n, describes the energy level on which the orbital resides. The values of n are integers ≥ 1.

49.    © 2009, Prentice-Hall, Inc. Angular Momentum Quantum Number (l) This quantum number defines the shape of the orbital. Allowed values of l are integers ranging from 0 to n − 1. We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

50.    © 2009, Prentice-Hall, Inc. Angular Momentum Quantum Number (l) Value of l0123 Type of orbitalspdf

51.    © 2009, Prentice-Hall, Inc. Magnetic Quantum Number (m l ) The magnetic quantum number describes the three-dimensional orientation of the orbital. Allowed values of m l are integers ranging from -l to l: −l ≤ m l ≤ l. Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

52.    © 2009, Prentice-Hall, Inc. Magnetic Quantum Number (m l ) Orbitals with the same value of n form a shell. Different orbital types within a shell are subshells.

53.    © 2009, Prentice-Hall, Inc. s Orbitals The value of l for s orbitals is 0. They are spherical in shape. The radius of the sphere increases with the value of n.

54.    © 2009, Prentice-Hall, Inc. s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.

55.    © 2009, Prentice-Hall, Inc. p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them.

56.    © 2009, Prentice-Hall, Inc. d Orbitals The value of l for a d orbital is 2. Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

57.    © 2009, Prentice-Hall, Inc. Energies of Orbitals For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. That is, they are degenerate.

58.    © 2009, Prentice-Hall, Inc. Energies of Orbitals As the number of electrons increases, though, so does the repulsion between them. Therefore, in many- electron atoms, orbitals on the same energy level are no longer degenerate.

59.    © 2009, Prentice-Hall, Inc. Spin Quantum Number, m s In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. The “spin” of an electron describes its magnetic field, which affects its energy.

60.    © 2009, Prentice-Hall, Inc. Spin Quantum Number, m s This led to a fourth quantum number, the spin quantum number, m s. The spin quantum number has only 2 allowed values: +1/2 and −1/2.

61.    © 2009, Prentice-Hall, Inc. Pauli Exclusion Principle No two electrons in the same atom can have exactly the same energy. Therefore, no two electrons in the same atom can have identical sets of quantum numbers.

62.    © 2009, Prentice-Hall, Inc. Electron Configurations This shows the distribution of all electrons in an atom. Each component consists of –A number denoting the energy level,

63.    © 2009, Prentice-Hall, Inc. Electron Configurations This shows the distribution of all electrons in an atom Each component consists of –A number denoting the energy level, –A letter denoting the type of orbital,

64.    © 2009, Prentice-Hall, Inc. Electron Configurations This shows the distribution of all electrons in an atom. Each component consists of –A number denoting the energy level, –A letter denoting the type of orbital, –A superscript denoting the number of electrons in those orbitals.

65.    © 2009, Prentice-Hall, Inc. Orbital Diagrams Each box in the diagram represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the relative spin of the electron.

66.    © 2009, Prentice-Hall, Inc. Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

67.    © 2009, Prentice-Hall, Inc. Periodic Table We fill orbitals in increasing order of energy. Different blocks on the periodic table (shaded in different colors in this chart) correspond to different types of orbitals.

68.    © 2009, Prentice-Hall, Inc. Some Anomalies Some irregularities occur when there are enough electrons to half- fill s and d orbitals on a given row.

69.    © 2009, Prentice-Hall, Inc. Some Anomalies For instance, the electron configuration for Cu and Cr. For Cr it is [Ar] 4s 1 3d 5 rather than the expected [Ar] 4s 2 3d 4.

70.    © 2009, Prentice-Hall, Inc. Some Anomalies This occurs because the 4s and 3d orbitals are very close in energy. These anomalies occur in f-block atoms, as well.

71.    Electron Configurations

72.    Energy 1s 7s 2s 2p 3s 3p 3d 6s 6p 6d6d 4s 4p 4d 4f 5s 5p 5d 5f

73.    Order of Subshell Filling in Ground State Electron Configurations 1s1s 2s2s2p2p 3s3s3p3p3d3d 4s4s4p4p4d4d4f4f 5s5s5p5p5d5d5f5f 6s6s6p6p6d6d 7s7s start by drawing a diagram putting each energy shell on a row and listing the subshells, (s, p, d, f), for that shell in order of energy, (left-to-right) next, draw arrows through the diagonals, looping back to the next diagonal each time

74.    2.Draw 9 boxes to represent the first 3 energy levels s and p orbitals 1s2s2p3s3p Example – Write the Ground State Orbital Diagram and Electron Configuration of Magnesium.

75.    3.Add one electron to each box in a set, then pair the electrons before going to the next set until you use all the electrons When pair, put in opposite arrows 1s2s2p3s3p  Example – Write the Ground State Orbital Diagram and Electron Configuration of Magnesium. 

76.    Example – Write the Ground State Orbital Diagram and Electron Configuration of Magnesium. 4.Use the diagram to write the electron configuration –Write the number of electrons in each set as a superscript next to the name of the orbital set 1s 2 2s 2 2p 6 3s 2 = [Ne]3s 2 1s2s2p3s3p 

77.    Valence Electrons the electrons in all the subshells with the highest principal energy shell are called the valence electrons electrons in lower energy shells are called core electrons chemists have observed that one of the most important factors in the way an atom behaves, both chemically and physically, is the number of valence electrons

78.    Valence Electrons Rb = 37 electrons = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 1 the highest principal energy shell of Rb that contains electrons is the 5 th, therefore Rb has 1 valence electron and 36 core electrons Kr = 36 electrons = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 the highest principal energy shell of Kr that contains electrons is the 4 th, therefore Kr has 8 valence electrons and 28 core electrons

79.    Electrons Configurations and the Periodic Table

80.    Electron Configurations from the Periodic Table elements in the same period (row) have valence electrons in the same principal energy shell the number of valence electrons increases by one as you progress across the period elements in the same group (column) have the same number of valence electrons and they are in the same kind of subshell

81.    Electron Configuration & the Periodic Table elements in the same column have similar chemical and physical properties because their valence shell electron configuration is the same the number of valence electrons for the main group elements is the same as the group number

82.    s1s1 s2s2 d 1 d 2 d 3 d 4 d 5 d 6 d 7 d 8 d 9 d 10 p 1 p 2 p 3 p 4 p 5 s2s2 p6p6 f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 f 9 f 10 f 11 f 12 f 13 f 14 12345671234567

83.    Electron Configuration from the Periodic Table the inner electron configuration is the same as the noble gas of the preceding period to get the outer electron configuration, from the preceding noble gas, loop through the next period, marking the subshells as you go, until you reach the element –the valence energy shell = the period number –the d block is always one energy shell below the period number and the f is two energy shells below

84.    Electron Configuration from the Periodic Table P = [Ne]3s 2 3p 3 P has 5 valence electrons 3p33p3 P Ne 12345671234567 1A 2A 3A4A5A6A7A 8A 3s23s2

85.    Electron Configuration from the Periodic Table As = [Ar]4s 2 3d 10 4p 3 As has 5 valence electrons As 12345671234567 1A 2A 3A4A5A6A7A 8A 4s24s2 Ar 3d 10 4p34p3

86.    The Noble Gas Electron Configuration the noble gases have 8 valence electrons –except for He, which has only 2 electrons we know the noble gases are especially nonreactive –He and Ne are practically inert the reason the noble gases are so nonreactive is that the electron configuration of the noble gases is especially stable

87.    Everyone Wants to Be Like a Noble Gas! The Alkali Metals the alkali metals have one more electron than the previous noble gas in their reactions, the alkali metals tend to lose their extra electron, resulting in the same electron configuration as a noble gas –forming a cation with a 1+ charge

88.    Everyone Wants to Be Like a Noble Gas! The Halogens the electron configurations of the halogens all have one fewer electron than the next noble gas in their reactions with metals, the halogens tend to gain an electron and attain the electron configuration of the next noble gas –forming an anion with charge 1- in their reactions with nonmetals they tend to share electrons with the other nonmetal so that each attains the electron configuration of a noble gas

89.    Everyone Wants to Be Like a Noble Gas! as a group, the alkali metals are the most reactive metals –they react with many things and do so rapidly the halogens are the most reactive group of nonmetals one reason for their high reactivity is the fact that they are only one electron away from having a very stable electron configuration –the same as a noble gas

90.    Stable Electron Configuration And Ion Charge Metals form cations by losing enough electrons to get the same electron configuration as the previous noble gas Nonmetals form anions by gaining enough electrons to get the same electron configuration as the next noble gas

91.    © 2009, Prentice-Hall, Inc.