Chapter 6. Electronic Structure of Atoms. Lecture Presentation. John D. Bookstaver St. Charles Community College Cottleville, MO

Transcription

1 Lecture Presentation Chapter 6 Electronic Structure of Atoms John D. Bookstaver St. Charles Community College Cottleville, MO

2 Waves Waves are periodic disturbances they repeat at regular intervals of time and distance.

3 Properties of Waves Wavelength (l) is the distance between one peak and the next. Frequency (n) is the number of waves that pass a fixed point each second. Units: Hz or s -1

4 Kinds of Electromagnetic Radiation The Electromagnetic Spectrum Song - by Emerson & Wong Yann

5 Speed of Light All electromagnetic waves travel at the same speed in a vacuum, m/s. The speed of a wave is the product of its frequency and wavelength, so for light: c ln m/s So, if either the wavelength or frequency is known, the other can be calculated.

6 Practice Exercise An FM radio station broadcasts electromagnetic radiation at a frequency of MHz (megahertz; 1 MHz = 10 6 s -1 ). Calculate the wavelength of this radiation. The speed of light is m/s to four significant digits. Answers: m Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

7 The Nature of Energy The wave nature of light does not explain how an object can glow when its temperature increases.

8 Quantization of Energy In 1900, Max Planck proposed that there is a smallest unit of energy, called a quantum. The energy of a quantum is E hn where h is Planck s constant, J s.

9 Quantized VS Continuous Change in Energy

10 The Photoelectric Effect The photoelectric effect: the process in which electrons are ejected from a metal when it is exposed to light. Einstein suggested an explanation by assuming light is a stream of particles called photons. The energy of each photon is given by Planck s equation, E = hn.

11 Sample Exercise 6.3 Energy of a Photon Calculate the energy of one photon of yellow light that has a wavelength of 589 nm. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

12 Practice Exercise A laser emits light that has a frequency of s -1. What is the energy of one photon of this radiation? Answers: J Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

13 Spectra A spectrum is a graph of light intensity as a function of wavelength or frequency. The light emitted by heated objects is a continuous spectrum; light of all wavelengths is present. Gaseous atoms produce a line spectrum one that contains light only at specific wavelengths and not at others. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

14 Line Spectra of Some Elements Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

15 The Hydrogen Spectrum Johann Balmer (1885) discovered a simple formula relating the four lines to integers. Johannes Rydberg advanced this formula. Neils Bohr explained why this mathematical relationship works. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

16 The Bohr Model Niels Bohr adopted Planck s assumption and explained these phenomena in this way: 1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies). Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

17 The Bohr Model 2. Electrons in permitted orbits have specific, allowed energies; these energies will not be radiated from the atom. 3. Energy is only absorbed or emitted in such a way as to move an electron from one allowed energy state to another; the energy is defined by E = hn Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

18 The Bohr Model The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation E = hcr ( ) H n 2 f n 2 i where R H is the Rydberg constant, m 1, and n i and n f are the initial and final energy levels of the electron. 1 1 Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

19 Schrödinger Wave Equation Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. This is known as quantum mechanics. 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. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

20 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. Three quantum numbers, represented by n, l, and m l, describe the distribution of the electron in three dimensional space. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

21 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. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

22 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. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

23 Angular Momentum Quantum Number (l) Value of l Type of orbital s p d f Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

24 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 to1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc Orbitals with the same value of n form a shell For example: All orbitals with n = 2 are said to be in the 2 nd shell Different orbital types within a shell are subshells. The set of orbitals that have the same n and l values = subshell Each subshell is designated by a # (the value of n) followed by a letter designation for l (either: s, p, d, f) For eg: if n =3 and l = 1, the orbital is called the 3p orbital

25 Magnetic Quantum Number (m l ) Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

26 Orbital Representation What we ve discussed so far: Orbitals are associated with a particular energy Wave function provides info about Electron location in space when it occupies an orbital Now we focus on: How to picture these orbitals by looking at their electron-density distributions Look at 3-D shape and directionality of the orbital Probability density changes as we move away from the nucleus Typical 3-D sketches used to describe orbitals

27 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. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

28 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. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

29 p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

30 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. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

31 For each of the following subshells, give the value of the n and the l quantum numbers. (a) 2s (b) 3d (c) 4p Test Your Skill

32 Test Your Skill For each of the following subshells, give the value of the n and the l quantum numbers. (a) 2s (b) 3d (c) 4p Answers: (a) n = 2, l = 0 (b) n = 3, l = 2 (c) n = 4, l = 1

33 Energies of Hydrogen Atom Orbitals For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. That is, they are degenerate. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

34 Energies of Orbitals for a Many-electron Atom As the number of electrons increases, though, so does the repulsion between them. Therefore, in manyelectron atoms, orbitals on the same energy level are no longer degenerate. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

35 Increasing Energy Order Based on experimental observations, subshells are usually occupied in the order 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d

36 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.

37 Pauli s 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 (n, l, m l, m s ) For a given orbital: n, l, m l are fixed but different m s values are assigned for electrons (i.e.: +1/2 or 1/2) Because there are only 2 such values it can be concluded that: An orbital can hold a maximum of two electrons and they must have opposite spins

38 The Aufbau Principle The aufbau principle: as electrons are added to an atom one at a time, they are assigned the quantum numbers of the lowest energy orbital that is available. The resulting atom is in its lowest energy state, called the ground state.

39 Electron Configurations 4p 5 This term shows the distribution of all electrons in an atom. Each component consists of A number denoting the energy level,

40 Electron Configurations 4p 5 This term 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,

41 Electron Configurations 4p 5 This term 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.

42 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. Practice : write electron configuration from H to C.

43 Electron Configurations of Elements Hydrogen contains one electron in the 1s subshell. 1s 1 Helium has two electrons in the 1s subshell. 1s 2

44 Electron Configurations of Elements Lithium has three electrons. 1s 2 2s 1 Beryllium has four electrons. 1s 2 2s 2 Boron has five electrons. 1s 2 2s 2 2p 1

45 Hund s Rule For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized. Example: Carbon, with six electrons

46 Other Elements in the Second Period N 1s 2 2s 2 2p 3 O 1s 2 2s 2 2p 4 F 1s 2 2s 2 2p 5 Ne 1s 2 2s 2 2p 6

47 Condensed Electron Configurations Heavier atoms follow aufbau principle in organization of electrons. Because their electron configurations can get long, larger atoms can use an condensed electron configuration, using a noble gas to represent core electrons. Ca: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 [Ar] 4s 2 Ar Valence electrons

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49 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.

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53 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.

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55 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. Pt

56 Some Anomalies Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. For example, electron configuration for copper is [Ar] 4s 1 3d 10 rather than the expected [Ar] 4s 2 3d 9.