Chapter 6 Electronic Structure of Atoms

1. CHEMISTRYThe Central Science 9th Edition Chapter 6Electronic Structure of Atoms David P. White Chapter 6

2. The Wave Nature of Light • All waves have a characteristic wavelength, l, and amplitude, A. • The frequency, n, of a wave is the number of cycles which pass a point in one second. • The speed of a wave, s, is given by its frequency multiplied by its wavelength: • For light, this speed is c. Chapter 6

3. The Wave Nature of Light Chapter 6

4. The Wave Nature of Light

5. The Wave Nature of Light • Modern atomic theory arose out of studies of the interaction of radiation with matter. • Electromagnetic radiation moves through a vacuum with a speed of 2.99792458  10-8 m/s (3 x 108 m/s). • Electromagnetic waves have characteristic wavelengths and frequencies. • Example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red). Chapter 6

6. The Wave Nature of Light

7. The Wave Nature of Light Chapter 6

8. Quantized Energy and Photons • Planck: energy can only be absorbed or released from atoms in certain amounts called quanta. • The relationship between energy and frequency is • where h is Planck’s constant (6.626  10-34 J.s). • To understand quantization consider walking up a ramp versus walking up stairs: • For the ramp, there is a continuous change in height whereas up stairs there is a quantized change in height. Chapter 6

9. Quantized Energy and Photons • The Photoelectric Effect and Photons • The photoelectric effect provides evidence for the particle nature of light -- “quantization”. • If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal. • The electrons will only be ejected once the threshold frequency is reached. • Below the threshold frequency, no electrons are ejected. • Above the threshold frequency, the number of electrons ejected depend on the intensity of the light. Chapter 6

10. Quantized Energy and Photons • The Photoelectric Effect and Photons • Einstein assumed that light traveled in energy packets called photons. • The energy of one photon: Chapter 6

12. Line Spectra and the Bohr Model • Line Spectra • Radiation composed of only one wavelength is called monochromatic. • Radiation that spans a whole array of different wavelengths is called continuous. • White light can be separated into a continuous spectrum of colors. • Note that there are no dark spots on the continuous spectrum that would correspond to different lines. Chapter 6

14. Line Spectra and the Bohr Model • Line Spectra • Balmer: discovered that the lines in the visible line spectrum of hydrogen fit a simple equation. • Later Rydberg generalized Balmer’s equation to: • where RHis the Rydberg constant (1.096776  107 m-1), h is Planck’s constant (6.626  10-34 J·s), n1 and n2 are integers (n2 > n1). Chapter 6

15. Line Spectra and the Bohr Model • Bohr Model • Rutherford assumed the electrons orbited the nucleus analogous to planets around the sun. • However, a charged particle moving in a circular path should lose energy. • This means that the atom should be unstable according to Rutherford’s theory. • Bohr noted the line spectra of certain elements and assumed the electrons were confined to specific energy states. These were called orbits. Chapter 6

16. Line Spectra and the Bohr Model • Bohr Model • Colors from excited gases arise because electrons move between energy states in the atom. Chapter 6

17. Line Spectra and the Bohr Model • Bohr Model • Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra. • After lots of math, Bohr showed that • where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else). Chapter 6

18. Line Spectra and the Bohr Model • Bohr Model • The first orbit in the Bohr model has n = 1, is closest to the nucleus, and has negative energy by convention. • The furthest orbit in the Bohr model has n close to infinity and corresponds to zero energy. • Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (hn). • The amount of energy absorbed or emitted on movement between states is given by Chapter 6

19. Line Spectra and the Bohr Model • Bohr Model • We can show that • When ni > nf, energy is emitted. • When nf > ni, energy is absorbed Chapter 6

20. Line Spectra and the Bohr Model Bohr Model

21. Line Spectra and the Bohr Model • Limitations of the Bohr Model • Can only explain the line spectrum of hydrogen adequately. • Electrons are not completely described as small particles. Chapter 6

22. Big Rapis Public Schools: The Wave Behavior of Matter • Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature. • Using Einstein’s and Planck’s equations, de Broglie showed: • The momentum, mv, is a particle property, whereas  is a wave property. • de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small. Chapter 6

23. The Wave Behavior of Matter • The Uncertainty Principle • Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously. • For electrons: we cannot determine their momentum and position simultaneously. • If Dx is the uncertainty in position and Dmv is the uncertainty in momentum, then Chapter 6

24. Quantum Mechanics and Atomic Orbitals • Schrödinger proposed an equation that contains both wave and particle terms. • Solving the equation leads to wave functions. • The wave function gives the shape of the electronic orbital. • The square of the wave function, gives the probability of finding the electron, • that is, gives the electron density for the atom. Chapter 6

25. Quantum Mechanics and Atomic Orbitals Chapter 6

26. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers • If we solve the Schrödinger equation, we get wave functions and energies for the wave functions. • We call wave functions orbitals. • Schrödinger’s equation requires 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. Chapter 6

27. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers • Azimuthal 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, ml. 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. Chapter 6

28. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers Chapter 6

29. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers • Orbitals can be ranked in terms of energy to yield an Aufbau diagram. • Note that the following Aufbau diagram is for a single electron system. • As n increases, note that the spacing between energy levels becomes smaller. Chapter 6

30. Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers Chapter 6

31. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers Chapter 6

32. Representations of Orbitals • The s-Orbitals • All s-orbitals are spherical. • As n increases, the s-orbitals get larger. • As n increases, the number of nodes increase. • A node is a region in space where the probability of finding an electron is zero. • At a node, 2 = 0 • For an s-orbital, the number of nodes is (n - 1). Chapter 6

33. Representations of Orbitals

34. Representations of Orbitals The s-Orbitals Chapter 6

35. Representations of Orbitals • The p-Orbitals • There are three p-orbitals px, py, and pz. • The three p-orbitals lie along the x-, y- and z- axes of a Cartesian system. • The letters correspond to allowed values of ml of -1, 0, and +1. • The orbitals are dumbbell shaped. • As n increases, the p-orbitals get larger. • All p-orbitals have a node at the nucleus. Chapter 6

36. Representations of Orbitals The p-Orbitals Chapter 6

37. Representations of Orbitals • The d and f-Orbitals • There are five d and seven f-orbitals. • Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes. • Two of the d-orbitals lie in a plane aligned along the x-, y- and z-axes. • Four of the d-orbitals have four lobes each. • One d-orbital has two lobes and a collar. Chapter 6

39. Many-Electron Atoms • Orbitals and Their Energies • Orbitals of the same energy are said to be degenerate. • For n 2, the s- and p-orbitals are no longer degenerate because the electrons interact with each other. • Therefore, the Aufbau diagram looks slightly different for many-electron systems. Chapter 6

40. Orbitals and Their Energies Many-Electron Atoms

41. Many-Electron Atoms • Electron Spin and the Pauli Exclusion Principle • Line spectra of many electron atoms show each line as a closely spaced pair of lines. • Stern and Gerlach designed an experiment to determine why. • A beam of atoms was passed through a slit and into a magnetic field and the atoms were then detected. • Two spots were found: one with the electrons spinning in one direction and one with the electrons spinning in the opposite direction. Chapter 6

42. Many-Electron Atoms Electron Spin and the Pauli Exclusion Principle

43. Many-Electron Atoms • Electron Spin and the Pauli Exclusion Principle • Since electron spin is quantized, we define ms = spin quantum number =  ½. • Pauli’s Exclusions Principle: no two electrons can have the same set of 4 quantum numbers. • Therefore, two electrons in the same orbital must have opposite spins. Chapter 6

44. Many-Electron Atoms • Electron Spin and the Pauli Exclusion Principle • In the presence of a magnetic field, we can lift the degeneracy of the electrons. Chapter 6

46. Electron Configurations • Hund’s Rule • Electron configurations tells us in which orbitals the electrons for an element are located. • Three rules: • electrons fill orbitals starting with lowest n and moving upwards; • no two electrons can fill one orbital with the same spin (Pauli); • for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule). Chapter 6

47. Electron Configurations • Condensed Electron Configurations • Neon completes the 2p subshell. • Sodium marks the beginning of a new row. • So, we write the condensed electron configuration for sodium as • Na: [Ne] 3s1 • [Ne] represents the electron configuration of neon. • Core electrons: electrons in [Noble Gas]. • Valence electrons: electrons outside of [Noble Gas]. Chapter 6

48. Electron Configurations • Transition Metals • After Ar the d orbitals begin to fill. • After the 3d orbitals are full, the 4p orbitals being to fill. • Transition metals: elements in which the d electrons are the valence electrons. Chapter 6

49. Electron Configurations • Lanthanides and Actinides • From Ce onwards the 4f orbitals begin to fill. • Note: La: [Xe]6s25d14f0 • Elements Ce - Lu have the 4f orbitals filled and are called lanthanides or rare earth elements. • Elements Th - Lr have the 5f orbitals filled and are called actinides. • Most actinides are not found in nature. Chapter 6

50. Electron Configurations and the Periodic Table • The periodic table can be used as a guide for electron configurations. • The period number is the value of n. • Groups 1A and 2A have the s-orbital filled. • Groups 3A - 8A have the p-orbital filled. • Groups 3B - 2B have the d-orbital filled. • The lanthanides and actinides have the f-orbital filled. Chapter 6