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Chapter 7

Chapter 7. Electrons in Atoms. Properties of Electrons. Electrons display both particle properties and wave properties. Electrons were discovered by JJ Thompson Thompson also measured the charge/mass ratio Milikan was able to determine the charge on an electron

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Chapter 7

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  1. Chapter 7 Electrons in Atoms

  2. Properties of Electrons • Electrons display both particle properties and wave properties. • Electrons were discovered by JJ Thompson • Thompson also measured the charge/mass ratio • Milikan was able to determine the charge on an electron • Davisson and Germer discovered the wave nature of an electron at Bell Labs in 1927

  3. The Atom Model Different models of atoms • Thompson developed the plumb pudding model of an atom 1898 • Rutherford suggested the planetary model (i.e. electrons orbit the nucleus) • Bohr applied concepts of quantization to Rutherford’s model to develop the Bohr model • Bohr model lasted 10 years, and was replaced by a wave model, called the quantum mechanical model, based on the wave nature of electrons.

  4. Properties of Waves Energy has properties of waves, for example electromagnetic energy Wavelength (m) Amplitude (m) Speed 3.0X108 m/s Energy (j) Frequency(1/s, Hz)

  5. Properties of Waves Wavelength () is the distance from one wave crest to another in meters. The frequency () of a wave expresses the number times a wave passes a given point in some unit of time in 1/s. Amplitude of a wave is the height of the crest or depth of the trough with respect to the center line of the wave in meters.

  6. Electromagnetic Radiation 10-12 10-8 10-10 10-4 10-2 10-7 102 100 Uv-rays Infrared rays Micro Waves (Radar) X- rays Visible rays Radio and Television waves Gamma rays Increasing wave length in meters Increasing energy

  7. Visible Radiation

  8. Electromagnetic Radiation Our major source of EM comes from our sun. EM travels at the speed of light 3.0x108m/s Has both wave properties and particle properties Photons are the particles possessed by EM

  9. Behavior of Waves • Waves refract or bend when they pass from one medium to another with different densities. • Diffraction is the bending of electromagnetic radiation as it passes around the edge of an object or through narrow openings. • Interference is the interaction of waves that results in either reinforcing their amplitudes or canceling them out.

  10. Diffraction and Interference

  11. Refraction White Light R O Y G The shortest wave lengths bend longer ones, thus violet is the shortest B I V Davisson and Germer discovered the wave nature of an electron at Bell Labs in 1927 by observing electron diffraction.

  12. Evidence ofQuantization The red-orange light from hydrogen gas passes through a prism to form a line spectra.Each different colored light has its own unique energy.

  13. Atomic Spectrum of Sodium

  14. Absorption Spectra

  15. Types of Spectra • Atomic emission spectra consist of bright lines on a dark background. • Atomic absorption spectra consist of characteristic series of dark lines produced when free gaseous atoms are illuminated by external sources of radiation.

  16. Hydrogen Line Spectrum

  17. Quantum Theory • Max Planck proposed that light can have both wavelike and particle-like properties. • A quantum is the smallest discrete quantity of a particular form of energy. • Particles of radiant energy are known as quanta. • Quantum theory is based on the idea that energy is absorbed and emitted in discrete quanta.

  18. Quantum Theory • Something that is quantized has values that are restricted to whole-number multiples of a specific base value. • The energy of a quantum of radiation is: • E = h where h is Planck’s constant • h = 6.6260755 x 10-34 J•s • Or E = hc/

  19. Particle Nature • Einstein called the packets photons. • Each packet of electromagnetic radiation energy is called a quantum.

  20. Photoelectric Effect • The photoelectric effect is the release of electrons from a metal as a result of electromagnetic radiation. • The photoelectric effect can be explained if electromagnetic radiation consists of tiny particles called photons.

  21. The Hydrogen Spectrum • Johannes Rydberg revised Balmer’s equation to describe the complete hydrogen spectrum. N1 is a whole number that remains fixed for a series of calculations in which n2 is also a whole number with values of n1+1, n1+2,… for successive line in the spectrum.

  22. Example What is the wavelength of the line in the visible spectrum corresponding to n1 = 2 and n2 = 4?

  23. The Bohr Model • The electron in a hydrogen atom occupies a discrete energy level and may exist only in the available energy levels. • The electron may move between energy levels by either absorbing or emitting specific amounts of energy. • Each energy level is designated by a specific value for n, called the principal quantum number.

  24. Energy of Electronic Transitions • Neils Bohr derived the following formula for the possible energy differences (E) be any pair of energy levels with values n1 and n2. m and e is the mass and charge of the electron.

  25. Hydrogen Spectrum • An energy level is an allowed state that an electron can occupy in an atom. • Movements of electrons between energy levels are called electron transitions.

  26. Electronic States • The lowest energy level available to an electron in an atom is its ground state. • An excited state of an electron in an atom is any energy state above the ground state.

  27. Excited and Relaxed Electrons In terms of the Bohr model absorption and emission looks like this.

  28. Excited and Relaxed Electrons Electrons move between energy levels by absorbing and emitting energy in the form of light. We call the lowest energy level the ground state. The higher energy level is called the excited state.

  29. Problems with the Bohr Model • The Bohr model applies only to one electron atoms. • The Bohr model doesn’t account for the observed spectra of multielectron elements or ions. • The movement of electrons in atoms is much less clearly defined than Bohr allowed.

  30. Particle or Waves? • If electromagnetic radiation behaves as a particle, de Broglie reasoned, why couldn’t a particle in motion, such as an electron, behave as a wave? • de Broglie’s Equation •  = h/mu (m in kg and u in m/s)

  31. Electrons as Waves • De Broglie reasoned that an electron in a hydrogen atom could behave as a circular wave oscillating around the nucleus. • If electrons are moving around the nucleus in a continuous manor, the state of the electron must be described by a quantum number, n.

  32. Tacoma Narrows Bridge http://www.youtube.com/watch?v=P0Fi1VcbpAI

  33. The Uncertainty Principle • Quantum mechanics allows us to predict the probabilities of where we can find an electron. • We cannot map out on the path an electron travels. • The Heisenberg’s uncertainty principle says that you cannot determine the position and momentum of an electron at the same time.

  34. Electron Wave Equations • The description of the behavior of particles as waves is called wave mechanics or quantum mechanics. • The mathematical description of an electron wave is called the wave equation. • Wave functions, , are mathematical descriptions of the motion of electron waves as they vary with location and with time.

  35. Quantum Numbers • The principle quantum number, n, is a positive integer that indicates the shell and relative size of orbital(s). • The angular momentum quantum number,l, is an integer from zero to n-1. It defines the shape of the orbital and subshell. Value of l 0 1 2 3 4 Letter identifier s p d f g

  36. Quantum Numbers • The magnetic quantum number, ml, is an integer with a value from -l to +l. It defines the orientation of an orbital in the space around the nucleus of an atom. • The spin magnetic quantum number, ms, is to account for the two possible spin orientations. The values for ms are +1/2 and -1/2.

  37. Quantum Number Relationships

  38. Electron Identifier It takes a total of 4 quantum numbers to identify an electron in a particular atom. Like it’s student ID no. 4py+1/2 spin QN; ms=1/2 (clockwise or counterclockwise magnetic QN; ml=0 (shape orientation) angularmomentum QN; l=1 (volume shape) principal QN; n=4 (size and energy)

  39. Quantum Numbers

  40. Practice What are the letter designations of all the subshells in the n = 5 energy level or shell? What is total number of orbitals in the n = 5 shell?

  41. Shape and Sizes of Orbitals • Psi squared, 2, defines the space, called an orbital, in atom where the probability of finding an electron is high. • A radial distribution plot is a graphical representation of the probability of finding an electron in a thin spherical layer near the nucleus of an atom.

  42. Probability Electron Density for 1s Orbital

  43. Comparison of s Orbitals

  44. The Three 2p Orbitals

  45. The Five 3d Orbitals

  46. Assigning Quantum Numbers • Pauli’s exclusion principle - no two electrons in an atom may have the same set of four quantum numbers. • An orbital can only hold two electrons and they must have opposite spins.

  47. Practice Write the set of quantum numbers which describe each electron in the three 2p orbitals.

  48. Practice Which of the following combinations of quantum number are allowed? • n = 1, l = 1, ml = 0 • n = 3, l = 0, ml = 0 • n = 1, l = 0, ml = -1 • n = 2, l = 1, ml = 2

  49. 3s 3p 3d E 2s 2p 1s Orbital Energy Notation Hydrogen Atom

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