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Atomic Structure and Periodicity

Atomic Structure and Periodicity. Chapter 7. Overview. Introduce Electromagnetic Radiation and The Nature of Matter. Discuss the atomic spectrum of hydrogen and Bohr model. Describe the quantum mechanical model of the atoms and quantum numbers.

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Atomic Structure and Periodicity

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  1. Atomic Structure and Periodicity Chapter 7

  2. Overview • Introduce Electromagnetic Radiation and The Nature of Matter. • Discuss the atomic spectrum of hydrogen and Bohr model. • Describe the quantum mechanical model of the atoms and quantum numbers. • Use Aufbau principle to determine the electron configuration of elements. • Highlight periodic table trends.

  3. Matter and Energy • Matter and Energy were two distinct concepts in the 19th century. • Matter was thought to consist of particles, and had mass and position. • Energy in the form of light was thought to be wave-like.

  4. Physical Properties of Waves Wavelength (l) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough.

  5. Properties of Waves Frequency (n) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (v or c) of the wave = l x n

  6. 1-waves can bend around small obstacles 2-and fan out from pinholes 3-particles effuse from pinholes

  7. Electromagnetic Radiation Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. • Electromagnetic radiation travels through space at the speed of light in a vacuum.

  8. Maxwell (1873), proposed that visible light consists of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 108 m/s All electromagnetic radiation l x n = c 7.1

  9. Electromagnetic Waves • Electromagnetic Waves have 3 primary characteristics: • 1. Wavelength: distance between two peaks in a wave. • 2. Frequency: number of waves per second that pass a given point in space. • 3. Speed: speed of light is 2.9979  108 m/s.

  10. http://www.colorado.edu/physics/2000/waves_particles/wpwaves5.htmlhttp://www.colorado.edu/physics/2000/waves_particles/wpwaves5.html

  11. Electromagnetic Wave Movie

  12. Wavelength and frequency can be interconverted. •  = c/ •  = frequency (s1) • = wavelength (m) • c = speed of light (m s1)

  13. Electromagnetic Spectrum

  14. Plank • Studied radiation emitted by heated bodies. • Results could not be explained by the old physics which stated that matter can absorb and emit any quantity of energy. Black Body Radiation

  15. Planck’s Constant n n Transfer of energy is quantized, and can only occur in discrete units, called quanta. • E = change in energy, in J • h = Planck’s constant, 6.626  1034 J s • = frequency, in s1 • = wavelength, in m n = integer = 1,2,3…

  16. Particle Properties of Light hn Photoelectric Effect Solved by Einstein in 1905 KE e- Photon is a “particle” of light hn = KE + BE KE = hn - BE 7.2

  17. Diffraction • X-Ray Diffraction showed also that light has particle properties.

  18. Figure 7.5: (a) Diffraction occurs when electromagnetic radiation is scattered from a regular array of objects, such as the ions in a crystal of sodium chloride. The large spot in the center is from the main incident beam of X rays. (b) Bright spots in the diffraction pattern result from constructive interference of waves. The waves are in phase; that is, their peaks match. (c) Dark areas result from destructive interference of waves. The waves are out of phase; the peaks of one wave coincide with the troughs of another wave.

  19. Diffraction Movie

  20. Photoelectric Effect Movie

  21. Energy and Mass • Energy has mass • E = mc2 Einstein Equation • E = energy • m = mass • c = speed of light

  22. Energy and Mass Radiation in itself is quantized

  23. Wavelength and Mass de Broglie’s Equation •  = wavelength, in m • h = Planck’s constant, 6.626  1034 J s = kg m2 s1 • m = mass, in kg • v= speed, in ms1

  24. A photon has a frequency of 6.0 x 104 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? l n Radio wave l x n = c l = c/n l = 3.00 x 108 m/s / 6.0 x 104 Hz l = 5.0 x 103 m l = 5.0 x 1012 nm

  25. Atomic Spectrum of Hydrogen Figure 7.6: (a) A continuous spectrum containing all wavelengths of visible light. (b) The hydrogen line spectrum contains only a few discrete wavelengths.

  26. Atomic Spectrum of Hydrogen • Continuous spectrum: Contains all the wavelengths of light. • Line (discrete) spectrum: Contains only someof the wavelengths of light.

  27. ( ) En = -RH z2 n2 Bohr’s Model of the Atom (1913) • e- can only have specific (quantized) energy values • light is emitted as e- moves from one energy level to a lower energy level n (principal quantum number) = 1,2,3,… RH (Rydberg constant) = 2.18 x 10-18J 7.3

  28. E = hn E = hn

  29. ni = 3 ni = 3 f i ni = 2 nf = 2 DE = RH i f ( ) ( ) ( ) Ef = -RH Ei = -RH nf = 1 nf = 1 1 1 1 1 n2 n2 n2 n2 Ephoton = DE = Ef - Ei

  30. What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? l = h/mv h in J•s m in kg u in (m/s) l = 6.63 x 10-34 / (2.5 x 10-3 x 15.6) l = 1.7 x 10-32 m = 1.7 x 10-23 nm

  31. Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. Ephoton = DE = RH i f ( ) 1 1 n2 n2 Ephoton = 2.18 x 10-18 J x (1/25 - 1/9) Ephoton = DE = -1.55 x 10-19 J Ignore the (-) sign for l and  Ephoton = h x c / l l = h x c / Ephoton l= 6.63 x 10-34 (J•s) x 3.00 x 108 (m/s)/1.55 x 10-19J l=1280 nm

  32. The Bohr Model • Ground State: The lowest possible energy state for an atom (n = 1). • Ionization: nf =  => 1/nf2 = 0 => E=0 for free electron. • Any bound electron has a negative value to this reference state.

  33. Ephoton = DE = RH i f hc ( ) E = h = l 1 1 n2 n2 To be well memorized P = mv E = mc2

  34. Schrodinger Wave Equation • In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e- • Wave function (Y) describes: • . energy of e- with a given Y • . probability of finding e- in a volume of space • Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.

  35. Quantum Mechanics • Based on the wave propertiesof the atom •  = wave function • = mathematical operator • E = total energy of the atom • A specific wave function is often called an orbital.

  36. n=1 n=2 n=3 Schrodinger Wave Equation Y = fn(n, l, ml, ms) principal quantum number n n = 1, 2, 3, 4, …. distance of e- from the nucleus

  37. Quantum Numbers (QN) • 1. Principal QN(n = 1, 2, 3, . . .) - related to size and energy of the orbital. • 2.Angular Momentum QN(l = 0 to n 1) - relates to shape of the orbital. • 3. Magnetic QN(ml = l to l) - relates to orientation of the orbital in space relative to other orbitals. • 4.Electron Spin QN(ms= +1/2, 1/2) - relates to the spin statesof the electrons.

  38. Pauli Exclusion Principle In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, ms). Therefore, an orbital can hold only two electrons, and they must have opposite spins.

  39. Probability Distribution • SQUARE of the wave function: Y2 • probability of finding an electron at a given position Radial probability distribution is the probability distribution in each spherical shell.

  40. Where 90% of the e- density is found for the 1s orbital e- density (1s orbital) falls off rapidly as distance from nucleus increases

  41. Figure 7.12: (a) Cross section of the hydrogen 1s orbital probability distribution divided into successive thin spherical shells. (b) The radial probability distribution.

  42. Figure 7.20: A comparison of the radial probability distributions of the 2s and 2p orbitals. P orbital is more diffuse Zero probability to be in the nucleus Probability to be in the nucleus

  43. Figure 7.21: (a) The radial probability distribution for an electron in a 3s orbital. (b) The radial probability distribution for the 3s, 3p, and 3d orbitals.

  44. Heisenberg Uncertainty Principle • x= position • mv = momentum • h = Planck’s constant • The more accurately we know a particle’s position, the less accurately we can know its momentum.

  45. Schrodinger Wave Equation Y = fn(n, l, ml, ms) angular momentum quantum number l for a given value of n, l= 0, 1, 2, 3, … n-1 l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e- occupies

  46. ml -l to +l

  47. Each orbital can take a maximum of two electrons and a minimum of Zero electrons. • Zero electrons does not mean that the orbital does not exist.

  48. Degenerate

  49. Figure 7.13: Two representations of the hydrogen 1s, 2s, and 3s orbitals.

  50. Figure 7.14: Representation of the 2p orbitals. (a) The electron probability distributed for a 2p orbital. (b) The boundary surface representations of all three 2p orbitals.

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