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Light and Atoms

Light and Atoms. When an atom gains a photon, it enters an excited state. This state has too much energy - the atom must lose it and return back down to its ground state, the most stable state for the atom. An energy level diagram is used to represent these changes.

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Light and Atoms

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  1. Light and Atoms • When an atom gains a photon, it enters an excited state. • This state has too much energy - the atom must lose it and return back down to its ground state, the most stable state for the atom. • An energy level diagram is used to represent these changes.

  2. The Line Spectra of Several Elements Hg Fig. 7.8

  3. Energy Level Diagram • Energy Excited States photon’s path Ground State Light Emission Light Emission Light Emission

  4. Figure 7.10: Energy-level diagram for the electron in the hydrogen atom.

  5. Figure 7.11: Transitions of the electron in the hydrogen atom.

  6. Three Series of Spectral Lines of Atomic Hydrogen Fig. 7.9

  7. A desktop analogy for the H atom’s energy Fig. 7.11

  8. Emission and Absorption Spectraof Sodium Atoms Fig. 7.B

  9. Fig. 7.C

  10. Fig. 7.D

  11. Emission Energetics - I Problem: A sodium vapor light street light emits bright yellow light of wavelength = 589 nm. What is the energy change for a sodium atom involved in this emission? How much energy is emitted per mole of sodium atoms? Plan: Calculate the energy of the photon from the wavelength, then calculate the energy per mole of photons. Solution: ( 6.626 x 10 -34J s)( 3.00 x 10 8m/s) h x c wavelength Ephoton = hv = = 589 x 10 -9m Ephoton = 3.37 x 10 -19J Energy per mole requires that we multiply by Avogadro’s number. Emole = 3.37 x 10 -19J/atom x 6.022 x 1023 atoms/mole = 2.03 x 105 J/mol Emole = 203 kJ / mol

  12. Emission Energetics - II Problem: A compact disc player uses light with a frequency of 3.85 x 1014 per second. What is this light’s wavelength? What portion of the electromagnetic spectrum does this wavelength fall? What is the energy of one mole of photons of this frequency? Plan: Calculate the energy of a photon of the light using E=hv, and wavelength x C = v . Then compare the frequency with the electromagnetic spectrum to see what kind of light we have. To get the energy per mole, multiply by Avogadro’s number. Solution: 3.00 x 108m/s 3.85 x 1014/s wavelength = c / v = = 7.78 x 10 -7 m = 778 nm 778 nm is in the Infrared region of the electromagnetic spectrum Ephoton = hv = (6.626 x 10 -34Js) x ( 3.85 x 1014 /s) = 2.55 x 10 -19 J Emole = (2.55 x 10 -19J) x (6.022 x 1023 / mole) = 1.54 x 105 J/mole

  13. 1 n12 1 n22 1 2 2 1 4 2 Using the Rydberg Equation Problem: Find the energy change when an electron changes from the n=4 level to the n=2 level in the hydrogen atom? What is the wavelength of this photon? Plan: Use the Rydberg equation to calculate the energy change, then calculate the wavelength using the relationship of the speed of light. Solution: Ephoton = -2.18 x10 -18J - = Ephoton = -2.18 x 10 -18J - = - 4.09 x 10 -19J h x c E (6.626 x 10 -34Js)( 3.00 x 108 m/s) wavelength = = = 4.09 x 10 -19J wavelength = 4.87 x 10 -7 m = 487 nm

  14. Wave Motion in Restricted Systems Fig. 7.12

  15. The de Broglie Wavelengths of Several Objects Substance Mass (g) Speed (m/s)  (m) Slow electron 9 x 10 - 28 1.0 7 x 10 - 4 Fast electron 9 x 10 - 28 5.9 x 106 1 x 10 -10 Alpha particle 6.6 x 10 - 24 1.5 x 107 7 x 10 -15 One-gram mass 1.0 0.01 7 x 10 - 29 Baseball 142 25.0 2 x 10 - 34 Earth 6.0 x 1027 3.0 x 104 4 x 10 - 63 Table 7.1 (p. 274)

  16. Figure 7.23: Orbital energies of the hydrogen atom.

  17. Figure 7.18: Plot of y2 for the lowest energy level of the hydrogen atom.

  18. Figure 7.19: Probability of finding an electron in a spherical shell about the nucleus.

  19. Figure 7.21: The scanning tunneling microscope.

  20. Figure 7.20: Scanning tunneling microscope of benzene molecules on a metal surface.Photo courtesy of IBM Almaden Research Center.

  21. Figure 7.22: Quantum corral.Photo courtesy of IBM Almaden Research Center; research done by Dr. Don Eigler and co-workers.

  22. Figure 7.24: Cross-sectional representations of the probability distributions of S orbitals.

  23. Figure 7.25: Cutaway diagrams showing the spherical shape of S orbitals.

  24. Figure 7.26: The 2p orbitals.

  25. Figure 7.27: The five 3d orbitals.

  26. Light Has Momentum • momentum = p = mu = mass x velocity • p = Plank’s constant / wavelength • or: p = mu = h/wavelength • wavelength = h / mu de Broglie’s equation • de Broglie’s expression gives the wavelength relationship of a particle traveling a velocity = u !!

  27. de Broglie Wavelength Calc. - I Problem: Calculate the wavelength of an electron traveling 1% of the speed of light ( 3.00 x 108m/s). Plan: Use the de Broglie relationship with the mass of the electron, and its speed. Express the wavelength in meters and nanometers. Solution: electron mass = 9.11 x 10 -31 kg velocity = 0.01 x 3.00 x 108 m/s = 3.00 x 106 m/s h m x u 6.626 x 10 - 34Js ( 9.11 x 10 - 31kg )( 3.00 x 106 m/s ) wavelength = = = kg m2 s2 J = therefore : wavelength = 0.24244420 x 10 - 9 m = 2.42 x 10 -10 m = 0.242 nm

  28. Fig. 7.14

  29. Heisenberg Uncertainty Principle • It is impossible to know simultaneously both the position and momentum (mass X velocity) and the position of a particle with certainty !

  30. Fig. 7.15

  31. A Radial Probability Distribution of Apples

  32. Quantum Numbers Allowed Values n 1 2 3 4 L 0 0 1 0 1 2 0 1 2 3 mL 0 0 -1 0 +1 0 -1 0 +1 0 -1 0 +1 -2 -1 0 +1 +2 -2 -1 0 +1 +2 -3 -2 -1 0 +1 +2 +3

  33. Determining Quantum Numbers for an Energy Level (Like S.P. 7.5) Problem: What values of the azimuthal (L) and magnetic (m) quantum numbers are allowed for a principal quantum number (n) of 4? How many orbitals are allowed for n=4? Plan: We determine the allowable quantum numbers by the rules given in the text. Solution: The L values go from 0 to (n-1), and for n=3 they are: L = 0,1,2,3. The values for m go from -L to zero to +L For L = 0, mL = 0 L = 1, mL = -1, 0, +1 L = 2, mL = -2, -1, 0, +1, +2 L = 3, mL = -3, -2, -1, 0, +1, +2, +3 There are 16 mL values, so there are 16 orbitals for n=4! as a check, the total number of orbitals for a given value of n is n2, so for n = 4 there are 42 or 16 orbitals!

  34. Fig 7.16

  35. Radial probability “Accurate” “Stylized” Combined area distribution representation of the 2p of the three 2p of the 2p distribution orbitals: 2px, 2py distribution and 2pz orbitals Fig. 7.17

  36. Fig. 7.18

  37. Fig. 7.19

  38. Quantum Numbers - I • 1) Principal Quantum Number = n • Also called the “energy “ quantum number, indicates the approximate distance from the nucleus . • Denotes the electron energy shells around the atom, and is derived directly from the Schrodinger equation. • The higher the value of “n” , the greater the energy of the orbital, and hence the energy of electrons in that orbital. • Positive integer values of n = 1 , 2 , 3 , etc.

  39. Quantum Numbers - II • 2) Azimuthal • Denotes the different energy sublevels within the main level “n” • Also indicates the shape of the orbitals around the nucleus. • Positive interger values of L are : 0 ( n-1 ) • n = 1 , L = 0 n = 2 , L = 0 and 1 n = 3 , L = 0 , 1 , 2

  40. Quantum Numbers - III • 3) Magnetic Quantum Number - mL Also called the orbital orientation quantum # • denotes the direction or orientation in a magnetic field - or it denotes the different magnetic geometriesound the nucleus - three dimensional space • values can be positive and negative (-L 0 +L) • L = 0 , mL = 0 L =1 , mL = -1,0,+1 L = 2 , mL = -2,-1,0,1,2

  41. Quantum Numbers Noble Gases Electron OrbitalsNumber of ElectronsElement 1s2 2 He 1s2 2s22p6 10 Ne 1s2 2s22p6 3s23p6 18 Ar 1s2 2s22p6 3s23p6 4s23d104p6 36 Kr 1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6 54 Xe 1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6 6s24f14 5d106p6 86 Rn 1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6 6s24f145d106p6 7s25f146d10?

  42. The Periodic Table of the Elements Electronic Structure H He Li Be B C N O F Ne Ar Na Mg Al Si P S Cl Kr K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Xe Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Rn Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Fr Ra Ac Rf Ha Sg Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr “ S” Orbitals “ P” Orbitals “ f ” Orbitals “ d” Orbitals

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