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Electronic Structure of Atoms

Electronic Structure of Atoms. Chapter 6. Light. Made up of electromagnetic radiation . Waves of electric and magnetic fields at right angles to each other. Parts of a wave. Wavelength. l. Frequency ( n = number of cycles in 1 second Measured in hertz 1 hertz = 1cycle/second.

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Electronic Structure of Atoms

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  1. Electronic Structure of Atoms Chapter 6

  2. Light • Made up of electromagnetic radiation. • Waves of electric and magnetic fields at right angles to each other.

  3. Parts of a wave Wavelength l Frequency (n = number of cycles in 1 second Measured in hertz 1 hertz = 1cycle/second

  4. Frequency = n

  5. Kinds of EM waves • There are many different EM waves • different l and n • Visible Light is only the part our eyes can detect. (colors of the rainbow) • Greater wavelength means, smaller frequency Gamma Rays Micro- wave X-Rays UV Infrared Radio

  6. Visible Spectrum

  7. The speed of light, c • in a vacuum is 2.998 x 108 m/s • c = 3.0 x 108 m/s • c = ln

  8. Examples What is the wavelength of light with a frequency 5.89 x 1014 Hz? c 3.0 x 108 m/s • = = = 5.09 x 10-7 m = 509 nm v 5.89 x 1014 Hz (green light) What is the frequency of blue light with a wavelength of 484 nm? c 3.0 x 108 m/s v = = = 6.20 x 1014 Hz  484 x 109 m

  9. Planck and the Quantum Theory • Energy is gained or lost in whole number multiples (n) of the quantity hv. • Similar to energy required to go up stairs (opposed to going up a ramp) • Planck found that Energy is transferred to matter in “energy packets” called a quantum (hv) • Frequency = v • Planck’s constant = h = 6.63 x 10-34 J-s DE = nhn

  10. Einstein, the Photoelectric Effect, and Photons • EM radiation is quantized a stream of particles -- “photons” • Ephoton = hn = hc/l • Combine this with E = mc2 • You get the apparent mass of a photon. m = h / (lc)

  11. Is light a Wave or does it consist of particles? • Both… • Macroscopically like a wave, • But consists of a collection of photons that we only see at the atomic level. • called The Wave-Particle Duality (Like describing an entire beach and then beginning to examine the grains of sand.)

  12. Examples • Calculate the energy of one photon of yellow light whose wavelength is 589nm • Find the frequency • 5.09 x 1014 s-1 • Then use Plank’s equation to find E • 3.37 x 10-19 J

  13. Matter as a wave • Using the velocity (v) instead of the frequency (n) we get: • De Broglie’s equation l = h/mv • Can calculate the wavelength of an object.

  14. Line Spectra • Spectrum = the range of frequencies present in light • Continuous Spectrum = contains all wavelengths of light. (white light… can be broken down into “rainbow”) • Line Spectrum = contains only specific wavelengths of light.

  15. Hydrogen spectrum • Emission spectrum because these are the colors it gives off or emits. • Called a bright line emission spectrum. • There are just a few discrete lines showing 656 nm 434 nm 410 nm 486 nm

  16. Visible Spectrum

  17. Bright Line Spectra • Excited electrons return to lower NRG states • NRG is emitted in the form of a photon of definite wavelength. • Definite change in energy corresponds to: • Definite frequency • Definite wavelength • Use DE = hn = hc / l • Only certain energies are possible within any atom.

  18. Niels Bohr • Developed the Quantum Model • Described the atom like a solar system • Electrons attracted to (+) nucleus because of their (-) charge • Electrons didn’t fall into nucleus because they were moving around

  19. Bohr’s atom • Found only certain NRGs were allowed; called them NRG levels. • Putting NRG into atom moves electron away from the nucleus (ground state  excited state) • When e- returns to ground state, it gives off light of a certain NRG

  20. The Bohr Atom n = 4 n = 3 n = 2 n = 1

  21. Available NRG levels E = -2.178 x 10-18 J (Z2 / n2 ) • n = quantum number (NRG level) • Z = nuclear charge (+1 for Hydrogen) • J = energy in joules • The more negative the NRG is, the more stable the atom will be.

  22. change in Energy • When the electron moves from one energy level to another: • DE = Efinal - Einitial DE = -2.178 x 10-18J [(1/ nf2)–(1/ ni2)] l = hc / DE

  23. Shortcomings of Bohr Model • Only works for Hydrogen atoms • Electrons don’t move in circular orbits • The quantization of energy is right, but not because they are circling like planets • Questions Bohr couldn’t answer: Why are e- confined to only certain energy levels? Why don’t e- eventually spiral and crash into the nucleus?

  24. The Quantum Mechanical Model • New approach that viewed electron as a standing wave of NRG • Standing waves don’t propagate through space • Standing waves are fixed at both ends (similar to vibrations of a stringed instrument)

  25. What’s possible? • You can only have a standing wave if you have complete waves. • There are only certain allowed waves. • In the atom there are certain allowed waves called electrons. • 1925 Erwin Schroedinger described the wave function of the electron. “The Schroedinger Equation” • Much math but what is important are the solutions.

  26. Schroedinger’s Equation 22 22 22  82m 2x2 2y2 2z2 h2 • The wave function,  is a F(x, y, z) • Solutions to the equation are called orbitals. • These are not Bohr orbits. • Each solution is tied to a certain energy. • These are the energy levels. • Many strange and seemingly impossible behaviors occur when the electron is treated as a wave!    (E  V)  = 0

  27. Orbitals • Orbitals are not circular orbits for electrons • Orbitals areareas of probability for locating electrons

  28. There is a limit to what we can know… • about how the electron is moving or how it gets from one energy level to another. • about both the position and the momentum of an object. • The Heisenberg Uncertainty Principle - “we cannot know the exact location and exact momentum of an electron at the same time.”

  29. Quantum Mechanical Model and Quantum Numbers • Note: A quantum mechanical orbital is not the same as a Bohr orbit because the motion of the electron in an atom cannot be precisely measured or tracked.(Heisenberg uncertainty Principle) • There are 4 quantum numbers to describe the “location” of an electron. (sort of like how a zip code works)

  30. Principal Quantum Number (n) • Indicates probable distance from the nucleus (old Bohr orbitals) • Gives the size and energy of the orbital • Has integer values >0 • According to the periodic table, what would the highest principal quantum number be?

  31. Angular Momentum Quantum (l ) • Gives the shape of the orbital (more detail to come) • Integral values from 0 to (n-1) for each principal quantum number (n) *letters s, p, d, f come from the words sharp, principal, diffuse, and fundamental, which were used to describe certain features of spectra before quantum mechanics was developed.

  32. Magnetic Quantum Number (ml) • Relates to the orientation of the orbital in space relative to the other orbitals. (It tells you if the orbital will be on the x, y or z axis.) • Integral values from l to –l including 0.

  33. Important Observations • The shell w/ quantum #n will have exactly n subshells. • Each subshell has a specific number of orbitals. Each orbital corresponds to a different allowed value of ml. For a given value of l, there are 2l + 1 allowed values of ml. • The total number of orbitals in a shell is n2. The resulting number of orbitals for the shells – 1, 4, 9, 16 – is related to a pattern seen in the periodic table… We see the number of elements in the table – 2, 8, 18, 32 – equal twice these numbers…

  34. S orbitals n = 1 n = 2 n = 3

  35. P orbitals At another energy level the solutions are “dumbell” shaped. There are 3 possible solutions for this energy level.

  36. P Orbitals All 3 p orbitals may exist at the same time.

  37. d orbitals At another energy we get “flower” shaped orbitals for a solution. All 5 may exist at the same time

  38. F orbitals And finally, at another energy, 7 f orbitals are the solution.

  39. Orbital Energies • All orbitals with the same value of n have the same energy • The lowest energy state is called the “ground state” • When the atom absorbs energy, electrons may move to higher energy orbitals – “excited state”

  40. Electron Spin Quantum Number (ms ) • An individual orbital can hold only 2 electrons • Electrons must have opposite spins (why important?) • Spin can have two values +½ or –½

  41. Pauli Exclusion Principle “in a given atom, no two electrons can have the same set of four quantum numbers” What this means for the atom? • Each atomic sub-orbital may contain a maximum of 2 electrons • Those electrons must have opposite spins

  42. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s Helium with 2 electrons

  43. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s Li with 3 electrons

  44. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s Boron with 5 electrons

  45. 2 more important rules: • Aufbau Principle – electrons enter orbitals of lowest energy first. • Hund’s Rule -- When electrons occupy orbitals of equal energy, one electron enters each orbital before they pair.

  46. For Example: 2s 2p After the s sublevel gets two electrons, three electrons enter the p orbitals before they pair.

  47. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s

  48. Electron Configuratoin p s d f

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