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Electromagnetic Spectrum

Electromagnetic Spectrum. Light as a Wave - Recap. Light exhibits several wavelike properties including Refraction : Light bends upon passing from one substance to another) Dispersion : White light can be separated into colors.

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Electromagnetic Spectrum

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  1. Electromagnetic Spectrum

  2. Light as a Wave - Recap Light exhibits several wavelike properties including Refraction: Light bends upon passing from one substance to another) Dispersion: White light can be separated into colors. Diffraction: Light sources interact to give both constructive and destructive interference. c = ln l = wavelength (m) n = frequency (s-1) c = speed of light (3.00  108 m/s)

  3. Blackbody Radiation & Max Planck The classical laws of physics do not explain the distribution of light emitted from hot objects. Max Planck solved the problem mathematically (in 1900) by assuming that the light can only be released in “chunks” of a discrete size (quantized like currency or the notes on a piano). We can think of these “chunks” as particles of light called photons. E = hn E = hc/l l = wavelength (m) n = frequency (s-1) h = Planck’s constant (6.626  10-34 J-s)

  4. Photoelectric Effect In 1905 Albert Einstein explained the photoelectric effect using Planck’s idea of quantized photons of light. He later won the Nobel Prize in physics for this work.

  5. n=6 n=5 n=4 n=3 Line Spectrum of Hydrogen In 1885 Johann Balmer, a Swiss schoolteacher noticed that the frequencies of the four lines of the H spectrum obeyed the following relationship: n = k [(1/2)2 – (1/n)2] Where k is a constant and n = 3, 4, 5 or 6.

  6. Rydberg Equation When you look at the light given off by a H atom outside of the visible region of the spectrum, you can expand Balmer’s equation to a more general one called the Rydberg Equation n = (cRH)[(1/n1)2 – (1/n2)2] 1/l = RH[(1/n1)2 – (1/n2)2] E = (hcRH)[(1/n1)2 – (1/n2)2] Where RH is the Rydberg constant (1.098  107 m-1), c is the speed of light (3.00  108 m/s), h is Planck’s constant (6.626  10-34 J-s) and n1 & n2 are positive integers (with n2 > n1)

  7. Bohr Model of the Atom In 1914 Niels Bohr proposed that the energy levels for the electrons in an atom are quantized En = -hcRH (1/n)2 En = (-2.18  10-18 J)(1/n2) Where n = 1, 2, 3, 4, … n=1 n=2 n=3 n=4

  8. Louis DeBroglie & the Wave-Particle Duality of Matter l = h/mv l = wavelength (m) v = velocity (m/s) h = Planck’s constant (6.626  10-34 J-s) While working on his PhD thesis (at the Sorbonne in Paris) Louis DeBroglie proposed that matter could also behave simultaneously as an particle and a wave. This is only important for matter that has a very small mass. In particular the electron. We will see later that in some ways electrons behave like waves.

  9. Electron Diffraction Electron Diffraction Pattern Transmission Electron Microscope

  10. Werner Heisenberg & the Uncertainty Principle Dx Dp = h/4p Dx = position uncertainty Dp = momentum uncertainty (p = mv) h = Planck’s constant While working as a postdoctoral assistant with Niels Bohr, Werner Heisenberg formulated the uncertainty principle. We can never precisely know the location and the momentum (or velocity or energy) of an object. This is only important for very small objects. The uncertainty principle means that we can never simultaneously know the position (radius) and momentum (energy) of an electron, as defined in the Bohr model of the atom.

  11. Schrodinger and Electron Wave Functions In Schrodinger’s wave mechanics the electron is described by a wave function, Y. The exact wavefunction for each electron depends upon four variables, called quantum numbers they are n = principle quantum number l = azimuthal quantum number ml = magnetic quantum number ms = spin quantum number Erwin Schrodinger, an Austrian physicist, proposed that we think of the electrons more as waves than particles. This led to the field called quantum mechanics.

  12. Y2 = Probability density s-orbital Electron Density (where does the electron spend it’s time) # of radial nodes =n – l – 1

  13. Velocity is proportional to length of streak, position is uncertain. Position is fairly certain, but velocity is uncertain. Schrodinger’s quantum mechanical picture of the atom 1. The energy levels of the electrons are well known 2. We have some idea of where the electron might be at a given moment 3. We have no information at all about the path or trajectory of the electrons

  14. s & p orbitals

  15. d orbitals # of nodal planes =l

  16. Electrons produce a magnetic field. All electrons produce a magnetic field of the same magnitude Its polarity can either be + or -, like the two ends of a bar magnet Thus the spin of an electron can only take quantized values (ms=+½,-½), giving rise to the 4th quantum number

  17. Single Electron Atom Multi Electron Atom

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