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Absorption / Emission of Photons and Conservation of Energy

hv. hv. Absorption / Emission of Photons and Conservation of Energy. E f - E i = hv. E i - E f = hv. Energy Levels of Hydrogen. Electron jumping to a higher energy level. E = 12.08 eV. Spectrum of Hydrogen, Emission lines. Bohr’s formula:.

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Absorption / Emission of Photons and Conservation of Energy

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  1. hv hv Absorption / Emission of Photonsand Conservation of Energy Ef - Ei = hv Ei - Ef = hv

  2. Energy Levels of Hydrogen

  3. Electron jumping to a higher energy level E = 12.08 eV

  4. Spectrum of Hydrogen, Emission lines Bohr’s formula:

  5. Hydrogen is therefore a fussy absorber / emitter of light It only absorbs or emits photons with precisely the right energies dictated by energy conservation

  6. Electron in a Hydrogen Atom • The three quantum numbers: • n = 1, 2, 3, … • l = 0, 1, …, n-1 • m = -l, -l+1, …, l-1, l • For historical reasons, l = 0, 1, 2, 3 is also known as s, p, d, f

  7. 1s Orbital

  8. Density of the cloud gives probability of where the electron is located

  9. 2s and 2p Orbitals

  10. Another diagram of 2p orbitals Note that there are three different configurations corresponding to m = -1, 0, 1

  11. 3d Orbitals Now there are five different configurations corresponding to m = -2, -1, 0, 1, 2

  12. 4f Orbitals There are seven different configurations corresponding to m = -3, -2, -1, 0, 1, 2, 3

  13. The excited atom usually de-excites in about 100 millionth of a second. • The subsequent emitted radiation has an energy that matches that of the orbital change in the atom. • This emitted radiation gives the characteristic colors of the element involved.

  14. Emission Spectra Continuous Emission Spectrum Slit White Light Source Prism Photographic Film

  15. Emission Spectra of Hydrogen Discrete Emission Spectrum Slit Film Low Density Glowing Hydrogen Gas Prism Photographic Film

  16. Discrete Emission Spectrum Discrete Absorption Spectrum Slit Hot Hydrogen Gas Film White Light Source Prism Photographic Film Portion of the Absorption Spectrum of Hydrogen

  17. Absorption Spectra • Frequencies of light that represent the correct energy jumps in the atom will be absorbed. • When the atom de-excites, it may emit the same kinds of frequencies it absorbed. • However, this emission can be in any direction.

  18. Continous Spectrum Hot Gas Portion of the Emission Spectrum Cold Gas Absorption Spectrum Emission and Absorption

  19. Absorption spectrum of Sun Emission spectra of various elements

  20. Usually the Emission spectrum has more “features” of the absorption spectrum Atom de-excitation, Emission lines from the excited states Atom excitation, Absorption lines from the ground state (n=1)

  21. Schrodinger equation for one electron atoms Coulomb potential

  22. Radial and angular part

  23. BORN POSTULATE What is the physical meaning of the wave function? The probability of finding an electron in a certain region of space is proportional to y2, the square of the value of the wavefunction at that region. y can be positive or negative. y2 is always positive y2 is called the “electron density”

  24. 1 1 3/2 y1s = e -r/ao (ao: first Bohr radius=0.529 Å) p ao 1 1 3 y21s = e -2r/ao p ao y21s r E.g., the hydrogen ground state

  25. Radial electron densitiesThe probability of finding an electron at a distance r from the nucleus, regardless of direction The radial electron density is proportional to r2y2 Dr Surface = 4pr2 Volume of shell = 4pr2 Dr

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