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Bohr vs. Correct Model of Atom

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Bohr vs. Correct Model of Atom

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    1. Bohr vs. Correct Model of Atom

    2. Early Model for Atom Plum Pudding positive and negative charges uniformly distributed throughout the atom like plums in pudding

    3. Rutherford Scattering

    5. Nuclear Atom (Rutherford)

    6. Recap Photons carry momentum p=h/l Everything has wavelength l=h/p Uncertainty Principle DpDx > h/(2p) Atom Positive nucleus 10-15 m Electrons “orbit” 10-10 m Classical E+M doesn’t give stable orbit Need Quantum Mechanics!

    7. Some Numerology h (Planck’s constant) = 6.63 x 10-34 J-s 1 eV = kinetic energy of an electron that has been accelerated through a potential difference of 1 V 1 eV = q x ?V = 1.6 x 10-19 J hc = 1240 nm-eV m = mass of electron = 9.1 x 10-31 kg mc2 = 511,000 eV 2?ke2/(hc) = 1/137 (dimensionless)

    9. Science fiction The Bohr model is complete nonsense. Electrons do not circle the nucleus in little planet-like orbits. The assumptions injected into the Bohr model have no basis in physical reality. BUT the model does get some of the numbers right for SIMPLE atoms… Fundamental assumption of Bohr model: atomic levels are quantizedFundamental assumption of Bohr model: atomic levels are quantized

    10. Hydrogen-Like Atoms

    11. An analogy: Particle in Hole The particle is trapped in the hole To free the particle, need to provide energy mgh Relative to the surface, energy = -mgh a particle that is “just free” has 0 energy ).).

    13. An analogy: Particle in Hole Quantized: only fixed discrete heights of particle allowed Lowest energy (deepest hole) state is called the “ground state” Mention: Quantized energy means particle cannot be anywhere in the hole but only at discrete heights (or energy levels).Mention: Quantized energy means particle cannot be anywhere in the hole but only at discrete heights (or energy levels).

    14. For Hydrogen-like atoms: Energy levels (relative to a “just free” electron): check numerology: 511000/(2*137*137)=13.6 eV 1240 *137/(2*pi*511000)=0.0529 nmcheck numerology: 511000/(2*137*137)=13.6 eV 1240 *137/(2*pi*511000)=0.0529 nm

    15. Preflight 24.1 If the electron in the hydrogen atom was 207 times heavier (a muon), the Bohr radius would be 207 Times Larger Same Size 207 Times Smaller

    16. ACT/Preflight 24.2 A single electron is orbiting around a nucleus with charge +3. What is its ground state (n=1) energy? (Recall for charge +1, E= -13.6 eV) 1) E = 9 (-13.6 eV) 2) E = 3 (-13.6 eV) 3) E = 1 (-13.6 eV) Again, basically guessed on this one. Might do it as an ACTAgain, basically guessed on this one. Might do it as an ACT

    17. ACT: What about the radius? Z=3, n=1 larger than H aton same as H atom smaller than H atom greater attraction, smaller radius, more binding This is doubly ionized Li greater attraction, smaller radius, more binding This is doubly ionized Li

    18. Transitions + Energy Conservation Each orbit has a specific energy: http://www.colorado.edu/physics/2000/quantumzone/bohr2.htmlhttp://www.colorado.edu/physics/2000/quantumzone/bohr2.html

    19. Line Spectra Demo with neon, Hg, H, He discharges and diffraction gratingDemo with neon, Hg, H, He discharges and diffraction grating

    21. ACT/Preflight 24.3

    22. Spectral Line Wavelengths

    23. ACT: Spectral Line Wavelengths

    25. ACT/Preflight 24.4 45% got this correct.45% got this correct.

    26. Preflights 24.6, 24.8

    27. Quantum Mechanics Predicts available energy states agreeing with Bohr. Don’t have definite electron position, only a probability function. Java Each orbital can have 0 angular momentum! Each electron state labeled by 4 numbers: n = principal quantum number (1, 2, 3, …) l = angular momentum (0, 1, 2, … n-1) ml = component of l (-l < ml < l) ms = spin (-˝ , +˝) Compare states with seats in auditorium n=row, l=seat ml=??? Ms=male/female Compare states with seats in auditorium n=row, l=seat ml=??? Ms=male/female

    29. Summary Bohr’s Model gives accurate values for electron energy levels... But Quantum Mechanics is needed to describe electrons in atom. Electrons jump between states by emitting or absorbing photons of the appropriate energy. Each state has specific energy and is labeled by 4 quantum numbers (next time).

    30. JAVA Links Bohr Atom de Broglie Atom Schroedinger Atom

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