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Niels Bohr and the quantum atom Contents: Problems in nucleus land

Niels Bohr and the quantum atom Contents: Problems in nucleus land Spectral lines and Rydberg’s formula Bohr’s quantum hypothesis Brief Derivation of the Bohr model de Broglie to the rescue Limitations of Bohr’s model. Niels Bohr 1881 - 1962. Problems with the Rutherford Atom.

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Niels Bohr and the quantum atom Contents: Problems in nucleus land

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  1. Niels Bohr and the quantum atom • Contents: • Problems in nucleus land • Spectral lines and Rydberg’s formula • Bohr’s quantum hypothesis • Brief Derivation of the Bohr model • de Broglie to the rescue • Limitations of Bohr’s model Niels Bohr 1881 - 1962

  2. Problems with the Rutherford Atom • Why doesn’t the electron radiate energy? • How does this explain the spectral lines they had been observing? TOC

  3. Spectral lines • Energy from excited atoms • demo Rydberg’s Formula: (FYI) 1/ = R(1/22 - 1/n2), n = 3, 4, ...(Balmer) (Visible) 1/ = R(1/12 - 1/n2), n = 2, 3, ...(Lyman) (UV) 1/ = R(1/32 - 1/n2), n = 4, 5, ...(Paschen) (IR) (R = 1.097 x 10-7 m-1) H He Sun TOC

  4. Bohr’s Quantum hypothesis • Bohr quantizes the angular momentum of the electrons: (Something needs to be quantized) • L = mvrn =nh/2, n = 1, 2, 3, ... (FYI) • Solves the condition of orbit • (Coulombic = centripetal) • Orbits are discrete TOC

  5. Bohr’s Quantum hypothesis • Expresses total energy of orbit. • Emitted photon energies represent differences in orbital energies • Derives the basis for the Rydberg formula TOC

  6. Energy levels and photon energy 1/ = R(1/22 - 1/n2), n = 3, 4, ...(Balmer) (Visible) 1/ = R(1/12 - 1/n2), n = 2, 3, ...(Lyman) (UV) 1/ = R(1/32 - 1/n2), n = 4, 5, ...(Paschen) (IR) Emitted photon energies represent differences in orbital energies Only now it’s based on physics and a quantum hypothesis. TOC

  7. Whiteboards: Bohr Photons 1 | 2 TOC

  8. What is the wavelength of the photon released from the third Lyman spectral line (from -.85 to -13.6 eV)? E = hf = hc/  E = -.85 - -13.6 = 12.75 eV E = (12.75 eV)(1.602E-19J/eV) = 2.04E-18J  = hc/E = 97.3 = 97 nm W 97 nm

  9. What is the wavelength of the photon released from the second Balmer spectral line (from –0.85 to -3.4 eV)? E = hf = hc/  E = -0.85 -3.4 = 2.55 eV E = (2.55 eV)(1.602E-19J/eV) = 4.09E-19J  = hc/E = 487 = 490 nm W 490 nm

  10. de Broglie to the rescue • Bohr’s model explained the spectral lines • It didn’t explain stationary states • de Broglie suggests standing waves TOC

  11. de Broglie to the rescue • Bohr’s quantum hypothesis: mvrn =nh/2 • Solve for circumference: 2rn =nh/mv =nh/p • de Broglie wavelength:  = h/p • Bohr orbits are multiples of de Broglie  They knew they were on to something TOC

  12. Limitations of Bohr’s model • Works well for H, but doesn’t even work for He • Did not explain • Spectral fine structure • Brightness of lines • Molecular bonds • Theory was not complete. • But otherwise it generally kicked tuckus TOC

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