Niels Bohr and the quantum atom Contents: Problems in nucleus land
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Transcript of 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 Bohr1881 - 1962
Problems with the Rutherford Atom
TOC
• Why doesn’t the electron radiate energy?
• How does this explain the spectral lines they had been observing?
Spectral lines•Energy from excited atoms•demo
H
He
Sun
TOC
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)
Bohr’s Quantum hypothesis
TOC
• 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
Bohr’s Quantum hypothesis
TOC
• Expresses total energy of orbit.• Emitted photon energies represent
differences in orbital energies• Derives the basis for the Rydberg formula
Energy levels and photon energy
TOC
Emitted photon energies represent differences in orbital energies
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)
Only now it’s based on physics and a quantum hypothesis.
Whiteboards: Bohr Photons
1 | 2
TOC
97 nm W
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
What is the wavelength of the photon released from the third Lyman spectral line (from -.85 to -13.6 eV)?
490 nm W
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
What is the wavelength of the photon released from the second Balmer spectral line (from –0.85 to -3.4 eV)?
de Broglie to the rescue
TOC
• Bohr’s model explained the spectral lines• It didn’t explain stationary states• de Broglie suggests standing waves
de Broglie to the rescue
TOC
• Bohr’s quantum hypothesis: mvrn = nh/2
• Solve for circumference: 2rn = nh/mv = nh/p• de Broglie wavelength: = h/p• Bohr orbits are multiples of de Broglie
They knew they were on to something
Limitations of Bohr’s model
TOC
• 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