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

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• 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

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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

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• 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

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• 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

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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

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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

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

de Broglie to the rescue

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• 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

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• 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