Niels Bohr and the quantum atom

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• Niels Bohr and the quantum atom
• Contents
• Problems in nucleus land
• Spectral lines and Rydbergs formula
• Bohrs quantum hypothesis
• Brief Derivation of the Bohr model
• de Broglie to the rescue
• Limitations of Bohrs model

Niels Bohr 1881 - 1962
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Problems with the Rutherford Atom

• Why doesnt the electron radiate energy?
• How does this explain the spectral lines they had
  been observing?

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• Spectral lines
• Energy from excited atoms
• demo

Rydbergs 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
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Bohrs 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

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Bohrs Quantum hypothesis

• Expresses total energy of orbit.
• Emitted photon energies represent differences in
  orbital energies
• Derives the basis for the Rydberg formula

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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 its based on physics and a quantum
hypothesis.
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Whiteboards Bohr Photons 1 2
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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
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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
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de Broglie to the rescue

• Bohrs model explained the spectral lines
• It didnt explain stationary states
• de Broglie suggests standing waves

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de Broglie to the rescue

• Bohrs 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
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Limitations of Bohrs model

• Works well for H, but doesnt 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

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