niels bohr and the quantum atom contents: problems in nucleus land spectral lines and rydberg’s...
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Niels Bohr and the quantum atom
Contents:•Problems in nucleus land•Spectral lines and Rydberg’s formula•Photon wavelengths from transition energies•Electron in a box•Schrödinger•Limitations of Bohr’s model
Niels Bohr1881 - 1962
Problems with the Rutherford Atom
TOC
• Acceleration/Radiation• Spectral Lines
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 Atom• Only certain orbits are allowed “stationary states”• Electron transitions create photons
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)
Example: What is the wavelength of the first Lyman line?
The first Lyman line is a transition from -3.4 eV to -13.6 eV, so it releases 10.2 eV of energy. A photon with this energy has this wavelength:E = (10.2)(1.602E-19) = 1.63404E-18 JE = hc/λ, λ = hc/E = (6.626E-34)(3.00E8)/(1.63404E-18) = 1.21649E-07 m = 122 nm
Whiteboards: Bohr Photons
1 | 2 | 3 | 4
TOC
What possible photon energies can you get from these energy levels? (there are 6 different ones)
-14.0 eV
-9.0 eV
-6.0 eV-5.0 eV
1, 4, 9, 3, 8, and 5 eV
1 4 9 3 8 5
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)?
12.1 eV W
E = hf = hc/ (6.626E-34)(3.00E8)/(86.4E-9) = 2.30069E-18 J(2.30069E-18 J)/(1.602E-19) = 12.1 eV
This could be the second Lyman line
An 102.5 nm photon is emitted. What is the energy of this photon in eV, and what transition occurred?
“Electron in a box”
TOC
• Why are only certain orbits allowed? (Demo)
nL2
h
p mp
Ek 2
2
2
22
8 Lm
hnE
ek
6 x 10-18 J W
Ek = 12(6.626E-34)2/(8(9.11E-31)(.1E-9)2) = 6.02413E-18 J (≈ 38 eV)
Try this: What would be the kinetic energy of an electron in the ground state of a “box” that is about 0.1 nm in length?me = 9.11x10-31 kg
2
22
8 Lm
hnE
ek
Schrödinger and the quantum atom
TOC
Schrödinger solves for hydrogen atomThe electron is represented by a waveCan only be solved for H, singly ionised He
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