Download 03-02BohrAtom

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 Bohr
1881 - 1962
Problems with the Rutherford Atom
• Acceleration/Radiation
• Spectral Lines
Spectral lines
•Energy from excited atoms
•demo
H
Rydberg’s
Formula: (FYI)
1He
/ =
1/ =

1Sun
/ =
R(1/22 - 1/n2), n = 3, 4, ...(Balmer) (Visible)
R(1/12 - 1/n2), n = 2, 3, ...(Lyman) (UV)
R(1/32 - 1/n2), n = 4, 5, ...(Paschen) (IR)
(R = 1.097 x 10-7 m-1)
Bohr’s Quantum Atom
Assumptions of Bohr’s model:
1. Only certain orbits are allowed “stationary states”
2. Electron transitions between states create photons:
Example 1: 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 J
E = hc/λ, λ = hc/E =
(6.626E-34)(3.00E8)/(1.63404E-18) =
1.21649E-07 m = 122 nm
3. Angular Momentum is Quantised: (show that mvr = I…..but why????)
Example 2: Show that mvr is angular momentum (L = I)
Ultimately, the energy levels can be
simplified to this expression.
Book derives it – triumph of HS algebra
Why is it negative?
Example 3: What is the energy level of the 4th orbital, and the 2nd
orbital?
What wavelength of light corresponds to a 4 to 2 transition for a
Hydrogen atom? (The 2nd Balmer line)
Whiteboards:
Bohr Photons
1|2|3|4
What possible photon energies can you get from these
energy levels? (there are 6 different ones)
-5.0 eV
-6.0 eV
-9.0 eV
-14.0 eV
5, 8, 9 and 3, 4 and 1 eV
5 89
3 4
1
What is the wavelength of the
photon released from the
third Lyman spectral line
(from -0.85 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
97 nm
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
490 nm
An 102.5 nm photon is emitted. What is
the energy of this photon in eV, and
what transition occurred?
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
12.1 eV
What is the energy of the n = 5 orbital?
What is the energy of the n = 3 orbital?
What is the wavelength of the photon released from a 5
to 3 transition? (Hydrogen atom)
solution
-0.544 eV, -1.51 eV, 1.28x10-6 m
What is the wavelength of the photon released from a 4
to 1 transition? (Hydrogen atom)
solution
97.3 nm
Quantisation of Angular Momentum
• Why are only certain orbits allowed? (demo)
•
Circumferences of Bohr orbits are integer multiples of de Broglie wavelength
p
h

Schrödinger and the quantum atom
Schrödinger solves  for hydrogen atom
The electron is represented by a wave
Can only be solved for H, singly ionised He
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