1. 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

2. Problems with the Rutherford Atom
Acceleration/Radiation
Spectral Lines

3. Rydberg’s Formula: (FYI)
Spectral lines
Energy from excited atoms
demo
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 = x 10-7 m-1) H He
Sun

4. Bohr’s Quantum Atom Assumptions of Bohr’s model:
1. Only certain orbits are allowed “stationary states”
2. Electron transitions between states create photons:

5. Example 1: What is the wavelength of the first Lyman line?
The first Lyman line is a transition from -3.4 eV to eV, so it releases 10.2 eV of energy. A photon with this energy has this wavelength:
E = (10.2)(1.602E-19) = E-18 J
E = hc/λ, λ = hc/E =
(6.626E-34)(3.00E8)/( E-18) =
E-07 m = 122 nm

6. 3. Angular Momentum is Quantised: (show that mvr = I…..but why????)
Example 2: Show that mvr is angular momentum (L = I)

7. 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)

8. Whiteboards:
Bohr Photons
1 | 2 | 3 | 4

9. What possible photon energies can you get from these energy levels
What possible photon energies can you get from these energy levels? (there are 6 different ones) 1 4 9 3 8 5
-5.0 eV
-6.0 eV
-9.0 eV
-14.0 eV
5, 8, 9 and 3, 4 and 1 eV

10. What is the wavelength of the photon released from the third Lyman spectral line (from to eV)?
E = hf = hc/ 
E = = eV
E = (12.75 eV)(1.602E-19J/eV) = 2.04E-18J
 = hc/E = 97.3 = 97 nm
97 nm

11. 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 = = 2.55 eV
E = (2.55 eV)(1.602E-19J/eV) = 4.09E-19J
 = hc/E = 487 = 490 nm
490 nm

12. An 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) =
E-18 J
( E-18 J)/(1.602E-19) = 12.1 eV
This could be the second Lyman line
12.1 eV

13. What is the energy of the n = 5 orbital?
What is the wavelength of the photon released from a 5 to 3 transition? (Hydrogen atom)
solution
eV, eV, 1.28x10-6 m

14. What is the wavelength of the photon released from a 4 to 1 transition
What is the wavelength of the photon released from a 4 to 1 transition? (Hydrogen atom)
solution
97.3 nm

15. Quantisation of Angular Momentum
Why are only certain orbits allowed? (demo)
Circumferences of Bohr orbits are integer multiples of de Broglie wavelength

16. 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

17. 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