1. The Bohr Model and the Quantum Mechanical Model of the Atom
Physics 12

2. Clip of the day: Minutesphysics on origins of Quantum model

3. The history lesson continues…

4. Dalton’s Atomic Model
Atom = solid, indivisible sphere

5. Plum Pudding Model (Thomson)
Proton and electrons spread through the atom

6. Rutherford Model: Nuclear model
Positive charge and most of the mass concentrated in centre of atom
Electrons circling nucleus

7. The Bohr Model: The Bohr Model built upon earlier models of the atom
Dalton – Billiard Ball
Thompson – Raisin Bread
Rutherford – Nuclear Model
Bohr began investigating the line spectra of hydrogen in order to determine the behaviour of electrons

8. Bohr Model:
Electrons orbit the nucleus in circular paths of fixed energy (energy levels).

9. Energy levels: Electrons can jump from energy level to energy level.
Electrons absorb or emit light energy when they jump from one energy level to another.
Energy is emitted by the electron as it leaps from the higher to the lower energy level
Energy is absorbed by the electron as it moves from the lower to the higher energy level
The energy is proportional to the frequency of the light wave.
Frequency defines the color of visible light emitted or absorbed
/simulations6e/index.htm?newwindow=true

10. Hydrogen Line Spectra:
Bohr studied gas discharge tubes filled with individual gases
Particularly hydrogen

11. Hydrogen Line Spectra:
When hydrogen is bombarded with cathode rays (beam of electrons), it will absorb specific wavelengths of light
Similarly, if a large amount of energy is passed through hydrogen gas, it will emit specific wavelengths of light
The line represent the specific levels of energy that are possible

12. Balmer and Rydberg:
Balmer showed that the visible lines could be predicted using:
Rydberg went on to show that all hydrogen lines could be predicted using:

13. Bohr Postulates: Electrons exist in circular orbits
Electrons exist only in allowed orbits
Electrons do not radiate energy within an orbit
Electrons can jump between orbits

14. So….
The Bohr model explained the emission spectrum of the hydrogen atom but did NOT always explain those of other elements.
Since the Bohr Model does well with hydrogen, it is likely that the theory needs to be expanded, not discarded!

15. Principal Quantum Number:
The Bohr model actually used a single quantum number (n) to describe an orbit (energy level/ring)
The Quantum model uses four quantum numbers to describe an orbital

16. Lead to the Quantum Mechanical Model:
1920’s
Credit to..
Werner Heisenberg (Uncertainty Principle)
Louis de Broglie (electron has wave properties)
Erwin Schrodinger (mathematical equations using probability, quantum numbers)

17. de Broglie Wavelength and the Electron:
de Broglie realized that as a result of his matter wave equation, the wavelength of an electron would play a role in how it orbits the nucleus
The orbital circumference would have to be an integral number of wavelengths and “pilot waves”

18. Schrödinger Wave Equation:
Erwin Schrödinger developed the Schrödinger wave equation that forms the foundation of quantum mechanics
This equation leads to the ability to plot an electron’s orbital
The Schrödinger Wave Equation leads to the addition of two additional quantum numbers in addition to the principal quantum number (n) from Bohr

19. Paul Dirac:
Paul Dirac modified the Schrödinger Wave Equation using a relativistic correction
Once this was applied, Bohr’s Model was able to predict the behaviour of the hydrogen atom even more accurately
Further, this correction allows the Schrödinger Wave Equation to work with other atoms and also predicts behaviour that had not even been discovered when Dirac did his original work

20. Quantum Model:
is based on mathematics and quantum theory, which says matter also has properties associated with waves.
It’s impossible to know the exact position and momentum of an electron at the same time (known as the Heisenberg Uncertainty Principle).
Uses complex shapes of orbitals (electron clouds), volumes of space in which there is likely to be an electron.
Based on probability not certainty

21. Orbitals:
A region in space in which there is high probability of finding an electron.
Electrons, instead of traveling in defined orbits or hard, spherical “shells,” as Bohr proposed, travel in diffuse clouds around the nucleus.

22. Quantum Numbers:
Specify the properties of atomic orbitals and their electrons.
There are four Quantum Numbers
Principal Quantum Number
Orbital Quantum Number
Magnetic Quantum Number
Spin Quantum Number

23. The principle quantum number (n):
Has integral values
n = 1, 2, 3, 4…
The maximum number of electrons in a principal energy level is given by:
2n2
As n increases the electron has a higher energy and is less tightly bound to the nucleus

24. The orbital (second) quantum number(l ):
The value of ℓ ranges from 0 to n − 1
describes the shape of the orbital
l = 0, 1, 2, 3, …
l = s, p, d, f, …
Example: if n =2
than l = 1, 0

26. Magnetic Quantum Number, ml:
Indicates the orientation of the orbital in space
ml = - l , …,0,…, l
Example:
for l= 2
ml = -2, -1, 0, +1, +2

27. Spin Quantum Number:
Finally, the Spin Quantum Number (ms) comes about due to the relativistic wave equation
This described the magnetic field that a spinning electron creates and explains why electrons pair up in an orbital
ms = -½ , ½

28. Pauli Exclusion Principle:
The Pauli Exclusion Principle states that no two electrons in the same atom can occupy the same state
This means that of the four quantum numbers, no two electrons in the same atom can have the same four quantum numbers

29. Recap:
Thus, it takes three quantum numbers to define an orbital but four quantum numbers to identify one of the electrons that can occupy the orbital.

30. Ex: the electron orbitals with a principle quantum number (n) of 3
Subshell ml
Number of orbitals in subshell 3 3s 1 3p
-1,0,+1 2 3d
-2,1,0,+1,+2 5

31. Practice #1:
What are the possible values of l and ml for an electron with the principle quantum number n=4?
If l=0, ml=0
If l=1, ml= -1, 0, +1
If l=2, ml= -2,-1,0,+1, +2
If l=3, ml= -3, -2, -1, 0, +1, +2, +3

32. Practice #2:
Can an electron have the quantum numbers n=2, l=2 and ml=2?
No, because l cannot be greater than n-1, so l may only be 0 or 1.
ml cannot be 2 either because it can never be greater than l

33. Practice #3:
List the values of the four quantum numbers for orbitals in the 3d (n=3, l=2) sublevel.
Answer:
n=3
l = 2
ml = -2,-1, 0, +1, +2
ms = +1/2, -1/2 for each pair of electrons

34. Orbital Energy Levels:
In any give atom, the electrons will fill the orbitals starting from the lowest energy state
Remember the number of electrons is equal to the atomic number of an atom
The energy of each orbital can be calculated in order to determine the filling order
However, there is also a diagram that provides this information without calculations

36. Energy Level Diagrams:
This model can be used to create an energy level diagram
Also, this model predicts the structure of the periodic table:
Groups 1A and 2A – s
Groups 3B – 8B – p
Transition Metals – d
Rare Earth/Synthetics - f

37. Let’s try some: Draw energy level diagrams for: a. sodium b. silicon
c. beryllium
d. strontium
e. chlorine
f. carbon
g. copper
h. bromine