1. Unit 4 –
Quantum Mechanics
Cartoon courtesy of NearingZero.net

2. Light and Energy
Much of what we know about electrons comes from study of light
Light behaves as waves
Light also behaves as particles (photons)

3. Wave properties Light waves are part of the electromagnetic spectrum
Can be characterized by 5 properties:
Amplitude
Wavelength
Frequency
Speed
Energy

4. Electromagnetic radiation propagates through space as a wave moving at the speed of light.
C = speed of light, a constant (3.00 x 108 m/s)
 = frequency, in units of hertz (hz, /s, s-1)
 = wavelength, in meters

5. Types of electromagnetic radiation:

6. Calculating the color of light…
Given that a beam of light has frequency of 6.0 x 1014 /s
what is the wavelength of this light?
What color is it? –use p.129

7. E = h  = frequency, in units of hertz (hz, /s, s-1)
The energy (E ) of electromagnetic radiation is directly proportional to the frequency () of the radiation. This is the energy of a photon of a particular frequency.
E = h
E = Energy, in units of Joules (kg·m2/s2)
h = Planck’s constant (6.63 x J·s)
 = frequency, in units of hertz (hz, /s, s-1)

8. Long Wavelength = Low Frequency Low ENERGY Short Wavelength =
Wavelength Table
Short
Wavelength =
High Frequency
High ENERGY

9. Spectroscopic analysis of the visible spectrum…
(such as seen from an incandescent light bulb)
…produces all of the colors in a “continuous spectrum”

10. Spectroscopic analysis of the hydrogen spectrum…
(as given off by a hydrogen gas-filled fluorescent light bulb)
…produces a “bright line” or “emission spectrum”

11. Electron transitions occur when electrons absorb energy in a
‘quantum jump’ to an ‘excited state’.
When they ‘fall’ back to their ’
‘ground state’
they emit photons of light with distinct
wavelengths, visible as bands on an ‘emission spectrum’
(not all are in the visible range).
VISIBLE
JUMPS

12. The Bohr Model of the Atom
I pictured electrons orbiting the nucleus much like planets orbiting the sun.
But it turns out they’re more like bees around a hive.
WRONG!!!
Neils Bohr

13. Quantum Mechanical Model of the Atom
Mathematical laws were used to identify the regions outside of the nucleus where electrons are most likely to be found.
These laws are beyond the scope of this class…
But here are two important examples:

14. Schrodinger Wave Equation
Equation for probability of a single electron being found along a single axis (x-axis)
Erwin Schrodinger

15. Heisenberg Uncertainty Principle
“One cannot simultaneously determine both the position and momentum of an electron.”
You can find out where the electron is, but not where it is going.
OR…
You can find out where the electron is going, but not where it is!
Werner
Heisenberg

16. Electron Energy Level (Shell)
Generally symbolized by n, it denotes the average distance of the electron from the nucleus.
Number of electrons that can fit in a shell:
2n2
1 holds holds holds 18 etc.

17. An orbital is a region within an energy level where there is a probability of finding an electron. This is a probability diagram for the…
s orbital… in the first energy level.
Orbital shapes are defined as the space that
contains the electron 90% of the time.

18. Quantum Numbers: Electron Addresses!
1st: Energy Level (n = 1, 2, 3, 4 …) Average distance of the electron in the electron cloud from the nucleus.
2nd: Sublevel (l = s, p, d, f) Shape of electron cloud.
energy levels have n sublevels.
3rd: Orbital (ml) Orientation of the cloud in 3-D space.
s sublevels have 1 orbital (spherical)
p sublevels have 3 orbitals (dumb bell shape)
d sublevels have 5 orbitals (varied)
f sublevels have 7 orbitals (varied)
4th: Spin (ms = +1/2 or -1/2) Direction of electron spin.
Each orbital holds 2 electrons, one with each spin.

19. Pauli Exclusion Principle: Each electron of an atom has its own unique set of quantum numbers. They may have three that are the same, but never all four.

20. Sizes of s orbitals Orbitals of the same shape (s, for instance) grow
larger as n increases…
Nodes are regions of low probability within an
orbital.

21. The s orbital the origin of the three axes in space
has a spherical shape centered around
the origin of the three axes in space
There is only one orientation for this shape

22. P orbital shape There are three dumbbell-shaped p orbitals in
each energy level above n = 1, each assigned to
its own axis (x, y and z) in space.

23. To remember the shapes, think of “double dumbells”
Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3.
To remember the shapes, think of “double dumbells”
d orbital shapes
…and a “dumbell
with a donut”!

24. In case you are too curious, here is what the f orbitals look like.

25. Energy Levels, Sublevels, Electrons
Sublevels in
main energy
level
(n sublevels)
Number of
orbitals per
sublevel
Electrons
per sublevel
electrons per
level (2n2) 1 2 3 4 s s p s p d d f

26. The Diagonal Rule: Sublevels in order of increasing energy
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s25f14…
The Diagonal Rule: Sublevels in order of increasing energy
5g18
6f14
7d10
8p6
8s2
4f14 5f14
3d10 4d10 5d10 6d10
2p6 3p6 4p6 5p6 6p6 7p6
1s2 2s2 3s2 4s2 5s2 6s2 7s2
Aufbau Principle: Electrons fill the lowest energy position available.

27. Energy levels and sublevels on the Periodic Table

28. Hund’s Rule: Electrons fill orbitals so that there are a maximum number of orbitals with a single electron.

29. Element notation Orbital notation
Configuration
notation
Orbital notation
Noble gas
Lithium
1s22s1
____ ____ ____ ____ ____
1s s p
[He]2s1
Beryllium
1s22s2
[He]2s2
Boron
1s22s22p1
[He]2s2p1
Carbon
1s22s22p2
[He]2s2p2
Nitrogen
1s22s22p3
1s s p
[He]2s2p3
Oxygen
1s22s22p4
[He]2s2p4
Fluorine
1s22s22p5
[He]2s2p5
Neon
1s22s22p6
[He]2s2p6

30. Electron configuration of the elements of the first three periods