1. The Electronic Structure of Atoms

2. The Dual Nature of the Electron
De Broglie argued that electron behave like a standing wave in the hydrogen atom
De Broglie’s reasoning led to the conclusion that waves can behave like particles and particles can exhibit wavelike properties.

3. The Uncertainty Principle
Heisenberg showed from quantum mechanics that it is impossible to know simultaneously, with absolute precision, both the position and the momentum of a particle such as an electron.
(x) (mv)  h 4
This is a result of the wave/particle duality of matter

4. Quantum Mechanics
In 1926 Schrödinger, using a complicated mathematical equation describes the behavior and energies of submicroscopic particles in general, an equation analogous to Newton’s laws of motion for macroscopic objects.
the equation incorporates both particle behavior, in terms of mass m, and wave behavior, in terms of a wave function Ψ (psi), which depends on the location in space of the system (such as an electron in an atom).

5. Quantum Mechanics
The wave function itself has no direct physical meaning. However, the probability of finding the electron in a certain region in space is proportional to the square of the wave function, Ψ2. Schrödinger’s equation began a new era in physics and chemistry, for it launched a new field, quantum mechanics (also called wave mechanics).

6. Quantum Mechanics Plot of 2 for hydrogen atom.
The closest thing we now have to a physical picture of an electron.
90% contour, will find electron in blue stuff 90% of the time.

7. Quantum Mechanics
The wave equation is designated with a lower case Greek psi ().
The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.

8. Quantum Numbers
In quantum mechanics, three quantum numbers are required to describe the distribution of electrons in hydrogen and other atoms. These numbers are derived from the mathematical solution of the Schrödinger equation for the hydrogen atom. They are called the principal quantum number, the angular momentum quantum number, and the magnetic quantum number. A fourth quantum number—the spin quantum number—describes the behavior of a specific electron and completes the description of electrons in atoms.

9. Quantum Numbers
The principal quantum number (n) can have integral values 1, 2, 3,….
The angular momentum quantum number (l) tells us the “shape” of the orbitals, The values l of depend on the value of the principal quantum number, n. For a given value of n, has possible integral values from 0 to (n-1, if n = 1, there
is only one possible value of l ; that is, n - 1 =1 - 1 = 0. If n 2, there are two values of l , given by 0 and 1. If n = 3, there are three values of , given by 0, 1, and 2. The value of l is generally designated by the letters s, p, d, as follows:).

10. Quantum Numbers
The Magnetic Quantum Number (ml) describes the orientation of the orbital in space. Within a subshell, the value of m depends on the value of the angular momentum quantum number, l.

11. Magnetic Quantum Number, ml
Orbitals with the same value of n form a shell.
Different orbital types within a shell are subshells (s, p, d, f).

12. Atomic Orbitals
Table shows the relation between quantum numbers and atomic orbitals

13. s Orbitals Value of l = 0. Spherical in shape.
Radius of sphere increases with increasing value of n.

14. p Orbitals
Value of l = 1.
Have two lobes with a nodal plane between them.
Note: always 3 p orbitals for a given n

15. d Orbitals Value of l is 2. 2 nodal planes
Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.
Note: always 5 d orbitals for a given n.

16. Energies of Orbitals
For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.
That is, they are degenerate.

17. Energies of Orbitals
As the number of electrons increases, though, so does the repulsion between them.
Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.

18. Energies of Orbitals For a given energy level (n): Energy:
s<p<d<f
s lowest energy, where electrons go first
Next p
Then d
Why?

19. Quantum Numbers
The Electron Spin Quantum Number (ms) This quantum number refers to the two possible orientations of the spin axis of an electron; possible values are +1/2 and -1/2. Due to the emission spectra of hydrogen and sodium atoms indicated that lines in the emission spectra could be split by the application of an external magnetic field.

20. Why do we call it “spin”
And charges that spin produce magnetic fields

21. Pauli Exclusion Principle
No two electrons in the same atom can have exactly the same energy.
For example, no two electrons in the same atom can have identical sets of quantum numbers.

22. Hund’s Rule (of maximum multiplicity)
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”
NOT:

23. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s
Orbital diagram
Aufbau is German for “building up”
We must follow this orbital energy diagram!
Notice that the 4s orbital will fill before the 3d because it is lower in energy!

25. Periodic Table
Periodic table tells you about the last electron that went in!!!
Periodic table also makes it easy to do electron configurations.

26. Short cut for writing electron configurations

27. Electron configurations of the elements

28. Exceptions to the Building-Up Principle
The building-up principle predicts the configuration of Cr (24) is [Ar]3d44s2, though the correct one is found experimentally to be [Ar]3d54s1.
These two configurations are actually very close in total energy because of the closeness in energies of the 3d and 4s orbitals.
Copper(29) is another exception to the building-up principle, which predicts the configuration [Ar]3d94s2, although experiment shows the ground-state configuration to be [Ar]3d104s1.