1. The Quantum Mechanical Model of the Atom

2. IF Bohr’s Atomic Model is not correct, Then what?
We need a new approach to the atom!
Big Three: de Broglie, Heisenberg & Schrodinger
Developed wave mechanics AKA quantum mechanics

3. Heisenberg Uncertainty Principle
“One cannot simultaneously determine both the position and momentum of an electron.”
The more certain you are about where the electron is, the less certain you can be about where it is going.
The more certain you are about where the electron is going, the less certain you can be about where it is.
Werner
Heisenberg

4. Schrodinger’s Wave Equation
Schrödinger proposed an equation that contains both wave and particle terms.
Solving the equation leads to wave functions .
The wave function gives the probability distribution of an electron.
We call wave functions orbitals.

5. Quantum Numbers
When we solve the Schrödinger equation for the hydrogen atom, we find many wave functions (orbitals) that satisfy it.
Each orbital is characterized by a series of numbers called quantum numbers that describe various properties of the orbital.

6. Principal Quantum Number, n
Related to the size and energy of the orbital – think energy level
n has integer values: 1,2,3…
As n becomes larger, the atom becomes larger and the electron is further from the nucleus.
A larger n value also corresponds to higher energy because the electron is less tightly bound to the nucleus.

7. Electron Energy Level (Shell)
Generally symbolized by n, it denotes the probable distance of the electron from the nucleus. “n” is also known as the Principal Quantum number
Number of electrons that can fit in a shell:
2n2

8. The Angular Momentum quantum number, l
The angular momentum quantum number, generally symbolized by l, denotes the orbital (subshell) in which the electron is located.
l Has integer values from 0 to n-1

9. Wat exactly is an Orbital?
An orbital is a region within an energy level where there is a probability of finding an electron.
Orbital shapes are defined as the surface that contains 90% of the total electron probability.

10. s Orbital shape The s orbital
(l = 0) has a spherical shape centered around
the origin of the three axes in space.

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

12. d orbital shapes
Things get a bit more complicated with the five d orbitals (l = 2) that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbells”
…and a “dumbell
with a donut”!

13. Shape of f (l = 3) orbitals

14. Energy Levels, Sublevels, Electrons
Sublevels in
main energy
level
(n sublevels)
Number of
orbitals per
sublevel
Electrons
per sublevel
electrons per
level (2n2) 1 s 2 p 3 6 8 d 5 10 18 4 f 7 14 32

15. Magnetic Quantum Number
The magnetic quantum number, has integer values from l to - l
generally symbolized by ml, denotes the orientation of the electron’s orbital with respect to the three axes in space.

16. Orbital filling table

17. Electron Spin
The Spin Quantum Number, m describes the behavior (direction of spin) of an electron within a magnetic field.
Possibilities for electron spin: