The Quantum Mechanical Model of the Atom

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

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

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.

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.

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.

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

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

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.

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

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.

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”!

Shape of f (l = 3) orbitals

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

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.

Orbital filling table

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