Chapter 7.5: The Quantum Mechanical Model of the Atom

“It is often stated that of all the theories proposed in this

century, the silliest is quantum theory. Some say the only

thing that quantum theory has going for it, in fact, is that it

is unquestionably correct.”

- R. Feynman, Physicist

The Quantum Mechanical Model •Quantum Mechanics broke away from the traditional particulate models and offered wave mechanics as the basis of describing electrons in an atom.

•The Quantum Mechanical Model is based on high levels of mathematics and visualizes the electron as a standing wave – fixed at both ends.

•In 1925, Erwin Schrodinger developed the mathematical formula that forms the basis of quantum mechanics.

• The wave function puts the electron in all possible states at once, (i.e. "in two places at once"). The act of observation or measurement changes the outcome.

•The wave function, Ψ: •A function of the coordinates (x, y, and z) of the electron’s position in a three-dimensional space.

•A specific wave function (an orbital), is an area of high probability of finding an electron.

•The probability of finding an electron is portrayed as a ‘cloud’ shape.

•The denser the cloud, the greater the probability of finding an electron in that area.

The propeller blade, just like an electron, has the same probability of being anywhere in the blurry region. One cannot predict its location at any one instant, so it assumes all locations at once.

•Schrödinger's equation predicts the shapes of the various orbitals – these are areas of high probability of finding an electron.

Schrödinger’s Cat

http://www.youtube.com/watch?v=IOYyCHGWJq4

http://www.youtube.com/watch?v=uWMTOrux0LM

Schrödinger’s Cat illustrates that since we don’t know where exactly an electron is at any given moment, it is actually in all possible states simultaneously, as long as we don't look to check. It is the measurement itself that causes the object to be limited to a single possibility.

http://www.youtube.com/watch?v=IOYyCHGWJq4http://www.youtube.com/watch?v=uWMTOrux0LM

Section 7.6: Quantum Numbers

•Quantum numbers: Each of the orbitals are characterized by a series of numbers which describe various properties of the orbital

•Assigning quantum numbers are no longer covered on the AP test so this section is beyond the scope of this course.

Section 7.7: Orbital Shapes and Energies

•The quantum mechanical model only represents the probability distribution of the electron in the orbital.

•This allows us to picture the orbitals in terms of probability distributions

PREVIEW OF INSIDE AN ATOM:

The nucleus is surrounded by a space in which the electrons orbit the nucleus: The electron cloud

The electron cloud is divided into 7 principal Energy levels numbered n=1 to n=7 with n=1 closest to the nucleus. n is called the quantum number.

Each energy level is divided into sublevels, referring to the cloud shape. (s, p, d, f)

Each sublevel contains atomic orbitals (s=1, p=3, d=5, f=7)

Each orbital can contain 2 electrons. (s=2, p=6, d=10, f=14). The total number of electrons in all of the orbitals equals the total number of electrons for that element.

Energy Levels Energy level is the distance from the nucleus

where the electron is most likely to be moving.

Energy levels are in designated quantum numbers (n). n = 1, 2, 3, 4, 5, 6 or 7...

• A Quantum number is equal to the period

• Higher the quantum number, the greater average distance from the nucleus

Nucleus

n = 1 n = 2

n = 3

n = 4

•Electrons do not remain between energy levels.

•To move from one energy level to another, an electron must gain or lose just the right amount of energy... a “quantum” of energy

•The steps, like the energy levels, are not equally spaced.

•The higher the step, the more energy it has, and the farther away it is from the nucleus

Energy levels are divided into sub-levels.

Each sub-level corresponds to a specific cloud shape.

Letters represent the different orbitals :

s – spherical

p – dumb-bell shaped

d – clover-leaf shaped

f – complex shape

S P

D

F

Note the Principal energy levels and sublevels . . .

Summary of Energy Levels / Sublevels

Principal Energy Level (Quantum Number)

Number of Sublevels

Sublevels

n = 1 1 1s

n = 2 2 2s, 2p

n = 3 3 3s, 3p, 3d

n = 4 4 4s, 4p, 4d, 4f

The principal quantum number always equals the number of sublevels within that principal energy level.

Review of Sublevels The max number of electrons that can occupy a given energy level is 2n2 where n = energy level.

Shape of

Orbital

Number of

orbitals

Number of

electrons

Orbital diagram

S (Spherical) 1 2 max

P (dumbbell) 3 6 max

D (clover) 5 10 max

F (complex) 7 14 max

• The 2nd energy level has how many sublevels?

• What orbital types are within the sublevel?

2s and 2p

Two

• The 3rd energy level has how many sublevels and what orbital types are within the sublevel?

Three 3s, 3p, 3d

How many electrons can be in the 3rd energy level?

2n2, n=3

2(3)2 18 e-

How many orbital types are in the 4th energy level?

Energy level = # of sublevels

4 orbital types – s, p, d, and f

How many TOTAL orbitals are in the 4th energy level?

Total orbital # = n2 42=16

1 s, 3 p, 5 d, 7 f

Metallic properties increase as you go down a group, and decrease as you go across a period.

X

Fr is the most metallic!