--THE QUANTUM

MECHANICAL MODEL

Bohr’s Energy Levels

Electrons reside in certain energy levels

Each level represents a certain amount of energy

Low Energy levels: closer to nucleus

High Energy levels: farther from nucleus

Ground State: Electron is in the lowest possible

energy level

Excited Atoms

Excited Atom- has absorbed energy

Unstable

Atoms soon emit the same amount of energy they

absorbed

Energy seen as visible light (different colors)

The Quantum Mechanical Model

Energy is quantized (comes in chunks)

A quanta is the amount of energy needed to

move from one energy level to another

Since the energy of an atom is never “in

between” there is a quantum leap in energy

Erwin Schrodinger derived an equation that

described the energy and position of electrons in

an atom

Quantum Mechanical Model

1920s

Louis de Broglie (electron has wave properties)

Werner Heisenberg (Uncertainty Principle)

Erwin Schrodinger (mathematical equations

using probability, quantum numbers)

Louis de Broglie, (France, 1892-1987)

Wave Properties of Matter (1923)

Since light waves have a particle

behavior (as shown by Einstein in the

Photoelectric Effect), then particles

could have a wave behavior.

Electrons act like waves confined

to a certain space around a nucleus

de Broglie wavelength

E=hv

Corresponds to quantized energies of

Bohr’s orbits

Electron Motion Around Atom Shown as a

de Broglie Wave

Werner Heisenberg: Uncertainty Principle

Things that are very small behave differently from things big enough to see

The Quantum mechanical model is a mathematical solution

Energy levels for electrons

Orbits are not circular

We can not know both the position and momentum of a particle at a given time.

Can only know the probability of finding an electron a certain distance from the nucleus

Erwin Schrodinger, 1925

Quantum (wave) Mechanical Model of the Atom

The atom is found inside a

blurry “electron cloud”

An area where there is a

chance of finding an electron

Four quantum numbers are

required to describe the

state of the hydrogen atom.

FYI: Schrodinger’s Equations!!!

y is called the wave function and indicates the probability of where an electron may be found.

The Electron Cloud

http://www.chemeng.uiuc.edu/~alkgrp/mo/gk12/quantum/H_S_orbital.jpg

The higher the electron density, the higher the probability that an electron may be found in that region.

Atomic Orbital:

A region in space in which there is high probability of finding an electron.

Within each energy level, Schrodinger’s equation describes several shapes

Shapes are called atomic orbitals (regions where there is a high probability of finding an electron)

Four Quantum Numbers

Used to describe an electron in an atom.

1. Principal Quantum Number (n)

2. Orbital Quantum Number (l)

3. Magnetic Quantum Number (m)

4. Spin Quantum Number (s)

Principal Quantum Number, n

Indicates main energy levels of electrons

n = 1, 2, 3, 4…

The maximum number of electrons in an

energy level is 2n2

Example: what is the maximum number of

electrons that can be in the 5th main

energy level?

Orbital Quantum Number, ℓ(Angular Momentum Quantum Number)

Indicates shape of the orbital (sublevel) within an energy level

ℓ = n-1

ℓsublevel0 s

1 p

2 d

3 f

4 g

Magnetic Quantum Number, ml

Indicates the orientation of the orbital in space.

S orbital is spherical and centered around nucleus, so

there is only 1 possible orientation (m=0)

P orbital can extend along x,y,or z axis so there are 3

p orbitals (m=-1 m= 0 m= 1)

There are 5 different d orbitals in each d sublevel

(m=-2 m=-1 m=0 m=1 m=2)

7 different f orbitals in each f sublevel

Magnetic Quantum Number

Values of ml : integers -l to l

The number of values represents the number of orbitals.

Example:

for l= 2, ml = -2, -1, 0, +1, +2

Which sublevel does this represent?

Answer: d

Electron Spin Quantum Number, (ms or s)

Indicates the spin of the electron (clockwise or

counterclockwise).

Values of ms: +1/2, -1/2

Example:

List the values of the four quantum numbers for

orbitals in the 3d sublevel.

Answer:

n=3

l = 2

ml = -2,-1, 0, +1, +2

ms = +1/2, -1/2 for each pair of electrons

List the values of the four quantum numbers for

orbitals in the…….

2s

3p

3d

4s

4p

4f

Atomic Orbital s

2s

The 3 p orbitals

http://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gif

The d orbitals

f orbitals

Comparing s, p, d, & f Orbitals

The Electron Cloud for Hydrogen

90% probability

of finding the

electron within

this space