I. Waves & Particles

Ch. 6 – Electronic Structure of Atoms

Properties of Waves

Many of the properties of light may be described in terms of waves even though light also has particle-like characteristics.

Waves are repetitive in nature

A. Waves

Wavelength () - length of one complete wave; units of m or nm

Frequency () - # of waves that pass a point during a certain time period hertz (Hz) = 1/s

Amplitude (A) - distance from the origin to the trough or crest

A. Waves

Agreater

amplitude

(intensity)

greater frequency

(color)

crest

origin

trough

A

Electromagnetic Radiation

Electromagnetic radiation: (def) form of energy that exhibits wavelike behavior as it travels through space

Types of electromagnetic radiation: visible light, x-rays, ultraviolet (UV),

infrared (IR), radiowaves, microwaves, gamma rays

Electromagnetic Spectrum

All forms of electromagnetic radiation move at a speed of about 3.0 x 108 m/s through a vacuum (speed of light)

Electromagnetic spectrum: made of all the forms of electromagnetic radiation

B. EM Spectrum

LOW

ENERGY

HIGH

ENERGY

B. EM Spectrum

LOW

ENERGY

HIGH

ENERGY

R O Y G. B I V

red orange yellow green blue indigo violet

B. EM Spectrum

Frequency & wavelength are inversely proportional

c = c: speed of light (3.00 108 m/s): wavelength (m, nm, etc.): frequency (Hz)

B. EM Spectrum

GIVEN:

= ?

= 434 nm = 4.34 10-7 m

c = 3.00 108 m/s

WORK: = c

= 3.00 108 m/s 4.34 10-7 m

= 6.91 1014 Hz

EX: Find the frequency of a photon with a wavelength of 434 nm.

C. Quantum Theory

Photoelectric effect: emission of electrons from a metal when light shines on the metal

Hmm… (For a given metal, no electrons were emitted if the light’s frequency was below a certain minimum – why did light have to be of a minimum frequency?)

C. Quantum Theory

Planck (1900)

Observed - emission of light from hot objects

Concluded - energy is emitted in small, specific amounts (quanta)

Quantum - minimum amount of energy change

C. Quantum Theory

Planck (1900)

vs.

Classical Theory Quantum Theory

C. Quantum Theory

Einstein (1905)

Observed - photoelectric effect

C. Quantum Theory

E: energy (J, joules)h: Planck’s constant (6.626 10-34 J·s): frequency (Hz)

E = h

The energy of a photon is proportional to its frequency.

C. Quantum Theory

GIVEN:

E = ? = 4.57 1014 Hzh = 6.6262 10-34 J·s

WORK:

E = h

E = (6.6262 10-34 J·s)(4.57 1014 Hz)

E = 3.03 10-19 J

EX: Find the energy of a red photon with a frequency of 4.57 1014 Hz.

C. Quantum Theory

Einstein (1905)

Concluded - light has properties of both waves and particles

“wave-particle duality”

Photon - particle of light that carries a quantum of energy

6.3. Bohr Model of the Atom

Ch.6-

Excited and Ground State

Ground state: lowest energy state of an atom

Excited state: an atom has a higher potential energy than it had in its ground state

When an excited atom returns to its ground state, it gives off the energy it gained as EM radiation

A. Line-Emission Spectrum

ground state

excited state

ENERGY IN PHOTON OUT

B. Bohr Model

2) e- exist only in orbits with specific amounts of energy called energy levels

When e- are in these orbitals, they have fixed energy

Energy of e- are higher when they are further from the nucleus

B. Bohr Model

Therefore…Bohr model leads us to conclude that:

e- can only gain or lose certain amounts of energy

only certain photons are produced

B. Bohr Model

1

23

456 Energy of photon depends on the difference in energy levels

Bohr’s calculated energies matched the IR, visible, and UV lines for the H atom

C. Other Elementssummersummersummer

Each element has a unique bright-line emission spectrum.

“Atomic Fingerprint”

Helium

Bohr’s calculations only worked for hydrogen!

III. Wave Behavior of Matter

Ch. 6 - Electrons in Atoms

A. Electrons as Waves

Louis de Broglie (1924)

Applied wave-particle theory to e-

e- exhibit wave properties

QUANTIZED WAVELENGTHS

A. Electrons as Waves

EVIDENCE: DIFFRACTION PATTERNS

ELECTRONSVISIBLE LIGHT

A. Electrons as Waves

Diffraction: (def) bending of a wave as it

passes by the edge of an object

Interference: (def) when waves overlap (causes reduction and increase in energy in some areas of waves)

6.5: Quantum Model

Chapter 6

A. Quantum Mechanics

Heisenberg Uncertainty Principle

Impossible to know both the velocity and position of an electron

A. Quantum Mechanics

σ3/2 Zπ

11s 0

eΨ a

Schrödinger Wave Equation (1926)

finite # of solutions quantized energy levels

defines probability of finding an e-

B . Quantum Mechanics

Schrodinger wave equation and Heisenberg Uncertainty Principle laid foundation for modern quantum theory

Quantum theory: (def) describes mathematically the wave properties of e- and other very small particles

B. Quantum Mechanics

Radial Distribution CurveOrbital

Orbital (“electron cloud”)

Region in space where there is 90% probability of finding an e-

C. Quantum Numbers

UPPER LEVEL

Four Quantum Numbers:

Specify the “address” of each electron in an atom

C. Quantum Numbers

1. Principal Quantum Number ( n )

Main energy level

Size of the orbital

n2 = # of orbitals in the energy level

C. Quantum Numbers

s p d f

2. Angular Momentum Quantum # ( l ) Energy sublevel Shape of the orbital (# of possible shapes equal to n) values from 0 to n-1

C. Quantum Numbers

If l equals… Then orbital shape is…

0 s

1 p

2 d

3 f

Principle quantum # followed by letter of sublevel

designates an atomic orbital

C. Quantum Numbers

3. Magnetic Quantum Number ( ml )

Orientation of orbital

Specifies the exact orbitalwithin each sublevel

C. Quantum Numbers

Values for ml:

m = -l… 0… +l

C. Quantum Numbers

px py pz

C. Quantum Numbers

Orbitals combine to form a spherical

shape.

2s

2pz2py

2px

C. Quantum Numbers

4. Spin Quantum Number ( ms )

Electron spin +½ or -½

An orbital can hold 2 electrons that spin in opposite directions.

C. Quantum Numbers

1. Principal # 2. Ang. Mom. # 3. Magnetic # 4. Spin #

energy level

sublevel (s,p,d,f)

orbital

electron

Pauli Exclusion Principle

No two electrons in an atom can have the same 4 quantum numbers.

Each e- has a unique “address”:

C. Quantum Numbers

n = # of sublevels per level

n2 = # of orbitals per level

Sublevel sets: 1 s, 3 p, 5 d, 7 f

Wrap-Up

Quantum # Symbol What it describes

Possible values

Principle quantum #

n main E level, size of orbital

n = positive whole integers

Angular Momentum Quantum #

l sublevels and their shapes

0 to (n-1)

Magnetic Quantum #

ml orientation of orbital

-l … 0 … +l

Spin Quantum #

ms

electron spin +1/2 or -1/2

Electron Configuration

Ch. 6 - Electrons in Atoms

a. ELECTRON CONFIGURATION

ELECTRON CONFIGURATION Notation to keep track of where electrons in an atom are distributed between shells and subshells

B. General Rules

Pauli Exclusion Principle

Each orbital can hold TWO electrons

with opposite spins.

B. General Rules

Aufbau Principle

Electrons fill the lowest energy orbitals first.

“Lazy Tenant Rule”

RIGHTWRONG

B. General Rules

Hund’s Rule

Within a sublevel, place one e- per orbital before pairing them.

“Empty Bus Seat Rule”

O

8e-

Orbital Diagram

Electron Configuration

1s2 2s2 2p4

C. Notation

1s 2s 2p

Shorthand Configuration

S 16e-

Valence Electrons

Core Electrons

S 16e- [Ne] 3s2 3p4

1s2 2s2 2p6 3s2 3p4

C. Notation

Longhand Configuration

© 1998 by Harcourt Brace & Company

sp

d (n-1)

f (n-2)

1234567

67

D. Periodic Patterns

C. Periodic Patterns

Period # energy level (subtract for d & f)

A/B Group # total # of valence e-

Column within sublevel block # of e- in sublevel

s-block

1st Period

1s11st column of s-block

C. Periodic Patterns

Example - Hydrogen

1

2

3

4

5

6

7

C. Periodic Patterns

Shorthand Configuration Core e-: Go up one row and over to the

Noble Gas. Valence e-: On the next row, fill in the #

of e- in each sublevel.

[Ar] 4s2 3d10 4p2

C. Periodic Patterns

Example - Germanium

Full energy level

1

2

3

4 5

6

7

Full sublevel (s, p, d, f)Half-full sublevel

E. Stability

Electron Configuration Exceptions

Copper

EXPECT: [Ar] 4s2 3d9

ACTUALLY: [Ar] 4s1 3d10

Copper gains stability with a full d-sublevel.

E. Stability

Electron Configuration Exceptions

Chromium

EXPECT: [Ar] 4s2 3d4

ACTUALLY: [Ar] 4s1 3d5

Chromium gains stability with a half-full d-sublevel.

E. Stability

E. Stability

Ion Formation Atoms gain or lose electrons to become

more stable. Isoelectronic with the Noble Gases.

O2- 10e- [He] 2s2 2p6

E. Stability

Ion Electron Configuration

Write the e- config for the closest Noble Gas

EX: Oxygen ion O2- Ne