Ch. 5 - Electrons in Atoms


Wavelength (  ) - length of one complete wave measured in m, cm, or nm

In light it tells us which color it is


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
 how much energy the wave is carrying. It is the height of the wave. It is measured in meters. In SOUND it tells us how LOUD it is. In LIGHT it tells how BRIGHT it is.

A


A

•
To understand the electronic structure of atoms we must understand light and how it is emitted or absorbed by substances.
•
We will examine visible light a type of
Electromagnetic Radiation (EM) which carries
(radiant) energy through space (speed of light) and exhibits wavelike behavior.
•
Also need to think of light as particle, to help understand how EM radiation and atoms interact

R
G
Y
E
N
E
H
I
G
H
R
G
Y
E
N
E
L
O
W

 Move through a vacuum at the ‘speed of light’ 3.00 x 10 8 m/s
 Behaves like waves that move through water, which are the result of a transfer of energy to the water (from a stone), expressed as up and down movement of water
 Both electric and magnetic properties

 Wave Speed = (distance between wave peaks) x (frequency)
= (wavelength) x (frequency)
EM radiation moves through a vacuum at the “ speed of light”
3.00 x 10 8 m/s also called c
 A lower energy wave ( infrared and red ) has a longer wavelength(

) and lower frequency( f )
 A higher energy wave ( blue - violet ) has a shorter wavelength(

) and higher frequency( f ).


Frequency & wavelength are inversely proportional c =
 

8




EX: Find the frequency of a photon with a wavelength of 434 nm.
GIVEN:

= ?

= 434 nm
= 4.34

10 -7 m c = 3.00

10 8 m/s
WORK :

= c


= 3.00
4.34


10
10
8
-7 m/s m

= 6.91

10 14 Hz


Planck (1900)

Observed - emission of light from hot objects

Concluded - energy is emitted (absorbed or released) in small, specific amounts (quanta)

Quantum - smallest energy packet that can be emitted or absorbed as EM radiation by an atom.

 Planck proposed that the energy, E, of a single quantum energy packet equals a constant (h) times its frequency
 The energy of a photon is proportional to its frequency.
E = h

E: energy (J, joules) h: Planck’s constant (6.6262  10 -34 J·s)
 : frequency (Hz)


EX: Find the energy of a red photon with a frequency of 4.57  10 14 Hz.
GIVEN:
E
= ?
 = 4.57  10 14 Hz h = 6.6262  10 -34 J·s
WORK :
E = h

E = (
6.6262  10 -34 J·s
)
(
4.57  10 14 Hz
)
E = 3.03

10 -19 J


Planck (1900)
Classical Theory
Quantum Theory


Energy is always emitted or absorbed in whole number multiples of hv, such as hv, 2 hv, 3 hv, 4hv, …. The allowed energies are quantized, that is their values are restricted to certain quantities.

The notion of quantized rather than continuous energies is strange. Consider a ramp and a staircase, on a ramp you can vary the length your steps and energy used on the walk up. When walking up steps you must exert exactly the specific amount of energy needed to reach the next step. Your steps on steps are quantized, you cannot step between them.


Einstein (1905)

Observed – photoelectric effect
 Dispersed light falls on metal samples, the different frequencies produce different energetic photoelectrons


Einstein (1905)

Concluded - light has properties of both waves and particles (photons)
“wave-particle duality”

Photon - particle of light that carries a quantum of energy

Used planck’s quantum theory to deduced that: E photon
= hv

Ch. 5 - Electrons in Atoms

 Set of frequencies of EM waves emitted by atoms an element when they absorb electrical energy, eˉ get excited, become somewhat unstable and release energy in the form of light
ENERGY IN PHOTON OUT

 e exist only in orbits with specific amounts of energy called energy levels

Therefore…
 e can only gain or lose certain amounts of energy
 only certain photons are produced

Ground state: lowest allowable atomic electron energy state

Excited state: any higher energy state

6
5
4
3
2
1

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


Each element has a unique bright-line emission spectrum.

“Atomic Fingerprint”

Examples:

Iron

Now, we can calculate for all elements and their electrons

Ch. 5 - Electrons in Atoms


Louis de Broglie (1924)

Proposed eˉ in their orbits behave like a wave

Wavelength of an eˉ depends on its mass(m) and its velocity (v): λ = _h _ mv
EVIDENCE: DIFFRACTION PATTERNS
VISIBLE LIGHT ELECTRONS


Heisenberg Uncertainty Principle

Impossible to know both the velocity and position of an electron at the same time

Attempting to observe an electron’s position changes its momentum and attempting to observe an electron’s momentum changes its position. Therefore electrons cannot be locked into well-defined circular orbits around the nucleus.




Schrödinger Wave Equation (1926) proposed a wave equation incorporating both the wave and particle nature of the electron.
The result of the equation, wave functions, shows the probability that an electron will be in a certain region of space at a given instant. This electron density is represented by a distribution of dots which represents where electrons are located about 90% of the time
 finite # of solutions  quantized energy levels
 defines probability of finding an e -




Orbital (“electron cloud”) a specific distribution of electron density in space.
Each orbital has a characteristic energy and shape.
Orbital

UPPER LEVEL

1. Principal Quantum Number (n = 1, 2, 3, …)
(see periodic table left column)

Indicates the relative size and energy of atomic orbitals

As (n) increases, the orbital becomes larger, the electron spends more time farther from the nucleus

Each major energy level is called a principle energy level
Ex: lowest level = 1 ground state, highest level = 7 excited state

2. Energy Sublevel



Defines the shape of the orbital (s, p, d, f)
# of orbital related to each sublevel is always an odd # s = 1, p = 3, d = 5, f = 7
Each orbital can contain at most 2 electrons


Specifies the exact orbital within each sublevel

p x p y p z

4. Spin Quantum Number
( m s

Electron spin  +½ or -½
)

An orbital can hold 2 electrons that spin in opposite directions.


Pauli Exclusion Principle

A maximum of 2 electrons can occupy a single atomic orbital

Only if they have opposite spins
1. Principal #

2. Energy sublevel

3. Orientation
4. Spin #

 energy level
(s,p,d,f) x, y, z exact electron

 Aufbau Principle
 Electrons fill the lowest energy orbitals first.
 “Lazy Tenant
Rule”

 Hund’s Rule
 Within a sublevel, place one e per orbital before pairing them.
 “Empty Bus Seat Rule”

s
5
6
7
3
4
1
2 f(n-2)
6
7 d (n-1) p
© 1998 by Harcourt Brace & Company

 Orbital Diagram
O
1s 2s
 Electron Configuration
1s 2 2s 2 2p 4
2p

 Longhand Configuration
1s 2 2s 2 2p 6 3s 2 3p 4
Core Electrons Valence Electrons
 Valence electrons: determine chemical properties of that element & are the electrons in the atoms outermost orbital
 Shorthand Configuration
[Ne] 3s 2 3p 4

 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.
1
2
3
4
5
6
7

 Example Germanium
1
2
3
4
5
6
7
[Ar] 4s 2 3d 10 4p 2

 Full energy level
 Full sublevel (s, p, d, f)
 Half-full sublevel
1
2
3
4
5
6
7

 Electron Configuration Exceptions
 Copper
EXPECT : [Ar] 4s 2 3d 9
ACTUALLY : [Ar] 4s 1 3d 10
 Copper gains stability with a full d-sublevel.

 Electron Configuration Exceptions
 Chromium
EXPECT : [Ar] 4s 2 3d 4
ACTUALLY : [Ar] 4s 1 3d 5
 Chromium gains stability with a half-full d-sublevel.

 Ion Formation
 Atoms gain or lose electrons to become more stable.
 Isoelectronic with the Noble Gases.
1
2
3
4
5
6
7

 Ion Electron Configuration
 Write the e config for the closest Noble
Gas
 EX: Oxygen ion

O 2-

Ne
2-
-
2
6

Read
Section 5-3!