Download Electrons in Atoms

5.1
Light & Quantized Energy
Objectives:
1. Describe electromagnetic (EM) wave properties & measures
2. Relate visible light to areas of the EM spectrum with higher & lower energy
3. Know the relationship between frequency & wavelength
4. Compare quanta, photons, & atoms
The Nuclear Atom & Unanswered Questions
 Rutherford’s atomic model explained the nucleus, but the structure of the
electron cloud was still pretty hazy
 As scientists continued their research they realized that light was somehow
related to the electrons of elements
Wave Nature of Light
 Electromagnetic Radiation
 EM Radiation
 Form of energy that exhibits
wavelike properties
 Consists of electric & magnetic
fields oscillating at right angles
to each other and to the direction
of motion of the wave
 Includes visible light,
radiowaves, x-rays
 Wave Characteristics
 Wavelength (λ - lambda) – the shortest distance between equivalent points
on a continuous wave
 Relates to the color of light
 Measured in length units (meter, nanometers, etc.)
 Frequency (ν - nu) – the number of waves that pass a given point per
second
 Relates to the energy of the wave
 Measured in cycles (wavelengths) per second. 1 cycle/second = 1
Hertz (Hz) also written as 1/s or s-1
 Amplitude – the wave’s height from
the origin to the crest
 Relates to the brightness of light
 Wave Speed – the rate at which waves
travel through space
 All EM waves move at the speed
of light (c = 3.00x108 m/s) through
a vacuum
 Wavelength and frequency are
related through the formula:
c = 
speed of light = wavelength x frequency
which means wavelength and frequency are inversely related
As frequency increases, wavelength decreases and vice-versa
 The Electromagnetic Spectrum
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White light is light made of a continuous range of wavelengths
A rainbow represents light separated into a continuous spectrum
The EM spectrum contains all forms of EM radiation
 Visible light resides in a tiny band of wavelengths (Roy G. Biv)
o Red - Orange - Yellow - Green - Blue - Indigo - Violet
Particle Nature of Light
 Light behaves as both a wave and a particle
 The Quantum Concept
 As objects absorb and release energy, they emit different colors of light

Max Planck – German Physicist (1858-1947)
 Suggested that energy is emitted or absorbed only in specific little
packets which he called “quanta”
 A quantum is the smallest amount of energy that may be gained or
lost by an atom
 When objects emit different colors of light they are emitting a specific
quantity (quanta)
 Planck’s equation
Equantum = h
Where E = energy, h = Planck’s constant and  = frequency
h = 6.6262x10-34Js
 Energy increases with frequency but only at set intervals (1h, 2h,
3h, etc.)
 The Photoelectric Effect
 Electrons (photoelectrons) are
emitted from a metal’s surface
when light of a certain frequency
shines on it
 A minimum frequency is
required to activate a metal
into ejecting photoelectrons
 Albert Einstein – German
Physicist (1879-1955)
 Proposed that EM radiation
has both particle and wave
properties
 A beam of light behaves both like a wave and a stream of particles
called photons
 Photon – a particle of EM radiation with no mass that carries a
quantum of energy
o
o
Ephoton = h
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5.2
Einstein extended Planck’s equation to photons
Einstein proposed that a photon of light must have a minimum
threshold value to eject a photoelectron
Quantum Theory & the Atom
Objectives:
1. Relate energy levels and orbitals
2.
3.
4.
5.
Describe the significance of line spectra
Describe how & why the quantum mechanical model was developed
Describe the quantum mechanical model
Describe the ways in which electrons are stored in the electron cloud
Bohr Model of the Atom
 Niels Bohr – Danish Physicist (1885-1962)
 Proposed that electrons travelling around the nucleus of an atom must
have energy that is quantized.
 If the energy of the electron is quantized, the orbits of electrons must
correspond to quantized changes in energy.
 Ground state = lowest allowable energy
state of an atom
 Excited state = state of the atom when
it has absorbed energy
 Atoms (even H) may have many
excited states
 Suggested that electrons may only follow
certain orbits based on the energy of the
electron
 The smaller the orbit, the lower the energy state
 The larger the orbit, the higher the energy state
 Bohr assigned numbers to these orbits based on their radius
 The number are called quantum numbers (n)
 n = 1 : first energy level, radius 0.0529 nm
 n = 2 : second energy level, radius 0.212 nm
 etc.
 Hydrogen’s Line Spectrum
 Hydrogen in the ground state does not
radiate energy
 When the electron absorbs the appropriate amount of energy, it jumps to a
higher energy level called an excited state. (n = 2, n = 3, etc.)
 When the electron falls from the excited state to a lower or ground state, it
gives off energy in the form of photons.
∆E = Ehigher-energy orbit – Elower-energy orbit = Ephoton = h
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Only certain frequencies may be
emitted because only certain energy
changes are possible
While Bohr’s model worked well for
hydrogen, it didn’t for other elements
and has been shown to be fundamentally incorrect
The Quantum Mechanical Model of the Atom
 Electrons as Waves
 Louis de Broglie – French student (1892-1987)
 only whole numbers of wavelengths
are allowed in a circular orbit of fixed
radius
 If light can be both a wave & particle,
can electrons be both particles &
waves?
 If electrons have wave-like motions,
they are restricted to orbits of fixed
frequencies and energies.
 = h/mv
Where  = wavelength, h = Planck’s constant, m = mass and v =
velocity
 de Broglie’s Equation predicts that all moving particles have wave
characteristics
The Heisenberg Uncertainty Principle
 Werner Heisenberg – German physicist (1901-1976)
 Proposed that one cannot predict exactly where a particle will move since
it’s impossible to measure the location and momentum of a particle
simultaneously.
 Leads to the proposition that electron position around a nucleus cannot be
precisely known, only predicted with a given probability.
 Erwin Schrodinger – Austrian physicist (1887-1961)
 Developed a model that treated the electron as a wave.
 Where the Bohr model worked only for hydrogen, Schrodinger’s model
worked for other atoms as well.
 Schrodinger’s wave model is referred to as the Quantum-Mechanical
Model of the Atom
 The Quantum-Mechanical Model
 Electrons’ energies are confined to certain values
 Electrons’ paths are neither simple nor predictable
 Describes electrons’ locations as probabilities of being found in a certain
area of space around the nucleus
 Atomic Orbitals
 Electron density – probability of finding an electron in a given area
around the nucleus.
 Electron density is high where there is a high probability of finding an
electron.
o
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An orbital represents the space around the nucleus where electron
density is high
Orbitals exist at different distances from the nucleus and have
different shapes and sizes
Differences from Bohr & Rutherford Models
Rutherford
Bohr
QuantumMechanical
Hydrogen’s Atomic Orbitals
 Orbitals
 An orbital represents an area where a given electron is likely to be found
90% of the time – the other 10% of the time it will be outside of this area.
 The orbital that an electron occupies is determined by the energy of the
electron.
 Orbital shapes are the result of electron energy and electron repulsion
(since electrons are all negatively charged and repel one another.)
 Quantum Numbers
 The probable locations of electrons can be described using 4 quantum
numbers (n, l, m, s).
 Principal Quantum Number (n)
 Electrons can occupy only specific energy levels or quantum levels
(distances from the nucleus).
 These energy levels are called principal energy levels and are
numbered. The number is an integer called the principal quantum
number (n). (n=1, n=2, n=3, etc.)
 Energy increases as n increases.
 The greatest number of electrons that can be found in any principal
energy level = 2n2.
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Sub-levels (l)
 Principal energy levels can be broken down into sub-levels
represented by the letter l.
 The number of sub-levels in a principal energy level is equal to the
principal quantum number. (# of sublevels n = n). There is 1 sub-level
in l1, 2 in l2, etc.
 Sub-levels are generally labeled using the letters (s,p,d,f). (They may
also be numbered 0 – 3.)
Orbitals (m)
 Sub-levels can be broken down into orbitals represented by the letter
m.
 An orbital is the space within a sub-level occupied by a pair of
electrons.
o
s has 1 orbital (can hold 2 e-)
o
p has 3 orbitals (can hold 6 e-)
o
d has 5 orbitals (can hold 10 e-)
o
f has 7 orbitals (can hold 14 e-)
 The quantum number m can be used to differentiate between orbitals
in a sub-level. m is an integer between –l and l.
 Each orbital has a characteristic shape.
o
s = spherical
o
p = dumbbell shaped (px, py , pz )
o
d = cloverleaf shaped (d x2-y 2, dxy , dxz , dyz , dz 2)
o
f = variable shapes
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5.3
Electron Spin (s)
 Each orbital can hold two electrons that spin in opposite directions.
 The electrons in an orbital can be labeled using the quantum number
s.
 The spin can be described as either clockwise (s = +1/2) or counterclockwise (s=-1/2).
Using these 4 quantum numbers (n, l, m, s) one may describe a specific
electron’s probable location in space.
Electron Configurations
Objectives:
1. Draw box-orbital diagrams from atoms
2. Write electron configurations for atoms
3. Draw Lewis Dot Diagrams for atoms
Ground-State Electron Configurations
 Electron configuration
 Distribution of electrons among orbitals within an electron cloud.
 Describe the location of electrons and the energies they possess
 Dictate the bonding characteristics of the atoms
 Are determined by distributing electrons into principal energy levels, sublevels and orbitals based on a stated set of principals.
 When the electrons are in their lowest, most compact state (close to the
nucleus) they are said to be in their ground state. This is the most stable
form of the atom and the one we usually work with.
 Aufbau Principle
 Electrons occupy the lowest energy orbitals available.
 Basics of the Aufbau principle:
 All orbitals within a sublevel are of equal energy
 Sublevels within a principal energy level have different energies
increasing in the order: s-p-d-f.
 Overlap may occur between orbitals in different energy levels
 Pauli Exclusion Principle
 Determined that an orbital may hold a maximum of 2 electrons and that
the electrons must have opposite spins to occupy the same orbital.
 These 2 electrons within an orbital are said to be “paired”.
 The Pauli Exclusion Principle states that no 2 electrons may have the
same set of 4 quantum numbers.
 Hund’s Rule
 Electrons are all negatively charged and repel one another.
 Electrons will fill equal energy orbitals in such a way that a maximum
number of unpaired electrons result.
Orbital Diagrams and Electron Configuration Notations
 Orbital Diagrams
 Orbitals are represented by boxes and arrows are placed in the boxes to
represent electrons.
 Arrows are placed in the boxes using the Aufbau, Pauli and Hund
Principles.
 Each of the arrows within a box is drawn as pointing up or down to
represent the spin of the electron. A paired set of electrons would have one
up arrow and one down arrow.
1s 2s
 

2p

3s
3p
4s
3d
4p
5s
4d
 Electron Configurations
 A shorthand way of writing electron configurations.
 Involves listing the sub-levels (1s, 2s, 2p, 3s, 3p, 4s, 3d, etc.) and the
number of electrons in each as a superscript following the sub-level. The
sum of the superscripts = the number of e-.
 Examples:
C = 1s 22s 22p2
2+2+2=6
C has 6 e-.
Mg = 1s 22s 22p63s 2
2+2+6+2 = 12
Mg has 12 e-.
 Exceptions to the Aufbau Principle
 In some circumstances electrons may be redistributed into orbitals that
provide more stable configurations than those expected.
 Chromium & copper are two common exceptions where electrons act
unexpectedly
 The actual configurations are more stable than the expected.
Chromium – Expected (1s2 2s2p6 3s2p6 4s2 3d4)
1s
2s
2p
3s
3p
4s
3d
          


4p
5s
4d
4p
5s
4d
4p
5s
4d
4p
5s
4d

Chromium – Actual (1s2 2s2p6 3s2p6 4s1 3d5)
1s
2s
2p
3s
3p
4s
         
3d





Copper – Expected (1s2 2s2p6 3s2p6 4s2 3d9)
1s
2s
2p
3s
3p
4s
3d
              
Copper – Actual (1s2 2s2p6 3s2p6 4s1 3d10)
1s
2s
2p
3s
3p
4s
3d
              
Valence Electrons
 Valence electrons
 The electrons in the outermost orbitals determine the chemical properties
of an element
 Abbreviated Electron Configurations
 Since the outermost electrons are the important ones, we sometimes
use abbreviations for electron configurations
 The inner core electrons are described by using the symbol of the
noble gas they represent
2
2 6
2 6
1
10
1
10
 Instead of 1s 2s p 3s p 4s 3d , we would write [Ar]4s 3d . [Ar] is
used instead of 1s2 2s2p6 3s2p6.
 Electron-Dot Structures
 Gilbert Lewis – American chemist (1875-1946)
Developed way of diagramming valence electrons for an atom that
can be used for predicting bonding properties.
Valence electrons are represented by dots placed around the atomic
symbol of the atom one at a time until all are accounted for.
There cannot be more than 2 electrons on any given side and no more than
8 total.
For main-group elements, the number of valence e- is equal to the group
number.
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