Chapter 7Electronic Structure

of Atoms

Recall:

• The concept of atoms proposed by Dalton explained many important observations:

- such as why compounds always have the same composition and how chemical rxns. occur• Once chemists were convinced of the

existence of atoms…..they naturally began to ask what atoms looked like?

The studies of Thomson, Rutherford and Chadwick

• Lead to our picture of the atom: - which includes a solid dense nucleus

containing protons and neutrons about which we find the negatively charged

electrons

In this Chapter we will look at the atomic structure in more detail.

• In particular we will develop a picture of the electron arrangements in atoms

• This picture will allow us to account for the chemistry of the elements

• With this knowledge we will revisit the arrangements of the elements in the periodic table and see why there are striking differences in the chemical properties of elements in the groups

Electromagnetic Radiation and Energy

• The sun is a central source of energy

• Energy from the sun travels through space in the form of electromagnetic radiation

Forms of Electromagnetic Radiation

• Visible light is a form of electromagnetic radiation• Microwaves are another form of electromagnetic

radiation• X-rays are yet another form of electromagnetic

radiation***all of these forms of energy are different, but they are

all forms of electromagnetic radiation

Electromagnetic Radiation

• All forms of electromagnetic radiation exhibit wave-like behavior and travel at the speed of light in a vacuum (airless space)

speed of light = 3.8 x 1010cm/s or 186,000 mi/s

Waves

• Waves have 3 primary characteristics:1. Wavelength- λ (Greek letter lambda) is the distance between 2

consecutive peaks or troughs in a wave2. Frequency- υ (Greek letter nu) it indicates how many waves

pass a given point per second3. Speed- indicates how fast a given peak moves through space

• Electromagnetic radiation from the sun is divided into various classes (forms) according to λ (wavelength)

• Energy from the sun reaches the earth in the form of visible and ultra-violet light

• Hot coals emit infrared radiation• Microwave ovens use microwave radiation to heat food**** all have different wavelengths

Visible Light

• Also known as white light• When passed through a prism

it separates into a continuous range of colors with one gradually blending into another called the continuous spectrum(rainbow)

• Separation is due to different speeds in the prisim

• Each color of light has a specific wavelength

Continuous Spectrum

• Violet has the shortest wavelength• Red has the longest wavelength

Wavelength and energy

• Wavelength and energy have an inverse relationship, as shown below

• h is Planck’s constant (6.626 10-34 J·s)

• c is the speed of light

hc

EE 1

Energy and Wavelength

• Red light with the longest wavelength has the lowest energy

• Purple light with the shortest wavelength has the highest energy

The Nature of Energy

• The wave nature of light does not explain how an object can glow when its temperature increases.

• Max Planck explained it by assuming that energy comes in packets called quanta.

Photoelectric Effect

A freshly polished, negatively charged zinc plate looses its charge if it is exposed to ultraviolet light. This phenomenon is called the photoelectric effect.

The Nature of Energy

• Einstein used this assumption to explain the photoelectric effect.

• He concluded that energy is proportional to frequency:

E = hwhere h is Planck’s constant, 6.63 10−34 J-s.

The Nature of Energy

• Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:

c = E = h

The Nature of Energy

Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

Heating an Element

• When an element is heated strongly to the point that the element changes phase to a gas, the gaseous atoms emit light like the sun

• One might think that the light produced would result in a continuous spectrum like light emitted from the sun…………instead…….

When an element is heated..

• Only definite or discrete colors are produced• Since colors are discrete (definite) and the colors

correspond to energies• The energy being emitted by the atoms of the

element is also discrete

An Elements Spectrum

• Is unique to that element• Are called Atomic Emission Spectra or Line

Spectra• Are the basis of a fireworks display

The Nature of Energy

• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:

1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies).

The Nature of Energy

• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:

2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

The Nature of Energy

• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:

3. Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by

E = h

The Nature of Energy

The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:

E = −RH ( )1nf

2

1ni

2-

where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron.

Electronic Structure

Good Points• Electrons in Quantized

Energy Levels• Maximum # electrons in

each n is 2n2

• Sublevels (s,p,d,f) and # electrons they hold

Bad Points• Electrons are placed in

orbits about nucleus• Only explains emission

spectra of H2

• Does not address all interactions

• Treats electron as particle

The Wave Nature of Matter

• Louis de Broglie postulated that if light can have material properties, matter should exhibit wave properties.

• He demonstrated that the relationship between mass and wavelength was

=h

mv

The Uncertainty Principle

• Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known:

• In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

(x) (mv) h4

Dual Nature of Electron

Previous Concept; A Substance is Either Matter or Energy

• Matter; Definite Mass and Position Made of Particles

• Energy; Massless and Delocalized Position not Specificed Wave-like

Dual Nature of Electron

• Electron is both “particle-like” and “wave-like” at the same time.

• Previous model only considered “particle-like” nature of the electron

Orbitals Replace Orbits

• Bohr Orbits- Both electron position and energy known with certainty

• Orbitals – Regions of space where an electrons of a given energy will most likely be found

Quantum TheoryOrbitals Replace Orbits

Orbits Orbitals

Quantum Mechanics

• Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated.

• It is known as quantum mechanics.

Schrodinger Wave Equation ()

Describes size/shape/orientation of orbitals

7.5

• Wave Equation is based on…

1. Dual Nature of Electron (Electron both particle and wave-like at the same time.)

2. Heisenberg Uncertainty Principle(Orbitals describe a region in space an electron will most likely be.)

Wave Equation ()

• Wave Equation describes the size, shape, and orientation of the orbital the electron (of a given energy) is in. There are four variables in the function

-n; Energy and size of orbital– l; Shape of orbital– ml; Orientation of orbital

– ms; Electron Spin

(n, l, ml, ms)

Quantum Mechanics

• The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.

1. Each electron has a unique set of 4 Quantum Numbers

2. Each orbital described by the Quantum Numbers can hold a maximum of 2 electrons.

Principal Quantum Number, n

• The principal quantum number, n, describes the energy level on which the orbital resides.

• The values of n are integers ≥ 0.• n= 1, 2, 3, 4, ….

distance of e- from the nucleus

Azimuthal Quantum Number, l

• This quantum number defines the shape of the orbital.

• Allowed values of l are integers ranging from 0 to n − 1.

• We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

Azimuthal Quantum Number, l

Value of l 0 1 2 3

Type of orbital s p d f

Magnetic Quantum Number, ml

• Describes the three-dimensional orientation of the orbital in space.

• Values are integers ranging from -l to l: −l ≤ ml ≤ l.

• Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

Magnetic Quantum Number, ml

• Orbitals with the same value of n form a shell.• Different orbital types within a shell are subshells.

s Orbitals

• Value of l = 0.• Spherical in shape.• Radius of sphere

increases with increasing value of n.

s Orbitals

Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.

p Orbitals

• Value of l = 1.• Have two lobes with a node between them.

d Orbitals

• Value of l is 2.• Four of the five

orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

f-orbitals

Orbital Shapes

Orbital Type Shape Name

s Spherical

p Dumbbell

d Complex

f More complex

Energies of Orbitals

• For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.

• That is, they are degenerate.

Energies of Orbitals

• As the number of electrons increases, though, so does the repulsion between them.

• Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.

Spin Quantum Number, ms

• In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.

• The “spin” of an electron describes its magnetic field, which affects its energy.

Spin Quantum Number, ms

• This led to a fourth quantum number, the spin quantum number, ms.

• The spin quantum number has only 2 allowed values: +1/2 and −1/2.

Pauli Exclusion Principle

• No two electrons in the same atom can have exactly the same energy.

• For example, no two electrons in the same atom can have identical sets of quantum numbers.

How many 2p orbitals are there in an atom?

2p

n=2

l = 1

If l = 1, then ml = -1, 0, or +1

3 orbitals

How many electrons can be placed in the 3d subshell?

3d

n=3

l = 2

If l = 2, then ml = -2, -1, 0, +1, or +2

5 orbitals which can hold a total of 10 e-

7.6

Three Manners to Convey How Electrons are Arranged

1. Electron Configuration ; List Orbitals and Number of Electrons in Each(1s22s22p63s2…)

2. Quantum Numbers (2,0,0,+1/2)3. Orbital Diagrams; List Orbitals and show

location of electrons and their spin

1s 2s 2p

Electron Configurations

• Distribution of all electrons in an atom

• Consist of – Number denoting the

energy level

Electron Configurations

• Distribution of all electrons in an atom

• Consist of – Number denoting the

energy level– Letter denoting the type of

orbital

Electron Configurations

• Distribution of all electrons in an atom.

• Consist of – Number denoting the

energy level.– Letter denoting the type of

orbital.– Superscript denoting the

number of electrons in those orbitals.

Writing Atomic ElectronConfigurations

Two ways of writing configurations:• One is called the spdf notation.spdf notation for H, atomic number = 1

1 s1

no. ofelectrons

value of lvalue of n

Writing Atomic ElectronConfigurations

• The spdf notation can be shortened using the noble gas notation.

spdf notation for K, atomic number = 191s22s22p63s23p64s1 OR [Ar]4s1

core e- valence e-

Orbital Diagrams

• Each box represents one orbital.

• Half-arrows represent the electrons.

• The direction of the arrow represents the spin of the electron.

Hund’s Rule

“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

7.7

Orbital Diagrams

1s 2s 2p

Carbon; 6 electrons

Electron Configuration; 1s22s22p2

Orbital Diagram

Paramagneticunpaired electrons

2p

Diamagneticall electrons paired

2p7.8

Periodic Table

• We fill orbitals in increasing order of energy.

• Different blocks on the periodic table, then correspond to different types of orbitals.

Order of orbitals (filling) in multi-electron atom

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s7.7

Some Anomalies

• This occurs because the 4s and 3d orbitals are very close in energy.

• Cu29 is also an anomaly with an expected config. of

[Ar] 4s2 3d9 and an actual config. of

[Ar] 4s1 3d10

• These anomalies occur in f-block atoms, as well.

Ion Configurations

• To form cations from elements remove e-’sfrom the subshell with the highest n.P [Ne] 3s2 3p3 - 3e- → P3+ [Ne] 3s2 3p0

• For transition metals, remove ns electronsand then (n - 1) electrons.Fe [Ar] 4s2 3d6

loses 2 electrons → Fe2+ [Ar] 4s0 3d6

Na+: [Ne] Al3+: [Ne] F-: 1s22s22p6 or [Ne]

O2-: 1s22s22p6 or [Ne] N3-: 1s22s22p6 or [Ne]

Na+, Al3+, F-, O2-, and N3- are all isoelectronic with Ne

What neutral atom is isoelectronic with H- ?

H-: 1s2 same electron configuration as He

8.2