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Chapter 7Atomic Structure and Periodicity

• Electromagnetic Radiation

Radiant energy that exhibits wavelength-likebehavior and travels through space at thespeed of light in a vacuum.

• Example: The sun light, energy used inmicrowave oven, the x-rays used by doctors.

Waves

Waves have 3 primary characteristics:

1. Wavelength (): distance between twoconsecutive peaks in a wave.

2. Frequency (): number of waves (cycles)per second that pass a given point in space.

3. Speed: speed of light is 2.9979 108

m/s. We will use 3.00 x108 m/s.

The Nature of Waves

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Wavelength and frequency can be interconvertedand they have an inverse relationship

= c/ = frequency (s1)

= wavelength (m)

c = speed of light (m s1)

• Wavelength is also given in nm (1 nm = 10-9 m)and Angstroms (Å) (1 Å = 10-10 m).

• The frequency value of s1 or 1/s is also called“hertz (Hz)” like KHz on the radio.

Classification of Electromagnetic Radiation

Example: When green light is emitted from anoxygen atom it has a wavelength of 558 nm.What is the frequency?

We know,

= c/ where, c = speed of light

= 3.00 x 108m/s

= wavelength

= 558 nm

(need to convert in m)

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Planck’s Constant• Transfer of energy is quantized, and can only

occur in discrete units, called quanta.

E = change in energy, in J

h = Planck’s constant, 6.626 1034 J s

= frequency, in s1

= wavelength, in m

• Example: The Blue color in fireworks is often achieved by heating copper (I) chloride (CuCl) to about 1200oC. Then the compound emits blue light having a wavelength of 450 nm. What is the increment of energy (the quantum) that is emitted at 4.50 x 102 nm by CuCl?The quantum of energy can be calculate from the equation

E = hThe frequency for this case can be calculated as follows:

So,E = h = (6.626 x 10-34J.s)(6.66 x 1014 s-1)

= 4.41 x 10-19JA sample of CuCl emitting light at 450 nm can only lose energy in increments of 4.41 x 10-19J, the size of the quantum in this case.

Energy and Mass

• According to Einstein theory of relativity-

Energy has mass; Einstein equation,

E = mc2 where, E = energy, m = mass

c = speed of light

• After rearrangement of the equation,

Now we can calculate the mass associated

with a given quantity of energy

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• Einstein suggested that electromagnetic radiationcan be viewed as a stream of “particles” calledphotons. The energy of each photon is given by,

• It was Einstein who realized that light could notbe explained completely as waves but had tohave particle properties. This is called the dualnature of light.

Electromagnetic Radiation

Wavelength and Mass

• de Broglie thought if waves like light could haveparticle properties that particles like electrons couldhave wave properties. We have,

de Broglie’s equation,

= wavelength (m); m = mass (kg); = velocity (m/s)h = Planck’s constant, 6.626 1034 J s = kg m2 s1

• This equation allows us to calculate the wavelength of aparticle. Matter exhibits both particulate and waveproperties.

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• Example: Compare the wavelength for an electron(mass = 9.11 x 10-31 kg) traveling at a speed of 1.0 x107 m/s with that for a ball (mass = 0.10 kg) traveling at35 m/s.

We use the equation = h/m, where

h = 6.626 1034 J.s or 6.626 1034 kg m2 /s

since, 1 J = 1 kg. m2 /s2

For the electron,

For the ball,

Atomic Spectrum of Hydrogen

• When H2 molecules absorb energy, some of the H-Hbonds are broken and resulting hydrogen atoms areexcited. The excess energy is released by emitting light ofvarious wavelengths to produce the emission spectrum ofhydrogen atom.

• Continuous spectrum: Contains all the wavelengths oflight.

Line (discrete) spectrum: Contains only some of thewavelengths of light. Only certain energies are allowed,i.e., the energy of the electron in the hydrogen atom isquantized.

A Continuous Spectrum (a) and A Hydrogen Line Spectrum (b)

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A Change between Two Discrete Energy Levels

The Bohr Model• The electron in a hydrogen atom moves around the

nucleus only in certain allowed circular orbits. Theenergy levels available to the hydrogen atom:

E = energy of the levels in the H-atomz = nuclear charge (for H, z = 1)n = an integer, the large the value, the larger is theorbital radius.

• Bohr was able to calculate hydrogen atom energy levelsthat exactly matched the experimental value. Thenegative sign in the above equation means that theenergy of the electron bound to the nucleus is lower thanit would be if the electron were at an infinite distance.

Electronic Transitions in the Bohr Model for the Hydrogen Atom

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• Ground State: The lowest possible energy state for an atom (n = 1).

• Energy Changes in the Hydrogen Atom

E = Efinal state Einitial state

= -2.178 x 10-18J

• The wavelength of absorbed or emitted photon can be calculated from the equation,

Example: Calculate the energy required to excitethe hydrogen electron from level n = 1 to level n =2. Also calculate the wavelength of light that mustbe absorbed by a hydrogen atom in its ground stateto reach this excited state.Using Equation, with Z = 1 we have

E1 = -2.178 x 10-18 J(12/12) = -2.178 x 10-18 JE2 = -2.178 x 10-18 J(12/22) = -5.445 x 10-19 J

E = E2 - E1 = (-5.445 x 10-19 J) – (-2.178 x 10-18 J) = 1.633 x 10-18 J

The positive value for E indicates that thesystem has gained energy. The wavelength oflight that must be absorbed to produce thischange is

(6.626 x 10-34 J.s)(2.9979 x 108 m/s)1.633 x 10-18 J

= 1.216 x 10-7 m

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Example: Calculate the energy required to removethe electron from a hydrogen atom in its groundstate.

Removing the electron from a hydrogen atom in itsground state corresponds to taking the electronfrom ninitial = 1 to nfinal = . Thus,

E = -2.178 x 10-18 J

= -2.178 x 10-18 J

The energy required to remove the electron from a hydrogen atom in its ground state is 2.178 x 10-18 J.

Quantum MechanicsBased on the wave properties of the atomSchrodinger’s equation is (too complicated to bedetailed here),

= wave function= mathematical operator

E = total energy of the atomA specific wave function is often called an orbital.This equation is based on operators – not simplealgebra. This is a mathematical concept you will nothave dealt with yet.

Heisenberg Uncertainty Principle

x = positionmv = momentumh = Planck’s constantThe more accurately we know a particle’sposition, the less accurately we can know itsmomentum. Both the position and momentumof a particle can not be determined precisely at agiven time. The uncertainty principle impliesthat we cannot know the exact motion of theelectron as it moves around the nucleus.

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Radial Probability Distribution

Quantum Numbers (QN)When we solve the Schrodinger equation, we find manywave functions (orbitals) that satisfy it. Each of theseorbitals is characterized by a series of numbers calledquantum numbers, which describe various properties ofthe orbital.1. Principal QN (n = 1, 2, 3, . . .) - related to size and energy of the orbital.2. Angular Momentum QN (l = 0 to n 1) - relates to shape of the orbital. l = 0 is called s; l = 1 is called p; l = 2 is called d; l = 3 is called f.3. Magnetic QN (ml = l to l including 0) - relates to orientation of the orbital in space relative to other orbitals.4. Electron Spin QN (ms = +1/2, 1/2) - relates to the spin states of the electrons.

Example: For principal quantum level n = 5,determine the number of allowed subshells(different values of l), and give the designation ofeach.

For n = 5, the allowed values of l run from 0 to 4(n – 1 = 5 – 1). Thus the subshells and theirdesignations are

l = 0 l = 1 l = 2 l = 3 l = 4

5s 5p 5d 5f 5g

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Orbital Shapes and EnergiesTwo types of representations for the hydrogen 1s, 2s and 3s orbitals are shown below. The s orbitals are spherical shape.

Two Representations of the Hydrogen 1s, 2s, and 3s Orbitals

Representation of p orbitalsThe p orbitals are not spherical like s orbital but have twoloves separated by a node at the nucleus. The p orbitals arelabeled according the axis of the xyz coordinate system.

The Boundary Surface Representations of All Three 2p Orbitals

Representation d orbitals

The five d orbital shapes are shown below. The d orbitals have two different fundamental shapes.

The Boundary Surfaces of All of the 3d Orbitals

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Energy Diagram for Hydrogen AtomThe energy of a particular orbital is determined by its valueof n. All orbitals with the same value of n have the sameenergy and are said to be degenerate. Hydrogen singleelectron occupy the lowest energy state, the ground state.If energy is put into the system, the electron can betransferred to higher energy orbital called excited state.

Orbital Energy Levels for the Hydrogen Atom

Pauli Exclusion Principle

• In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, ms).

• Therefore, an orbital can hold only two electrons, and they must have opposite spins.

Polyelectronic Atoms

• For polyelectronic atoms in a given principalquantum level all orbital are not in same energy(degenerate). For a given principal quantum levelthe orbitals vary in energy as follows:

Ens< Enp < End < Enf

• In other words, when electrons are placed in aparticular quantum level, they prefer the orbital inthe order s, p, d and then f.

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Aufbau Principle

As protons are added one by one to the nucleusto build up the elements, electrons are similarlyadded to these hydrogen-like orbitals.

H : 1s1, He : 1s2, Li : 1s2 2s1, Be : 1s2 2s2

B : 1s2 2s2 2p1, C : 1s2 2s2 2p2.

Hund’s Rule

The lowest energy configuration for an atom isthe one having the maximum number ofunpaired electrons allowed by the Pauli principlein a particular set of degenerate orbitals.

N : 1s2 2s2 2p3, O : 1s2 2s2 2p4,

F : 1s2 2s2 2p5, Ne : 1s2 2s2 2p6,

Na : 1s2 2s2 2p63s1 OR [Ne] 3s1

The Electron Configurations in the Type of Orbital Occupied Last for the First 18 Elements

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Valence Electrons

The electrons in the outermost principle quantum level of an atom.

Valence electron is the most important electronsto us because they are involved in bonding.Elements with the same valence electronconfiguration show similar chemical behavior.Inner electrons are called core electrons.

Electron Configurations for Potassium Through Krypton

The Orbitals Being Filled for Elements in Various Parts of the Periodic Table

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The Periodic Table With Atomic Symbols, Atomic Numbers, and Partial Electron Configurations

Broad Periodic Table Classifications

• Representative Elements (main group): filling sand p orbitals (Na, Al, Ne, O)

• Transition Elements: filling d orbitals (Fe, Co, Ni)

• Lanthanide and Actinide Series (inner transition elements): filling 4f and 5f orbitals (Eu, Am, Es)

The Order in which the Orbitals Fill in Polyelectronic Atoms

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Ionization Energy

The quantity of energy required to remove an electron from the gaseous atom or ion.

X(g) X+ (g) + e-

where, the atom or ion is assumed to be in its ground state.

Periodic Trends

First ionization energy:

increases from left to right across a period;

decreases going down a group.

The Values of First Ionization Energy for The Elements in the First Six Periods

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Trends in Ionization Energies for the Representative Elements

Electron Affinity

The energy change associated with the additionof an electron to a gaseous atom.

X(g) + e X(g)

These values tend to be exothermic (energyreleased). Adding an electron to an atom causes itto give off energy. So the value for electronaffinity will carry a negative sign.

The Electronic Affinity Values for Atoms Among the First 20 Elements that Form Stable, Isolated X- Ions

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Periodic TrendsAtomic Radii: Atomic radii can be obtained bymeasuring the distances between atoms in chemicalcompounds and atomic radius is assumed to be halfthis distance.

• Decrease going from left to right across a period.This decrease can be explained in terms of theincreasing effective nuclear charge in going fromleft to right. The valence electron are drawn closerto the nucleus, decreasing the size of the atom.

• Increase going down a group, because of theincrease in orbital sizes in successive principalquantum levels.

The Radius of an Atom

Atomic Radii for Selected Atoms

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Information Contained in the Periodic Table

1. Each group member has the same valence electronconfiguration. Group elements exhibit similar chemicalproperties.

2. The electron configuration of any representative element canbe obtained from periodic table. Transition metals – twoexceptions, chromium and copper.

3. Certain groups have special names (alkali metals, halogens,etc).

4. Metals and nonmetals are characterized by their chemicaland physical properties. Many elements along the divisionline exhibit both metallic and non metallic properties whichare called metalloids or semimetals.

Special Names for Groups in the Periodic Table

Summary• Electromagnetic Radiation: Wavelength like

behavior.• Frequency, = c/ ( = wavelength, c = speed of

light).• Energy Transfer, E = h = hc/• de Broglie’s Equation: = h/m• The Bohr Model: electron in a hydrogen atom moves

around the nucleus only in certain allowed circularorbits.

• Quantum Mechanics: H= E• Heisenberg Uncertainty Principle: Position and

momentum cannot be determined precisely at agiven time.

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• Quantum Numbers: Principal QN, Angular momentum QN, Magnetic QN, an Electron Spin QN.

• Orbital Shapes and Energies: s, p, and d orbitals.• Pauli Exclusion Principle:• Aufbau Principle:• Hund’s Rule:• Periodic Table:• Ionization Energy:• Electron Affinity:• Periodic Trends: