Atomic StructureAtomic Structure

Chapter 6Chapter 6

6.1 Electromagnetic Radiation6.1 Electromagnetic Radiation

All forms of radiation (such as light, All forms of radiation (such as light, microwaves, radio) are forms of energy microwaves, radio) are forms of energy that can be described in a mathematical that can be described in a mathematical theory called theory called electromagnetic radiationelectromagnetic radiation..

The distance between successive crests The distance between successive crests of a wave (or between successive of a wave (or between successive troughs) is the troughs) is the wavelengthwavelength of a wave. of a wave. Wavelength is symbolized by Wavelength is symbolized by λλ (lambda) (lambda) and usually measured in meters or and usually measured in meters or nanometers. nanometers.

Wave PropertiesWave Properties

FrequencyFrequency is the number of wavelengths (or is the number of wavelengths (or cycles) that pass a given point in a second. It is cycles) that pass a given point in a second. It is symbolized by symbolized by νν (nu). (nu). number of events per timenumber of events per time unit of sunit of s-1-1 (1 per second) or Hz (hertz) (1 per second) or Hz (hertz)

Wave PropertiesWave Properties

Wave height is called Wave height is called amplitudeamplitude and points and points of zero amplitude are called of zero amplitude are called nodesnodes. . Nodes occur at intervals of Nodes occur at intervals of λλ/2./2.

Speed of a wave can be calculated by Speed of a wave can be calculated by multiplying wavelength times frequency.multiplying wavelength times frequency.

C = C = λλνν

where C is the speed of light (3.0 x 10where C is the speed of light (3.0 x 1088 m/s) m/s)

Electromagnetic SpectrumElectromagnetic Spectrum

The electromagnetic spectrum includes all the The electromagnetic spectrum includes all the wavelengths of radiant energy from short gamma rays wavelengths of radiant energy from short gamma rays to long radio waves.to long radio waves. The visible spectrum is the part of the spectrum visible to the The visible spectrum is the part of the spectrum visible to the

eye, usually with wavelengths between 400 and 700 nm. eye, usually with wavelengths between 400 and 700 nm.

Example ProblemExample Problem

The wavelength of the radiation which The wavelength of the radiation which produces the yellow color of a sodium produces the yellow color of a sodium vapor light is 589.0 nm. What is the vapor light is 589.0 nm. What is the frequency of radiation?frequency of radiation?

Orange light has a _____ frequency and a Orange light has a _____ frequency and a _____ wavelength than blue light. (see _____ wavelength than blue light. (see page 271)page 271)

6.2 Planck, Einstein, Energy and 6.2 Planck, Einstein, Energy and PhotonsPhotons

Before Planck, predictions to describe the relationship Before Planck, predictions to describe the relationship between wavelength and radiation failed in the ultraviolet between wavelength and radiation failed in the ultraviolet region. region.

Max Planck introduced the concept of Max Planck introduced the concept of quantizedquantized vibrations. vibrations. Quantization means that only certain vibrations (specific Quantization means that only certain vibrations (specific frequencies) are allowed.frequencies) are allowed.

Planck, Einstein, Energy and Planck, Einstein, Energy and PhotonsPhotons

A quantum (or photon) is a particle of light A quantum (or photon) is a particle of light energy that can be absorbed (or emitted) by a energy that can be absorbed (or emitted) by a molecule. The energy of that molecule is molecule. The energy of that molecule is increased (decreased) by an amount equal to increased (decreased) by an amount equal to the energy of the photon.the energy of the photon.

Planck’s constant is a proportionality constant Planck’s constant is a proportionality constant that describes the energy of a photon.that describes the energy of a photon.

E = E = hvhvwhere E is energy (J), where E is energy (J), hh is Planck’s constant is Planck’s constant

(J(J∙s), and ∙s), and vv is frequency (s is frequency (s-1-1))

Planck, Einstein, Energy and Planck, Einstein, Energy and PhotonsPhotons

Light can cause chemical reactions to Light can cause chemical reactions to occur! (paint fades, cloth decomposes)occur! (paint fades, cloth decomposes)

As frequency increases, energy of As frequency increases, energy of radiation increases. Energy also radiation increases. Energy also increases as the wavelength decreases.increases as the wavelength decreases.

E = E = hvhv = ( = (hhc)/c)/λλ

(example: UV light has more energy than (example: UV light has more energy than visible light due to shorter wavelengths)visible light due to shorter wavelengths)

Planck, Einstein, Energy and Planck, Einstein, Energy and PhotonsPhotons

higher intensity of light would mean there are higher intensity of light would mean there are more photons to strike a surface per unit of timemore photons to strike a surface per unit of time

photons have to have enough energy to remove photons have to have enough energy to remove electrons from an atomelectrons from an atom

once the minimum energy (light frequency) is once the minimum energy (light frequency) is exceeded, the photons have enough energy to exceeded, the photons have enough energy to displace electronsdisplace electrons

more high energy photons means more more high energy photons means more electrons displacedelectrons displaced

νν = c/ = c/λλ E = hE = hνν E = hc/E = hc/λλ

λλ = wavelength = wavelength in nmin nm

V = frequency V = frequency in 1/s or Hzin 1/s or Hz

E = energy of a E = energy of a single photon in single photon in joulesjoules

C = speed of C = speed of light = 3.00 x light = 3.00 x 10101717 nm/s nm/s

h = Planck’s h = Planck’s constant = 6.63 constant = 6.63 x 10x 10-34-34 J-s J-s

Planck, Einstein, Energy and Planck, Einstein, Energy and PhotonsPhotons

The The photoelectric effectphotoelectric effect occurs when light occurs when light strikes the surface of a metal and strikes the surface of a metal and electrons are ejected. electrons are ejected.

Einstein combined Planck’s equation with Einstein combined Planck’s equation with the concept of the concept of photonsphotons, the “particles” of , the “particles” of light. Electromagnetic radiation is thought light. Electromagnetic radiation is thought of a stream of photons. of a stream of photons. Matter is allowed to emit or absorb energy Matter is allowed to emit or absorb energy

only in discrete amounts. only in discrete amounts.

Practice ProblemPractice Problem

What is the frequency, the energy of a What is the frequency, the energy of a single photon, and the energy of a mole of single photon, and the energy of a mole of photons of light having a wavelength of photons of light having a wavelength of 555 nm?555 nm?

Practice ProblemPractice Problem

Calculate (a) the energy in joules of a Calculate (a) the energy in joules of a photon emitted by an excited sodium atom photon emitted by an excited sodium atom (wavelength 600 nm) and (b) the energy in (wavelength 600 nm) and (b) the energy in kJ of a mole of photons.kJ of a mole of photons.

HomeworkHomework

After reading sections 6.1 and 6.2, you After reading sections 6.1 and 6.2, you should be able to do the following…should be able to do the following…

p. 297 (3-12)p. 297 (3-12)

6.3 Atomic Line Spectra and Niels 6.3 Atomic Line Spectra and Niels BohrBohr

Atomic Line SpectraAtomic Line Spectra A spectrum that consists of light of all A spectrum that consists of light of all

wavelengths is called a wavelengths is called a continuous spectrumcontinuous spectrum.. A A line emission spectrumline emission spectrum (or atomic emission (or atomic emission

spectrum) occurs when light from excited spectrum) occurs when light from excited electrons emit only certain wavelengths of electrons emit only certain wavelengths of light. light. • Each element produces a characteristic and Each element produces a characteristic and

identifiable pattern.identifiable pattern.

Line Emission SpectraLine Emission Spectra

Hydrogen’s series of 4 lines is referred to as the Hydrogen’s series of 4 lines is referred to as the Balmer series.Balmer series.

Bohr ModelBohr Model

Niels Bohr connected the emission spectra Niels Bohr connected the emission spectra with Planck and Einstein’s ideas.with Planck and Einstein’s ideas.

Bohr proposed that electrons move in Bohr proposed that electrons move in circular, fixed energy orbits around the circular, fixed energy orbits around the nucleus.nucleus. Each circular orbit corresponds to a stable Each circular orbit corresponds to a stable

energy state. energy state. Bohr introduced quantization into electronic Bohr introduced quantization into electronic

structure!structure!

Bohr ModelBohr Model

An atom with electrons in the lowest An atom with electrons in the lowest possible energy levels is said to be in its possible energy levels is said to be in its ground stateground state. When the electron of a . When the electron of a hydrogen atom occupies an orbit with n hydrogen atom occupies an orbit with n greater than 1, it is said to be greater than 1, it is said to be excited excited statestate. .

Bohr ModelBohr Model

Energy (a photon) is emitted or absorbed Energy (a photon) is emitted or absorbed by an electron when it changes from one by an electron when it changes from one allowed energy state to another.allowed energy state to another.

The lines of the atomic emission spectrum The lines of the atomic emission spectrum of hydrogen result when an electron falls of hydrogen result when an electron falls from a higher allowed state to a lower from a higher allowed state to a lower allowed state.allowed state. The increment between each allowed state is The increment between each allowed state is

proportional to Planck’s constant, the speed proportional to Planck’s constant, the speed of light, and the Rydberg constant, Rof light, and the Rydberg constant, RHH..

Atomic Line SpectraAtomic Line Spectra The Rydberg equation allows us to calculate the wavelengths of different lines in the visible The Rydberg equation allows us to calculate the wavelengths of different lines in the visible

emission spectra of hydrogen atoms. emission spectra of hydrogen atoms. You can use the Rydberg constant and Planck’s constant to calculate the energy states at You can use the Rydberg constant and Planck’s constant to calculate the energy states at

different levels.different levels.

where where R = 1.0974 x 10R = 1.0974 x 1077 m m-1-1

Practice ProblemPractice Problem

Calculate the energies of the n = 3 states Calculate the energies of the n = 3 states of the hydrogen atom in joules per atom of the hydrogen atom in joules per atom and in kilojoules per mole. and in kilojoules per mole.

Bohr Theory and SpectraBohr Theory and Spectra

Electrons stay in lower energy levels unless they Electrons stay in lower energy levels unless they absorb or evolve energy due to some absorb or evolve energy due to some disturbance. disturbance.

Electrons in the ground state have energy with a Electrons in the ground state have energy with a large negative value. As the electron absorbs large negative value. As the electron absorbs energy and moves to a higher energy level, its energy and moves to a higher energy level, its energy becomes less negative. energy becomes less negative. positive change in energy – absorptionpositive change in energy – absorption negative change in energy – emissionnegative change in energy – emission

Bohr Theory and SpectraBohr Theory and Spectra

As electrons naturally As electrons naturally move back to lower move back to lower levels, they emit levels, they emit energy which is energy which is observed as light. observed as light.

This is the atomic emission This is the atomic emission spectrum! The movement spectrum! The movement of electrons between of electrons between quantized energy states. quantized energy states.

Bohr’s model only applies Bohr’s model only applies to H atoms or systems with to H atoms or systems with

one electron.one electron.

6.4 Particle Wave Duality6.4 Particle Wave Duality

Louis Victor de Broglie proposed that Louis Victor de Broglie proposed that matter, such as an electron, could exhibit matter, such as an electron, could exhibit wavelike properties. He said that an wavelike properties. He said that an electron with mass (m) moving with electron with mass (m) moving with velocity (v) should have a wavelength…velocity (v) should have a wavelength…

λλ = h/(mv) = h/(mv) Electrons were experimentally shown to Electrons were experimentally shown to

be diffracted (like light waves) by a thin be diffracted (like light waves) by a thin sheet of foil, so therefore electrons can sheet of foil, so therefore electrons can have wave properties. have wave properties.

Practice ProblemPractice Problem

Calculate the wavelength associated with Calculate the wavelength associated with an electron of mass m = 9.109 x 10an electron of mass m = 9.109 x 10-28-28 g g traveling at 60.0% of the velocity of light.traveling at 60.0% of the velocity of light.

HomeworkHomework

After reading sections 6.3 and 6.4, you After reading sections 6.3 and 6.4, you should be able to do the following…should be able to do the following…

p. 298 (14-20,23-26)p. 298 (14-20,23-26)

6.5 Quantum Mechanical View6.5 Quantum Mechanical View

The general approach to understanding atomic The general approach to understanding atomic behavior that includes theories of Bohr, behavior that includes theories of Bohr, Schrodinger, and others is called Schrodinger, and others is called quantum quantum mechanicsmechanics or wave mechanics. or wave mechanics.

Like light, electrons have properties of both a Like light, electrons have properties of both a wave and a particle. wave and a particle.

Werner Heisenberg concluded that it is Werner Heisenberg concluded that it is impossible to fix both electron position and impossible to fix both electron position and energy if the electron is described as a wave.energy if the electron is described as a wave.

Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle

The uncertainty principle, applied to The uncertainty principle, applied to electrons in an atom, states that it is electrons in an atom, states that it is inherently impossible to simultaneously inherently impossible to simultaneously determine exact position and momentum determine exact position and momentum of an electron. The best that can be done of an electron. The best that can be done is to predict probability of finding an is to predict probability of finding an electron in a certain region of space.electron in a certain region of space.

Schrodinger’s ModelSchrodinger’s Model

Erwin Schrodinger developed Erwin Schrodinger developed mathematical equations with solutions mathematical equations with solutions called called wave functionswave functions ( (ψψ – psi) that are – psi) that are chemically important.chemically important.

The square of a wave function is an The square of a wave function is an orbital.orbital. orbital - probability of finding an electron of a orbital - probability of finding an electron of a

given energy in a region of space (given energy in a region of space (electron electron densitydensity))

Schrodinger’s ModelSchrodinger’s Model

The region of space in which an electron The region of space in which an electron of a given energy is most probably located of a given energy is most probably located is called its is called its orbitalorbital..

Three integer numbers – the Three integer numbers – the quantum quantum numbersnumbers n, ln, l, and , and mmll – are an integral part – are an integral part

of the mathematical solution.of the mathematical solution.

Practice QuestionsPractice Questions

Who proposed the wave-particle properties of Who proposed the wave-particle properties of electrons?electrons?

Who discovered the charge-mass ratio of an Who discovered the charge-mass ratio of an electron?electron?

Who provided the theoretical explanation of the Who provided the theoretical explanation of the photoelectric effect?photoelectric effect?

Who first postulated that the sharp lines in the Who first postulated that the sharp lines in the emission spectra of elements were caused by emission spectra of elements were caused by electrons going from high energy levels to low electrons going from high energy levels to low energy levels?energy levels?

Quantum Mechanical ModelQuantum Mechanical Model

The quantum mechanical model of the The quantum mechanical model of the atom is a mathematical model that atom is a mathematical model that incorporates both wave and particle incorporates both wave and particle characteristics of electrons in atoms.characteristics of electrons in atoms.

HomeworkHomework

After reading section 6.5, you should be After reading section 6.5, you should be able to do the following…able to do the following…

p. 299 (34-38) – needs to be adjusted for p. 299 (34-38) – needs to be adjusted for quantum numbers!quantum numbers!

6.6 Shapes of Atomic Orbitals6.6 Shapes of Atomic Orbitals

Electrons with the Electrons with the highest value of n are highest value of n are valence electrons. valence electrons.

s - orbitals - orbital electrons cluster around the nucleus most of the electrons cluster around the nucleus most of the

time (probabilty is that electrons will be found time (probabilty is that electrons will be found within that radius about 90% of the time) – within that radius about 90% of the time) – electron cloud pictureelectron cloud picture

electron density is greater closer to nucleuselectron density is greater closer to nucleus square of wave function (square of wave function (ΨΨ22) is ) is probability probability

densitydensity – high for points around nucleus – high for points around nucleus s orbital is spherical in shapes orbital is spherical in shape the size of s orbitals and their energy increases the size of s orbitals and their energy increases

as n increasesas n increases

p - orbitalsp - orbitals

All p orbitals have a nodal surface that All p orbitals have a nodal surface that slices through the nucleus and divides the slices through the nucleus and divides the region of electron density in halfregion of electron density in half

dumbbell shapeddumbbell shaped 3 possible orientations3 possible orientations

d - orbitalsd - orbitals

Orientation possibilities are equal to the Orientation possibilities are equal to the number of nodal surfaces that slice number of nodal surfaces that slice through the nucleusthrough the nucleus

2 nodal surfaces divides into four regions 2 nodal surfaces divides into four regions of electron density of electron density

5 d orbitals5 d orbitals

f - orbitalsf - orbitals

seven orbitalsseven orbitals 7 regions of electron density7 regions of electron density

6.7 Electron Spin6.7 Electron Spin

Electrons have an intrinsic property known Electrons have an intrinsic property known as spin that can result in atoms having a as spin that can result in atoms having a magnetic moment. magnetic moment.

At most, two electrons can be At most, two electrons can be accommodated in an orbital, and these accommodated in an orbital, and these electrons must have opposite spin. electrons must have opposite spin.

MagnetismMagnetism

Electrons act as “micromagnets”, and there are Electrons act as “micromagnets”, and there are only two spins possible…only two spins possible…

A material that is slightly repelled by a strong A material that is slightly repelled by a strong magnet is said to be magnet is said to be diamagneticdiamagnetic,, materials that materials that are attracted to a strong magnet are are attracted to a strong magnet are paramagneticparamagnetic; they lose their magnetism once ; they lose their magnetism once removed from the field. removed from the field. Ferromagnetic Ferromagnetic materials retain magnetism upon introduction to materials retain magnetism upon introduction to removal from a magnetic field.removal from a magnetic field.

MagnetismMagnetism

How can we account for the fact that the H How can we account for the fact that the H atom is paramagnetic and the He atom is atom is paramagnetic and the He atom is diamagnetic?diamagnetic?

Atomic Orbitals and ChemistryAtomic Orbitals and Chemistry

By thinking about orbitals of atoms in By thinking about orbitals of atoms in molecules, and by making simple molecules, and by making simple assumptions that they resemble those of assumptions that they resemble those of the hydrogen atom, we can understand the hydrogen atom, we can understand much of the chemistry of complex much of the chemistry of complex systems. systems.