Atomic Theory, the Atomic Theory, the Quantum RevolutionQuantum Revolution

Max Planck’s work on black Max Planck’s work on black body radiationbody radiation

In 1900, In 1900, Max PlanckMax Planck was investigating was investigating why opaque hot why opaque hot objects will glow objects will glow red red hothot, , yellow hotyellow hot, , white hotwhite hot, but not , but not ultraviolet hot.ultraviolet hot. (He (He wanted to find why wanted to find why there is a maximum there is a maximum energy of radiated energy of radiated light.)light.)

Classical physics had predicted Classical physics had predicted the the ultraviolet catastrophe…ultraviolet catastrophe…

……where the spectrum of light emitted where the spectrum of light emitted from a blackbody should show from a blackbody should show unlimited intensity at high frequency, unlimited intensity at high frequency, yet a maximum limit in the spectrum yet a maximum limit in the spectrum was observed, and that could not be was observed, and that could not be explained.  explained. 

Eventually, Max Planck was Eventually, Max Planck was able to explain this…able to explain this…

Planck assumed that light was Planck assumed that light was emitted in small packages of emitted in small packages of energy he called energy he called quanta quanta (singular: quantum)(singular: quantum)

He received the Nobel prize in 1918.He received the Nobel prize in 1918.

The quantized energy The quantized energy existed in integral multiples existed in integral multiples

ofof EE = = hh (Energy = Planck's constant x (Energy = Planck's constant x frequency of frequency of

radiation). radiation).    

Planck made a deduction of this Planck made a deduction of this formula while renouncing classical formula while renouncing classical physics and introducing the physics and introducing the revolutionary idea of revolutionary idea of quantized quantized energy. energy.

Planck’s constant (Planck’s constant (hh) = ) = 6.626 x 106.626 x 10-34-34 J J..ss

Problem:Problem: What is the energy of green light with What is the energy of green light with

a frequency of 6.0 x 10a frequency of 6.0 x 101414 s s-1-1??

EE = = hh E = (6.626 x 10E = (6.626 x 10-34-34 J J..s)(6.0 x 10s)(6.0 x 101414 s s--

11)) E = 4.0 x 10E = 4.0 x 10-19-19 JJ

The Nature of Light: The Nature of Light: Is light a particle or a wave?Is light a particle or a wave?

In 1690,In 1690, Christian Huygens Christian Huygens published his published his wavewave theory theory of lightof light. He observed many . He observed many wave properties of light, wave properties of light, such as the bending such as the bending (refraction) of light through (refraction) of light through a prism.a prism.

He correctly predicted that He correctly predicted that light should propagate light should propagate slower in a denser medium. slower in a denser medium.

Light as a waveLight as a wave

The Nature of Light: The Nature of Light: Is light a particle or a wave?Is light a particle or a wave?

At the same time as At the same time as HuygensHuygens Isaac Newton, Isaac Newton, already famous for his already famous for his theory of gravity,theory of gravity, was was working on hisworking on his particleparticle theorytheory of lightof light. He made . He made many observations of light many observations of light behaving as particles, such behaving as particles, such as reflecting as it bounced as reflecting as it bounced off mirrors, and creating off mirrors, and creating straight line shadows.straight line shadows.

By the way:By the way:

Newton is considered the greatest Newton is considered the greatest scientist ever because he was the scientist ever because he was the first to incorporate experiment and first to incorporate experiment and theory as a way of defining science: theory as a way of defining science: proposing something and then using proposing something and then using experiments to confirm it or not. experiments to confirm it or not.

All of science after him works in the All of science after him works in the same exact way. same exact way.

By 1820, light is By 1820, light is considered a wave…considered a wave…

Newton’s Newton’s particle theory of particle theory of lightlight dominated for 50 years, dominated for 50 years, until 1819, with the until 1819, with the mathematical work of Fresnel, mathematical work of Fresnel, when the when the wave theory of lightwave theory of light became firmly established for became firmly established for the next 100 years.the next 100 years.

Einstein and the Photoelectric Einstein and the Photoelectric EffectEffect

Einstein received a Einstein received a Nobel Prize in 1921 for Nobel Prize in 1921 for his explanation of the his explanation of the photoelectric effect,photoelectric effect, a phenomenon that a phenomenon that occurs when you shine occurs when you shine a light upon certain a light upon certain metals and a stream of metals and a stream of electrons is emitted electrons is emitted from that metal. from that metal.

Einstein and the Photoelectric Einstein and the Photoelectric EffectEffect

The emitted electrons have The emitted electrons have been found to have certain been found to have certain

properties:properties: The The numbernumber of electrons emitted by the metal of electrons emitted by the metal

depends on the depends on the intensityintensity of the light beam of the light beam applied on the metal;  more intense the beam, applied on the metal;  more intense the beam, higher the number of electrons emitted. higher the number of electrons emitted.

The emitted electrons move with greater The emitted electrons move with greater speedspeed if the applied light has a higher if the applied light has a higher frequencyfrequency. .

No electron is emitted until the light has a No electron is emitted until the light has a thresholdthreshold frequency, frequency, no matter how intense the no matter how intense the light islight is. .

Einstein and the Photoelectric Einstein and the Photoelectric EffectEffect

These observations baffled physicists These observations baffled physicists for many decades, since they cannot be for many decades, since they cannot be explained explained if light is thought of only as a if light is thought of only as a wave. wave.

If light were to be a If light were to be a wavewave, , bothboth the the energy energy andand the number of the electrons the number of the electrons emitted from the metal should increase emitted from the metal should increase with the intensity of light.  Observations with the intensity of light.  Observations contradicted this prediction.contradicted this prediction.

Einstein described light as composed of Einstein described light as composed of quantaquanta, now called , now called photonsphotons, rather than , rather than continuous waves. continuous waves.

Based on Planck’s theory, Einstein Based on Planck’s theory, Einstein found that the energy in each photon found that the energy in each photon was equal to its frequency multiplied by was equal to its frequency multiplied by Planck’s constant (Planck’s constant (EE(photon)(photon) = = hh). ).

This discovery led to the This discovery led to the quantum quantum revolutionrevolution in physics. in physics.

Einstein and the Photoelectric Einstein and the Photoelectric EffectEffect

So, is light ultimately a So, is light ultimately a wavewave, , or or a stream of photonsa stream of photons??

The answer is: The answer is: bothboth.  Light behaves .  Light behaves as a wave under certain conditions, as a wave under certain conditions, and as a stream of particles under and as a stream of particles under others.  It is said to have a others.  It is said to have a dual dual naturenature:  we can understand it as :  we can understand it as either wave or particle, depending either wave or particle, depending on our context of observation. on our context of observation. 

Dual nature of lightDual nature of light

Light as a wave

Light as a photon (quantum of light energy)

Standing WavesStanding Waves

If you tie down a string at both ends If you tie down a string at both ends (as on a guitar) and pluck the string, (as on a guitar) and pluck the string, it will vibrate as a it will vibrate as a standing wavestanding wave..

At the fixed ends, the amplitude is At the fixed ends, the amplitude is zero. The wave does not appear to zero. The wave does not appear to travel down the line.travel down the line.

Standing waves occur in Standing waves occur in whole- number multiples of whole- number multiples of ½ ½

Standing WavesStanding Waves

There are always two or more places There are always two or more places where the vibrating string never where the vibrating string never moves, the amplitude is zero at moves, the amplitude is zero at these points, called these points, called nodesnodes. .

The distance between nodes is The distance between nodes is always always ½ ½ ..

Standing WavesStanding Waves

An important property of standing An important property of standing waves is you can't have any frequency waves is you can't have any frequency you want because ends are fixed. you want because ends are fixed. When the ends are fixed only certain When the ends are fixed only certain discrete wavelengths (frequencies) discrete wavelengths (frequencies) are allowed. are allowed.

Standing waves are an example of Standing waves are an example of quantized energyquantized energy (energy in discrete (energy in discrete packets).packets).

Standing WavesStanding Waves

The Bohr ModelThe Bohr Model

In 1912, In 1912, Niels Niels BohrBohr adapted adapted Rutherford's Rutherford's atomic model to atomic model to Planck’s quantum Planck’s quantum theory and so theory and so developed his developed his theory of atomic theory of atomic structure. structure.

Atoms can give off lightAtoms can give off light Bohr’s model explained the atomic Bohr’s model explained the atomic

emission spectrum of hydrogen. For emission spectrum of hydrogen. For this he received the Nobel Prize in this he received the Nobel Prize in 1922. His atomic model is based on 1922. His atomic model is based on these ideas.these ideas.

The The atomic emission spectrumatomic emission spectrum of of an element is emission of particular an element is emission of particular frequencies (colors) of light by frequencies (colors) of light by energized atoms of that element. energized atoms of that element.

Each atom's atomic emission Each atom's atomic emission spectrum is unique. spectrum is unique.

Atomic emission spectrum and Atomic emission spectrum and absorption spectrumabsorption spectrum

The emission spectrum of The emission spectrum of hydrogen:hydrogen:

The most prominent spectral lines are The most prominent spectral lines are violet, blue, blue-green, and red. violet, blue, blue-green, and red.

Which of the lines has the lowest frequency?Which of the lines has the lowest frequency? Which of the lines has the shortest wavelength?Which of the lines has the shortest wavelength?

Atomic emission spectrum and Atomic emission spectrum and absorption spectrumabsorption spectrum

The Energies of ElectronsThe Energies of Electrons

The energy of an atom The energy of an atom changes as the electrons changes as the electrons absorb or release energy absorb or release energy Ground stateGround state – atom in the – atom in the

lowest possible energy state lowest possible energy state Excited stateExcited state – atom with – atom with

excess energy excess energy

When an H atom absorbs When an H atom absorbs energy from an outside source energy from an outside source

it enters an it enters an excited state.excited state.

The excited electrons emit The excited electrons emit photons of light and return to photons of light and return to the low energy the low energy ground state.ground state.

Atoms can give off lightAtoms can give off light Flame Test ColorsFlame Test Colors

Barium Barium Pale greenPale green Calcium Calcium Orange/redOrange/redCesium Cesium BlueBlue Copper Copper Blue/greenBlue/greenIron Iron GoldGold Potassium Potassium LavenderLavenderLithium Lithium MagentaMagenta Magnesium Magnesium Bright whiteBright whiteSodium Sodium Intense yellowIntense yellow Strontium Strontium CrimsonCrimson

Firework ColorantsFirework Colorants

RedRed: strontium salts, lithium salts : strontium salts, lithium salts

OrangeOrange: calcium salts : calcium salts

GoldGold: incandescence of iron: incandescence of iron

YellowYellow: sodium nitrate, cryolite: sodium nitrate, cryolite

Electric WhiteElectric White: white-hot metal, barium oxide: white-hot metal, barium oxide

GreenGreen: barium compounds : barium compounds

BlueBlue: copper compounds + chlorine producer: copper compounds + chlorine producer

PurplePurple: mixture of strontium and copper : mixture of strontium and copper compoundscompounds

SilverSilver: burning aluminum, titanium, or magnesium: burning aluminum, titanium, or magnesium

Bohr’s ModelBohr’s Model In 1913, Bohr In 1913, Bohr

proposed his model proposed his model of the atom. He of the atom. He determined that determined that electrons can be electrons can be located in certain located in certain discrete energy discrete energy states, called states, called energy energy levelslevels..

Energy levelsEnergy levels

The principal energy level is an The principal energy level is an important part of Bohr’s model that important part of Bohr’s model that remains important in the modern remains important in the modern model of the atom.model of the atom.

The letter The letter nn is used to represent the is used to represent the energy level (energy level (nn = 1, 2, 3, etc.). It is = 1, 2, 3, etc.). It is referred to as the referred to as the principal quantum principal quantum numbernumber..

Bohr related his model to a Bohr related his model to a ladderladder……

As person can stand on one rung of a As person can stand on one rung of a ladder or the next, yet it is impossible ladder or the next, yet it is impossible for a person to stand between the for a person to stand between the rungs... an electron can be found in rungs... an electron can be found in one energy level or the next, but not one energy level or the next, but not between levels.between levels.

The only way for the electron to jump The only way for the electron to jump to the next level is for it to have a to the next level is for it to have a quantum leapquantum leap, which is the leap from , which is the leap from one energy level to another.one energy level to another.

The energy of the electron has a The energy of the electron has a definite value in a stationary orbit. definite value in a stationary orbit. The electron can jump from one The electron can jump from one stationary orbit to another. stationary orbit to another.

If it jumps from an orbit of If it jumps from an orbit of lowerlower energy Eenergy E11 to an orbit of to an orbit of higher higher energy Eenergy E22 , it , it absorbs a photon. absorbs a photon.

If it jumps from an orbit of If it jumps from an orbit of higherhigher energy Eenergy E22 to an orbit of to an orbit of lower lower energy energy EE11, it , it emits a photon. emits a photon.

The Energy Levels of The Energy Levels of Hydrogen Hydrogen

Energy level diagramEnergy level diagram

• The amount of energy released is the same amount of energy absorbed by the atom to reach the excited state.

How many How many emission emission lines are lines are possible for possible for a hydrogen a hydrogen atom atom considering considering energy energy levels 1 levels 1 through 7?through 7?

The Bohr Model of the AtomThe Bohr Model of the Atom Quantized energy

levels Electron moves in a

circular orbit Electron jumps

between levels by absorbing or emitting photon of a particular wavelength

Bohr's atomic model was ultimately not successful.

Bohr’s model considered the electron Bohr’s model considered the electron as a as a particleparticle, and classical physics , and classical physics shows that a charged particle shows that a charged particle accelerating around a circular path accelerating around a circular path would lose energy, and so the would lose energy, and so the electrons would fall into the nucleus.electrons would fall into the nucleus.

The modern model of the atom The modern model of the atom considers the electron, not as a considers the electron, not as a particleparticle, but as a , but as a matter-wavematter-wave..

Bohr's atomic model was ultimately not successful.

There was a major defect in the Bohr There was a major defect in the Bohr model. model.

It did not explain the behavior of atoms It did not explain the behavior of atoms with more than one electron.with more than one electron.

Electrons as wavesElectrons as waves In 1925, Victor de In 1925, Victor de

Broglie proposed the Broglie proposed the Wave-Particle Duality Wave-Particle Duality TheoryTheory. .

If light can sometimes If light can sometimes be considered waves be considered waves and other times and other times particles, why doesn’t particles, why doesn’t matter behave matter behave similarly? similarly?

He received a Nobel Prize in He received a Nobel Prize in 1929.1929.

Electrons as wavesElectrons as waves De Broglie’s theory stated that a tiny De Broglie’s theory stated that a tiny

particle, such as an electron, also exhibits particle, such as an electron, also exhibits wave properties in some experiments.wave properties in some experiments.

Unstable wave orbitUnstable wave orbit Stable wave orbitStable wave orbit

                                         

De Broglie’s equationDe Broglie’s equation= = h h ( (mv)mv)

This equation was revolutionary!This equation was revolutionary! It linked It linked particle propertiesparticle properties

[mass x velocity ([mass x velocity (mv mv )] with )] with wave propertieswave properties [wavelength ( [wavelength ()].)].

Remember Remember hh = 6.626 x 10 = 6.626 x 10-34-34 JJ .. s s (Planck’s constant)(Planck’s constant)

Question:Question: Calculate the wavelength associated with Calculate the wavelength associated with

an electron of mass an electron of mass mm = 9.109 x 10 = 9.109 x 10-31-31 kgkg traveling at 1.20 x 10traveling at 1.20 x 1088 m/sm/s..

= = h h ( (mv)mv)

= = 6.626 x 106.626 x 10-34-34 JJ .. ss

((9.109 x 109.109 x 10-31-31 kgkg)(1.20 x 10)(1.20 x 1088 m/s)m/s)

= 6.06 x 10= 6.06 x 10-12-12 m m

(which is 1/20(which is 1/20thth the diameter of the H atom) the diameter of the H atom)

Electrons as wavesElectrons as waves

Heisenberg’s Uncertainty Heisenberg’s Uncertainty PrinciplePrinciple

Werner Heisenberg expanded Werner Heisenberg expanded on de Broglie’s ideas; he on de Broglie’s ideas; he stated that the exact location stated that the exact location of the electron couldn’t be of the electron couldn’t be determined. However, he determined. However, he could predict a region in could predict a region in space where the probability of space where the probability of finding the electron is high. finding the electron is high.

Heisenberg received a Nobel Heisenberg received a Nobel Prize in 1932. Prize in 1932.

Heisenberg’s Uncertainty Heisenberg’s Uncertainty PrinciplePrinciple

On the basis of Heisenberg’s idea, On the basis of Heisenberg’s idea, the the Uncertainty PrincipleUncertainty Principle says that if says that if we choose to know the energy of an we choose to know the energy of an electron in an atom with only a small electron in an atom with only a small uncertainty, then we must accept a uncertainty, then we must accept a correspondingly large uncertainty correspondingly large uncertainty about it’s position in the space about it’s position in the space around the atom’s nucleus.around the atom’s nucleus.

We can only calculate the We can only calculate the probabilityprobability of finding the electron (of given of finding the electron (of given energy) within a given space.energy) within a given space.

Schrödinger’s Wave Schrödinger’s Wave Mechanical ModelMechanical Model

Erwin Schrödinger Erwin Schrödinger combined de Broglie’s combined de Broglie’s equation with classical equation with classical equations for wave equations for wave motion to derive the motion to derive the wave equationwave equation (which (which we call the we call the Schrödinger equationSchrödinger equation) ) used to predict used to predict electron behavior. electron behavior.

Schrödinger’s Wave Schrödinger’s Wave Mechanical ModelMechanical Model

In the equation, Schrödinger provides In the equation, Schrödinger provides a three dimensional picture of the a three dimensional picture of the electron electron matter-wavematter-wave (called (called atomic atomic orbitalorbital). ).

Schrödinger's theory of the atom is Schrödinger's theory of the atom is our current model of the atom. our current model of the atom.

Anyone who is not shocked by Anyone who is not shocked by quantum theory has not quantum theory has not understood it"understood it"

- Niels Bohr

Atomic OrbitalsAtomic Orbitals

An An atomic orbitalatomic orbital is a region around is a region around the nucleus where there is a high the nucleus where there is a high probability (90%) of finding an probability (90%) of finding an electron.electron.

Orbitals of the same shape grow larger as the principal energy level (n) increases

Atomic Orbitals Atomic Orbitals

Each principal energy level is divided Each principal energy level is divided into sublevels. into sublevels.

– Labeled with numbers and letters – Indicate the shape of the orbital

Orbital Shapes and Energies

The s - Orbital

s - orbital shape: Spherical Occur in all energy levels, n = 1, 2, 3, etc. Sublevel s consists of 1 spherical orbital

Orbital Shapes and Energies Three p - Orbitals

p - orbital shape: Two lobes each Occur in levels n = 2 and greater Each orbital lies along an axis (2px, 2py, 2pz) Sublevel p consists of 3 dumbbell shaped orbitals

Atomic OrbitalsAtomic Orbitals – s and p – s and p orbitalsorbitals

Size increases as energy level increasesSize increases as energy level increases

s and p orbitalss and p orbitals

Orbital Shapes and Energies Five d - Orbitals

d - orbital shape: Complex Occur in levels n=3 and greater Sublevel d consists of 5 complex orbitals

Orbital Shapes and Energies Seven f - Orbitals

f - orbital shape: Highly complex

Occur in levels n=4 and greater

Electron configurationsElectron configurations

The ways in which electrons are The ways in which electrons are arranged around the nuclei of atoms arranged around the nuclei of atoms are called are called electron configurationselectron configurations..

Three rules tell you how to find Three rules tell you how to find electron configurations of electron configurations of

atoms:atoms:

1.1. The aufbau principleThe aufbau principle

2.2. The Pauli exclusion principleThe Pauli exclusion principle

3.3. Hund’s ruleHund’s rule

The Aufbau Principle

Electrons enter orbitals of lowest energy first.

The Pauli Exclusion Principle

An orbital can hold only two electrons, and they must have opposite spins.

Wolfgang Pauli received the Nobel Prize in 1945.

Hund's Rule

When electrons enter orbitals of equal energy, one electron enters each orbital until all the orbitals contain one electron with parallel spins.

Exceptions to the aufbau Exceptions to the aufbau orderorder

CopperCopper and and chromiumchromium have have exceptionalexceptional electron configurations. electron configurations.

One electron in the 4s sublevel is One electron in the 4s sublevel is promoted to the 3d sublevel. This makes promoted to the 3d sublevel. This makes the atoms more stable.the atoms more stable.

Your text explains that half filled and Your text explains that half filled and completely filled sublevels are more stable completely filled sublevels are more stable than partially filled sublevels.than partially filled sublevels.

Instead of the aufbau order…Instead of the aufbau order… Cu: 1sCu: 1s22, 2s, 2s22, 2p, 2p66, 3s, 3s22, 3p, 3p66, 3d, 3d55, 4s, 4s22

The actual configuration is….The actual configuration is…. Cu: 1sCu: 1s22, 2s, 2s22, 2p, 2p66, 3s, 3s22, 3p, 3p66, 3d, 3d66, 4s, 4s11