Chapter 7

Beyond Rutherford to“The Most Successful Theory of the

20th Century”

http://www.learnerstv.com/animation/chemistry/ruther14.swf

View Rutherford’s experiment

Rutherford’s Atomic Model(“planetary model”)

e-

NucleusDiameter = 10-15 m

Empty spaceOrbiting electron(fixed radius)

Diameter of atom = 10-10 m

Problem with Rutherford’s Model !! It did not obey the classical laws of physicsIt did not obey the classical laws of physics

But atoms don’t collapse, yet Rutherford’s experiment But atoms don’t collapse, yet Rutherford’s experiment showed that electrons can be located a distance away showed that electrons can be located a distance away from the nucleus.from the nucleus.

So, the model of the So, the model of the ______________ behavior is flawed. behavior is flawed.

According to Newton’s According to Newton’s classical laws, electrons classical laws, electrons orbiting the nucleus should orbiting the nucleus should radiate energy, slow down, radiate energy, slow down, and be pulled into the and be pulled into the nucleus & collapse the atomnucleus & collapse the atom

Collision of Ideas

Dalton

Thomson

Rutherford

Newton

Maxwell

Plank

Einstein

MatterMatter

LightLight

?Bohr &de Broglie

What is the nature of light?

Isaac Newton: “Light is a particle”

Newton’sprism

By the 17th century, light was found toBy the 17th century, light was found to travel in straight linestravel in straight lines reflect & refractreflect & refract transmit energy from one place to anothertransmit energy from one place to another

The The WAVE THEORYWAVE THEORY, advocated by, advocated by

Robert Hooke

Christian Huygens argued thatargued that light is a wavelight is a wave..

The The PARTICLEPARTICLE THEORYTHEORY, advocated by, advocated by Isaac Newton and and Pierre Laplace,, argued thatargued that light was made up of a stream of tiny particles (“corpuscles”).

Two Competing Theories

The The theory of lighttheory of light

The The theory of lighttheory of light

“white light” light energy composed of a continuous spectrum of visible electromagnetic radiation

ultraviolet

infrared

Wavelength = distance between wave crests (m)

Frequency = cycles per second (Hz)

11 or

Basics of wave theory

Electromagnetic Wave Theory (1865)Electromagnetic Wave Theory (1865)

Electromagnetic waves have a variety of wavelengths, Electromagnetic waves have a variety of wavelengths, but all travel at the speed of lightbut all travel at the speed of light,,

Based on conservation of energy, Maxwell derived theBased on conservation of energy, Maxwell derived the wave equation,wave equation,

Based on experiments ofBased on experiments of Michael Faraday

Theory developed byTheory developed by James Clerk Maxwell

cc ==

cc == 2.9982.998 ×× 101088 m/s m/s

Electromagnetic Spectrum

1020 Hz 1014 Hz 1010 Hz

10-6 nm 108 nm

higher energy lower energy

ROY G BIVROY G BIVlow energy low energy high energy high energy

Colors in the visible spectrum:Colors in the visible spectrum: RRed, ed, OOrange, range, YYellow, ellow, GGreen, reen, BBlue, lue, IIndigo & ndigo & VVioletiolet

Problems with the Wave Theory of Light

1.1. Blackbody RadiationBlackbody Radiation

2.2. The Photoelectric EffectThe Photoelectric Effect

3.3. Emission Spectra of AtomsEmission Spectra of Atoms

By the mid-1800s, the wave theory became predominant, By the mid-1800s, the wave theory became predominant, but……but……

When light interacted with matter, the wave theory failed. When light interacted with matter, the wave theory failed.

The important examples are:The important examples are:

Problem #1. Blackbody Radiation

blackbodyblackbody““object that absorbs all theobject that absorbs all thecolors in the spectrum”colors in the spectrum”

When heated to a high enough temperature, the blackbody When heated to a high enough temperature, the blackbody radiates white light. radiates white light.

The wave theory predicts a continuous spectrum of emitted light, The wave theory predicts a continuous spectrum of emitted light, but the but the theory fails to match experimenttheory fails to match experiment..

Blackbody Simulation

actualspectrum

Planck’s Quantum Theory

Measured blackbody radiation did not produce a Measured blackbody radiation did not produce a continuous spectrum, as wave theory predictedcontinuous spectrum, as wave theory predicted

In 1900, German Physicist Max Planck proposed a new In 1900, German Physicist Max Planck proposed a new quantum theory of light:quantum theory of light:

Light is taken up and given off by a blackbody not as a Light is taken up and given off by a blackbody not as a continuous wave, but in little continuous wave, but in little “packets” of light energy “packets” of light energy of of specific valuesspecific values

Planck called these packets “Planck called these packets “quantaquanta” (singular is ” (singular is quantum) of energyquantum) of energy

Quantum Theory of Light and Quantum Physics

Plank’s quantum theory of light was Plank’s quantum theory of light was a historical turning point in physics, a historical turning point in physics, transitioning classical physics from transitioning classical physics from the 18the 18thth and 19 and 19thth centuries to the centuries to the quantum physics of the 20quantum physics of the 20thth centurycentury. .

Problem #2Photoelectric

Effect

Animation

Problem #2. Photoelectric Effect Imagine shining light of various wavelengths (energies) on the surfaces of different metalsImagine shining light of various wavelengths (energies) on the surfaces of different metals

Only light energies Only light energies above a certain thresholdabove a certain threshold cause electrons to be ejected from the metal surface cause electrons to be ejected from the metal surface This conflicts with predictions of the wave theoryThis conflicts with predictions of the wave theory

Animation

Einstein’s Photons In 1905, a Swiss patent clerk proposed that light In 1905, a Swiss patent clerk proposed that light

consists of particles called consists of particles called photonsphotons.. As Planck proposed, Einstein’s photons have a As Planck proposed, Einstein’s photons have a

certain quanta of energy (based on wavelength)certain quanta of energy (based on wavelength) His model of light solved the problem of the His model of light solved the problem of the

photoelectric effect.photoelectric effect.

Duality of LightDuality of Light

Wave behaviorWave behavior

Particle behaviorParticle behavior

Solar Sail (based on Einstein’s photon theory) - Light reflecting off a mirror imparts momentum - Yet light has no mass (experiment by Compton in 1923)

Cosmos 1 concept

Energy of Photons

At a specific frequency (or wavelength) At a specific frequency (or wavelength) photonsphotons possess a specific quantity of energy (possess a specific quantity of energy (EE ))

Planck’s constantPlanck’s constant

EE == hh

hh == 6.6266.626 xx 1010-34-34 J·s J·s

EE == hh c/c/

Question: Is 400 nm light (violet light) more or less energetic than 750 nm light (red light)?

Concept Check

The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275 kJ/mol.

What wavelength (in nm) has sufficient energy per photon to dislodge an electron from the surface of sodium?

sodium

Concept Check

Which photons have the highest energy?

A) Cell phone operating at 1900 MHz

B) A laser pointer using 635 nm light

Problem #3. Atomic Line Spectra

Periodic Table of Line SpectraPeriodic Table of Line Spectra

Flame testshttp://college.cengage.com/chemistry/general/ebbing/general_chem/9e/assets/instructors/protected/videos.html#Chapter 7

Problem #3. Atomic Line Spectra

Periodic Table of Line SpectraPeriodic Table of Line Spectra

Emission spectra for pure elements

Fireworks

Niels Bohr (1885-1962) Danish physicist who worked with J.J. Thomson at Danish physicist who worked with J.J. Thomson at

Cambridge University in 1911. He didn’t agree with Cambridge University in 1911. He didn’t agree with Thomson’s atomic model, Thomson’s atomic model, so worked for Rutherford in 1912.so worked for Rutherford in 1912.

In 1912, in a bold step, he suggested that the In 1912, in a bold step, he suggested that the classical classical laws of physics cannot be appliedlaws of physics cannot be applied to matter as small as to matter as small as atoms and electrons. Instead, atoms and electrons. Instead, new laws are needednew laws are needed

Bohr sought to solve the problem with Rutherford’s Bohr sought to solve the problem with Rutherford’s atomic model and explain the phenomenon of atomic atomic model and explain the phenomenon of atomic spectra, by spectra, by applying the quantum theory of light to applying the quantum theory of light to atoms and electronsatoms and electrons

Bohr’s Quantum Atomic Model

Postulated that the Postulated that the energy of the energy of the electron must be quantizedelectron must be quantized. Only . Only certain electron energies are possible.certain electron energies are possible.

Orbit radii (energy levels) correspond Orbit radii (energy levels) correspond to definite energiesto definite energies

Energy is emitted or absorbed by the Energy is emitted or absorbed by the electron only as the electron changes electron only as the electron changes from one allowed energy level to from one allowed energy level to anotheranother

nn = = energy level number or principal quantum number

Why does an electron possess energy? Why does an electron possess energy? 1)1) 2)2)

How do quantized energy levels explain spectral lines?

Atoms “place” electrons in lowest possible energy levels Atoms “place” electrons in lowest possible energy levels ((“ground state”“ground state”))

When electrons are provided with enough energy, they When electrons are provided with enough energy, they “jump” to higher energy levels, where they are unstable “jump” to higher energy levels, where they are unstable ((“excited state”“excited state”))

The electrons then fall back down to the lower possible The electrons then fall back down to the lower possible energy levels, releasing absorbed energy as a photon of lightenergy levels, releasing absorbed energy as a photon of light

We see these photons as the spectral lines emitted by excited We see these photons as the spectral lines emitted by excited atomsatoms

Stairstep Stairstep

analogyanalogy

Energy of H electron = E = -RH/n2

n = 1, 2, 3, … ∞RH = 2.179 x 10-18 J

energylevels

“quantum jump”∆E4→2 = E2 - E4 = h4→2

H emission spectrum

A “quantum jump”

EmissionEmission ∆E = E2 - E4 = h4→2

AbsorptionAbsorption ∆E = E4 – E2 = h2→4

Simulations of Bohr Model

Visible emission spectral lines of hydrogenVisible emission spectral lines of hydrogen

Success & Limitation of Bohr’s Quantum Model

Explained the existence of spectral linesExplained the existence of spectral lines Solved the problem with Rutherford’s model of the Solved the problem with Rutherford’s model of the

hydrogen atomhydrogen atom But, the mathematics only worked for atoms with 1 But, the mathematics only worked for atoms with 1

electron!electron!

How can this model be made to How can this model be made to work for all elements?work for all elements?

de Broglie’s Novel NotionLight was “known” (thought) to be a wave, but Light was “known” (thought) to be a wave, but

Einstein showed that it also acts particle-like.Einstein showed that it also acts particle-like.

Electrons were “known” to be particles mass & charge.Electrons were “known” to be particles mass & charge.

French physicist:French physicist:

What if ……What if ……

1923

electrons behaved as waves also

Diffraction pattern obtained by firing

a beam of electrons through

a crystal.

Dr. Quantum videoDr. Quantum video

Werner Heisenberg

In 1927, German physicist, proposed that the In 1927, German physicist, proposed that the dual nature of dual nature of the electronthe electron places limitations on how precisely we can know places limitations on how precisely we can know both the location and speed of the electronboth the location and speed of the electron

Instead, we can only describe electron behavior in terms of Instead, we can only describe electron behavior in terms of probabilityprobability

The Uncertainty Principle

speedspeed

positionposition

Heisenberg’sUncertainty Principle

Wave behavior limits what can be known!Wave behavior limits what can be known!

What if the particle has a small mass?What if the particle has a small mass?

What if the electron’s position is known very precisely?What if the electron’s position is known very precisely?

What if the electron’s speed is known very precisely?What if the electron’s speed is known very precisely?

(±x)(±v(±x)(±vxx))

Can the electron’s orbit be precisely defined?

± position ± speed

hh44mm

Erwin Schrodinger

In 1926, Austrian physicist, proposed an equation that In 1926, Austrian physicist, proposed an equation that incorporates both the wave and particle behavior of the incorporates both the wave and particle behavior of the electronelectron

When applied to hydrogen’s 1 electron atom, solutions provide When applied to hydrogen’s 1 electron atom, solutions provide the the most probable locationmost probable location of finding the electron in the first of finding the electron in the first energy levelenergy level

Can be applied to more complex atoms too!Can be applied to more complex atoms too!

Wave Equation &

Wave Mechanics

• Extremely small mass• Located outside the nucleus• Moving at very high speeds• Have specific energy levels• Standing wave behavior

• Extremely small mass• Located outside the nucleus• Moving at very high speeds• Have specific energy levels• Standing wave behavior

Electron Characteristics

A baseball behaves as a particle and follows a predictable path.

BUT

An electron behaves as a wave, and its path cannot be predicted.

All we can do is to calculate the probability of the electron following a specific path.

Baseball v. Electron

What if a baseball behaved like an electron?

Characteristic wavelength ()• baseball 10-34 m• electron 0.1 nm

So, all we can predict is…..

== hh /(/(mumu))mass speed

“deterministic” “probabilistic”

Bohr Model v. Quantum Mechanics

Energy

Electron

Position/Path

Elements

Bohr Quantum Mechanics

The electron's movement cannot be known precisely.

We can only map the probability of finding the electron at various locations outside the nucleus.

The probability map is called an orbital.

The orbital is calculated to confine 99% of electron’s range.

Energy of the electron is quantized into sublevels.

Quantum Mechanics Model

Quantum Mechanics ModelDescribes the energy, arrangement and space occupied

by electrons in atoms

Quantum

Mechanics

Electron’s energy is quantized

Mathematics of waves to define orbitals(wave mechanics)

“Most Successful Theory of the 20th Century”

Dalton

Thomson

Rutherford

Newton

Maxwell

Plank

Einstein

Matter

Light

Schrödinger

Heisenberg

WaveMechanics

Quantum

MechanicsBohr &de Broglie