History of Quantum Theory

Niels Bohr

Learning GoalsStudents will be able to:1) understand the Quantum Mechanical Model

of the Atom2) understand how to describe the atom in

terms of the Quantum Mechanical Model (energy level, shapes of orbits, sub-orbitals and quantum numbers)

Success CriteriaStudents will:1) record the important facts in an information

chart.2) understand the advancements of each new

atomic model.3) identify the weakness of the model that lead

to further investigation.

Review – Rutherford’s ModelRutherford used the Gold Foil Experiment to

theorize that:1) atoms contain a tiny, dense, positively

charged nucleus.2) the nucleus was orbited by very light,

negatively charged electrons.3) most of the volume of an atom was empty

space.

An electron accelerating around the nucleus would continuously emit electromagnetic radiation and lose energy

Therefore, it would eventually fall into the nucleus and the atom would collapse

However, this is not consistent with real-world observations – atoms are stable

Limitations of Rutherford’s Model

Bohr and Quantum TheoryWatch Structure of the Atom 4: The Bohr

Model (9:08) http://www.youtube.com/watch?v=hpKhjKrBn9s

Bohr used recent work by Max Planck.Planck and his teacher, Kirchhoff, studied the

light emitted from hot, dark objects (blackbodies).Planck noticed that when radiation (light, UV, IR) is

emitted from a heated solid, the energy (blackbody radiation) is not released at all wavelengths, but is released at only specific wavelengths of energy

Energy is quantized. It comes in chunks.

Bohr and SpectroscopyA quanta is the amount of energy needed to move

from one energy level to another.Since the energy of an atom is never “in between”

there must be a quantum leap in energy.Bohr looked at the spectra released by light

produced by an excited gas.Bohr chose Hydrogen because it is the simplest

element.https://www.youtube.com/watch?v=LA9juHlyhKw

(Mr. Causey – Bohr’s Planetary Model)http://www.youtube.com/watch?v=Nv1_YB1IedE

(Quantum Mechanics – The Fabric of the Cosmos – Brian Greene)

A short Review on Spectroscopy – remember grade 10! (neither do I)

When white light is shone through a prism, it is broken into a spectrum.

Each colour corresponds to a different wavelength of light.

Each wavelength corresponds to a particular amount of energy.

Comparing SpectraAbsorption

spectra are produced when light is shone through a cooler gas.

Emission spectra are produced when light is emitted by the gas.

The Atomic Spectra of HydrogenBohr specifically

used the spectra of hydrogen since it is the simplest of atoms.

Spectra of Other Atoms and Luminous Objects

Note that each element has its own distinctive spectra.

Bohr-ing MathBohr knew that he could

measure the wavelength of the spectral lines.

When hydrogen is “excited” by the addition of energy (electricity is used in a gas discharge tube), an electron jumps up from a low orbit and moves into a higher orbit.

Eventually this electron falls back down and releases a specific amount of energy (a quanta).

When the electrons falls back down it emits energy that we can “see” as a spectral line. (note some lines appear in the infrared and ultraviolet portions of the spectrum)

Bohr-ing MathBohr postulated that an

electron cannot exist between orbits – electrons can only exist in orbits and each orbit occupies a specific energy level.

Each line in the spectrum is produced by the quantum of energy released when one electron falls back down to a lower orbit.

Examples:1. drop from 4th orbital to 2nd

orbital (blue line)2. drop from the 3rd orbital to

1st orbital (ultraviolet line)3. drop from 5th orbital to 3rd

orbital (infrared line)

Wavelength EquationBohr knew that the wavelength of

light could be used to determine its energy level and its velocity using the equations below:

Bohr eventually expanded his math to determine the distance of each orbital from the nucleus and the energy level of each permissible energy level for hydrogen.

Successes and Weaknesses of Bohr’s ModelSuccesses1) Bohr’s mathematics

explained all the observations for Hydrogen perfectly

2) This is a major success for Quantum Mechanics – to this day it has never failed

3) He solved Rutherford’s problem

Weaknesses1) Bohr’s method only worked for

Hydrogen2) Although the quantum theory

of light  was experimentally proven, other experiments had proven that light had also continuous  wavelike properties.Einstein suggested that there were "two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do". Hence light and photons display wave and particle properties

deBroglie (1924) & Schrödinger (1925)Responding to the

difficulties in the Bohr model, Louis deBroglie , from France, suggested that matter like light, has the properties of both particles and waves. This  particle-wave duality  -derived from the work of Einstein and Planck - was experimentally confirmed, for the electron, in 1927.

Austrian physicist   Erwin Schrodinger   formed a model of a complete atom as interacting waves.

The particles became like vibrations on a violin string, only they were closed in circles.

His partial differential equation seemed to bear a similar relation to the mechanics of the atom as Newton's equations of motion bear to planetary astronomy.

deBroglie (1924) & Schrödinger (1925)A representation of energy levels and sub-levels as

waves instead of particles in circular orbits. Note the math – Schrodinger’s wave function being applied.

Heisenberg (1926)German physicist   Werner

Heisenberg   formulated his  Uncertainty Principle which says that you cannot know by measurement the position and momentum of a particle simultaneously.

The better you know one, the worse you know the other.

Particles and fields undulate and jump between all possible values consistent with the quantum uncertainty.

Atoms were now visualized as a nucleus surrounded by a cloud of electrons distributed according to a wave pattern by the Schrodinger equation.

Clouds of electrons determined by Heisenberg and Schrodinger’s mathematical models and borne out by X-ray studies.

Dirac (1926)Paul Dirac  devised a form

of quantum mechanics (developed by Schrodinger and Heisenberg), which provides the laws of motionthat govern atomic particles.

The electron could now be described by four wave functions, satisfying four simultaneous differential equations. As before the electrons still cannot be pinpointed but exist as a sort of  cloud of probability outside the nucleus.

It followed from Dirac's equations that the electron must rotate, or spin, on its axis, and also that there must be states of negative energy.

Quantum NumbersUsing high resolution spectra,

Michelson noticed that the main lines found in spectra were often split into smaller lines.

Sommerfeld (1915) was able to explain these small lines using elliptical orbits.

deBroglie and schrodinger’s work clarifies this

He explained that each level has sub-levels or subshells.

Therefore each one of Bohr’s energy levels can be divided into smaller levels.

Secondary Quantum NumberBOHR – his energy levels (orbitals) were labeled the

Primary Quantum Number (n)SOMMERFELD – Secondary Quantum Number (l)

l = 0 to n-1, therefore if l = 3, n can equal 0, 1, 2Therefore the 3rd energy level contains 3 sublevels.

The secondary quantum number caused orbitals to take on different shapes

l = 0 (speherical orbital)l = 1 (dumb-bell shaped 2-lobed orbitals)l = 2 (4-lobed orbitals)l = 3 (6 and 8-lobed orbitals)

Magnetic Quantum NumberZeeman (1896) noticed that the spectral lines

could also be split if placed in a magnetic field.Sommerfeld and DeBye used this information to

produce another Quantum number, the Magnetic Quantum Number (ml)

ml = -l to +l

Therefore if l = 1; ml can be -1, 0, +1

This means that each sublevel can have further sublevels.This causes the orbitals to have different orientations in

space

Spin Quantum NumberWork by Pauli (1925) determine that two

electrons could occupy each orbital.These electrons have opposite spins given the

values +1/2 and -1/2.The Spin Quantum Number (ms)

ms = -l/2 and +l/2

This means that each sublevel can be occupied by two electrons!

SummaryThis time line

draws nice comparisons between the Quantum view of the Atom with the Bohr-Rutherford model and the Lewis Structures we have used in the past.

Senior Physics – TVO programsStructure of the Atom 1: The Earliest Models (9:04) http://

www.youtube.com/watch?v=BhWgv0STLZs Structure of the Atom 2: Smaller than the Smallest (8:47)

http://www.youtube.com/watch?v=WmmglVNl9OQ Structure of the Atom 3: The Rutherford Model (9:10)

http://www.youtube.com/watch?v=FfY4R5mkMY8 Structure of the Atom 4: The Bohr Model (9:08) http://

www.youtube.com/watch?v=hpKhjKrBn9s Structure of the Atom 5: Spectra (9:28) http://

www.youtube.com/watch?v=5z2ZfYVzefs Structure of the Atom 6: The Wave Mechanical Model

(9:08) http://www.youtube.com/watch?v=IsA_oIXdF_8 These programs provide excellent review of the History

of the Atomic Model and how Quantum Mechanics is important!