The Bohr model describes definite electron energy levels within atoms Bohr’s model only applied to hydrogen – it has been replaced by more sophisticated models. Quantum Mechanics is the present model – it incorporates the wave and particle nature of matter.

Quantum effects are only noticeable on the atomic scale

Erwin Shroedinger (1925)- Developed a system of wave mechanics based upon de Broglie’s matter waves

08

2

2

2

2

VE

h

m

x

rate of change of the rate of change of the

wavefunction with distance

rate of change of the rate of change of the

wavefunction with distance

The energy of the

particle wave

The energy of the

particle wave

The electrical potential in which

the particle is travelling

The electrical potential in which

the particle is travelling

Due to the wave nature of matter, the exact position and momentum of an electron cannot be determined.

A two dimensional standard distribution

Interference of light waves (wave nature)

electrons

Interference of electrons (wave nature)

The Strange World of Quantum Physics

One Photon Or Electron

Where does it hit the screen??

Let’s watch one at a time…

Screen

Screen

Given ONE photon, we cannot predict exactly where it will hit.

We can only predict the PROBABILITY that it will hit a certain place on the screen: i.e., we can predict the pattern that many photons will make!!

Hyperlink to folder with video!

Shroedinger’s math treated multiple electrons as waves interfering in three dimensions.

Vibrations on Vibrations on a drum skina drum skin

Water hitting

Water hitting

water

water

“The normalized position wavefunctions for hydrogen, given in spherical coordinates are:”

Max Born (1926)- represents the probability of a

particle’s position at a particular time.

2

The region where the probability of finding an electron is high is called the electron cloud, or orbital

3D Orbitals

Free and trapped quantum particlesSchroedinger’s wave equation, and Born’s interpretation, can equally be applied to “free” particles, or those which are trapped

Schroedinger’s wave equation, and Born’s interpretation, can equally be applied to “free” particles, or those which are trappedClassically, a particle trapped in a potential well cannot escape….

Classically, a particle trapped in a potential well cannot escape….

….but a trapped quantum particle (eg a particle in an atomic nucleus) can tunnel out of the well, even when it does not have sufficient energy to climb over the barrier

….but a trapped quantum particle (eg a particle in an atomic nucleus) can tunnel out of the well, even when it does not have sufficient energy to climb over the barrier

Heisenburg and Schrodinger developed sets of equations that give the probability of any event in atomic physics

including why some spectral lines are brighter than others (some electron transitions are more likely to occur so with a large number of atoms, there are more atoms emitting that wavelength)

•The duality of matter makes it impossible to develop a set of equations that tells us both exactly where an electron is and what its momentum might be (Heisenburg’s Uncertainty Principle)

•the Uncertainty Principle and other quantum mechanical effects are not noticeable for large objects because of the large number of atoms

Quantum mechanics also explains why all the electrons in any atom do not fall into the ground state; no two electrons can have the same exact state (distance from the nucleus, energy, direction of rotation, etc.)

Quantum theory also gives the number of electrons possible in each of the energy levels (and therefore the number of elements in each period of the periodic table)

•Dirac developed equations that treated light as either a wave or as a particle

•Dirac’s equations also predicted the existence of antimatter, particles that are the exact opposite of the regular particles (anti-electron, antiproton, antineutron)

Dirac’s TheoryDirac’s theory removed the paradox of particle-wave duality:Dirac’s theory removed the paradox of particle-wave duality:

It showed that if a particle was probed in a way that was meant to demonstrate its particle like properties - it would appear to be a particle…...

It showed that if a particle was probed in a way that was meant to demonstrate its particle like properties - it would appear to be a particle…...…….if it was probed in a way that was meant to demonstrate its wave like properties - it would appear to be a wave

…….if it was probed in a way that was meant to demonstrate its wave like properties - it would appear to be a wave

It seems that it is our own inability to conjure up an appropriate or adequate mental picture of photons, atoms, electrons and other quantum particles that is at the heart of the particle-wave duality paradox

It seems that it is our own inability to conjure up an appropriate or adequate mental picture of photons, atoms, electrons and other quantum particles that is at the heart of the particle-wave duality paradox

Why is quantum physics important? All of physics, chemistry and the biosciences, as well as almost all of modern technology rely upon quantum mechanics

All of physics, chemistry and the biosciences, as well as almost all of modern technology rely upon quantum mechanics

Semiconductors, microelectronics, magnetism, superconductivity, lasers, radioactivity, solar energy, computers, polymers, batteries, recording media, microwave ovens, mobile phones, medical imaging, pharmaceuticals etc etc etc………..all require a detailed knowledge of the quantum world

Semiconductors, microelectronics, magnetism, superconductivity, lasers, radioactivity, solar energy, computers, polymers, batteries, recording media, microwave ovens, mobile phones, medical imaging, pharmaceuticals etc etc etc………..all require a detailed knowledge of the quantum world

…...and quantum theory has never let us down…...and quantum theory has never let us down

Some paradoxes do remain , but each time a test is carried out to resolve a paradox quantum mechanics is only strengthened.

Some paradoxes do remain , but each time a test is carried out to resolve a paradox quantum mechanics is only strengthened.

The story so farThe first 25 years of the 20thCentury saw a dramatic change in the way that physicists viewed the nature of matter and electromagnetic radiation

The first 25 years of the 20thCentury saw a dramatic change in the way that physicists viewed the nature of matter and electromagnetic radiation

Quantum mechanics had provided a radically different description of the substance of the universe to that offered by Classical Physics

Quantum mechanics had provided a radically different description of the substance of the universe to that offered by Classical Physics Each experimental test of Quantum Mechanics reinforced the new theory and provided yet more evidence for:

Each experimental test of Quantum Mechanics reinforced the new theory and provided yet more evidence for:

Wave-particle duality of both light and matter Wave-particle duality of both light and matter

A probabilistic rather than deterministic view of the Universe in which uncertainty is a physical concept

A probabilistic rather than deterministic view of the Universe in which uncertainty is a physical concept

A quantisation of energy A quantisation of energy

An underlying symmetry in which both particles and antiparticles play a role An underlying symmetry in which both particles and antiparticles play a role

But...

…despite these dramatic developments our perception and experience of the world around us has not significantly changed

…despite these dramatic developments our perception and experience of the world around us has not significantly changed

The physical laws developed by Newton and by Maxwell continued to provide a perfectly adequate description of the every day world - and still do today

The physical laws developed by Newton and by Maxwell continued to provide a perfectly adequate description of the every day world - and still do today

Quantum Physics had revolutionary impact upon our understanding of light and matter at the atomic level but...

Quantum Physics had revolutionary impact upon our understanding of light and matter at the atomic level but...

However, at precisely the same time that Quantum Mechanics was demonstrating the complete inadequacy of these Classical Laws at an atomic scale, developments were taking place which showed that they were also inadequate on the scale of the Universe

However, at precisely the same time that Quantum Mechanics was demonstrating the complete inadequacy of these Classical Laws at an atomic scale, developments were taking place which showed that they were also inadequate on the scale of the Universe

These developments changed our perception of time itself!!These developments changed our perception of time itself!!