 The Bohr model describes definite electron energy levels within atoms  Bohr’s model only applied to hydrogen – it has been replaced by more sophisticated models.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 rate of change of the rate of change of the wavefunction with distance The energy of the particle wave 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

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!video

Shroedinger’s math treated multiple electrons as waves interfering in three dimensions. Vibrations on a drum skin Water hitting 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.

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

3D Orbitals

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

 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 Theory 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…... …….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

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

The story so far 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 Each experimental test of Quantum Mechanics reinforced the new theory and provided yet more evidence for: 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 quantisation of energy 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 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... 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!!