-The Bohr Model -The Quantum Mechanical Model. a) The Bohr Model.
The Bohr model describes definite electron energy levels within atoms Bohr’s model only applied...
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Transcript of The Bohr model describes definite electron energy levels within atoms Bohr’s model only applied...
The Bohr model describes definite electron energy levels within atoms Bohr’s model only applied to hydrogen – it has been replaced by more sophisticated models.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
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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
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!!
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.
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The region where the probability of finding an electron is high is called the electron cloud, or orbital
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!!