QUANTUM MECHANICS

 

Radiation

·         Definition: transmission outward in all directions of some emanation

·         e.g. electromagnetic waves, or, more simply, light

·         Henri Becquerel (1896)

·         measured fluorescence of materials after being in the sun

·         found that uranium salts glow even when they have not been in the light

·         they are radioactive.

·         Marie Curie refined and purified these salts producing purer uranium, polonium, and radium

 

Cathode Rays

·         William Crookes in the 1870s invented a vacuum tube in which when electricity was pumped into a metal plate at one end (the cathode) it caused a glow in the direction of a metal plate the anode) at the other end.

 

X-Rays

·         Wilhelm Röntgen discovered in 1895 that a cathode ray tube also caused illumination of a coated paper screen up to 2 metres away.

Electrons

·         J. J. Thomson in 1897 at the Cavendish Laboratories at Cambridge:

·         tried to measure effects of cathode ray tubes

·         found that cathode rays could be generated from any element

·         found that they behaved like a stream of particles

·         Thomson believed the particles came out of chemical atoms.

·         He called cathode rays electrons. Therefore, the “atom” had parts and was not an indivisible ultimate unit.

·          

Rutherford’s Rays

·         Ernest Rutherford – 1911

·         from New Zealand

·         student of J. J. Thomson at Cambridge

·         later taught at McGill University

·         ultimately set up a laboratory at the University of Manchester

·         Set out to analyze the different “rays” that could be produced. Gave them names from the Greek alphabet:

·         alpha rays – later found to be the nucleus of helium atoms

·         beta rays – turned out to be the same as cathode rays or electrons

·         gamma rays – light of a small wave length, something like x-rays

Rutherford’s Experiment

·         To explore the structure of the atom, Rutherford set up an experiment to bombard thin foils of metal with (heavy) alpha particles and see what happens.

·         Though most passed through the foil, some were deflected back.

·         Rutherford concluded that the mass of atoms must be concentrated in a very small space compared to the whole volume occupied by an atom.

 

Black Body Radiation

·         A “black body” is one that does not reflect light (or other radiation)

 

The Ultraviolet Catastrophe

 

Planck’s Quanta

·         Max Planck – German physicist (work done in 1899-1900)

·         Realized that Maxwell’s (continuous) wave equations led to the “catastrophe” because it allowed for infinitely small amounts of energy.

·         A quantity divided by an infinitely small amount = an infinitely large quantity.

·         If Planck used discrete equations (as Boltzman did for statistical mechanics), he could get around the division by zero problem.

 

hthe quantum of energy

·         Planck found that energy could not be radiated at all in units smaller than an amount he called h – the quantum of energy.

·         When he introduced the restriction h into his equations, the ultraviolet catastrophe disappeared.

·         But what was the physical meaning of a smallest amount of energy?

 

Einstein and the Photoelectric Effect

·         Einstein took Planck’s constant, h, to have serious physical meaning.

·         He suggested that light comes in discrete bits, which he called light quanta (now called photons).

·         This would explain how light can produce an electric current in a sheet of metal.

·         Einstein’s Nobel Prize was for this work (not for relativity).

 

The Bohr Atom

·         Niels Bohr (1885-1962)

 

The Bohr Atom and the Periodic Table

·         Bohr found that each “orbit” or “shell” had room for a fixed maximum number of electrons.

·         2 in the first, 8 in the second, 18 in the third, 32 in the fourth, etc.

·         This accounted for properties revealed by the Periodic Table

·         The Group number corresponds to the number of electrons in the outer shell.

Matter Waves

·         Louis de Broglie (1924) suggested that if waves can behave like particles, maybe particles can behave like waves.

·         He proposed that electrons are waves of matter. The reason for the size and number of electrons in a Bohr electron shell is the number of wave periods that exactly fit.

 

Schrödinger’s Wave Equations

·         Erwin Schrödinger in 1926 published a general theory of “matter waves”

·         Schrödinger’s equations describe 3-dimensional waves using probability functions

·         Gives the probability of an electron being in a given place at a given time, instead of being in an orbit

·         The probability space is the electron cloud.

 

Heisenberg’s Uncertainty Principle

·         Werner Heisenberg

·         Schrödinger’s equations give the probability of an electron being in a certain place and having a certain momentum.

·         Heisenberg wished to be able to determine precisely what the position and momentum were.

·         To “see” an electron and determine its position it has to be hit with a photon having more energy than the electron – which would knock it out of position.

·         To determine momentum, a photon of low energy could be used, but this would give only a vague idea of position.

·         Using any means we know to determine position and momentum, the uncertainty of position, Dq, and the uncertainty of momentum, Dp, are trade-offs.

·         DqDp³ h/2p, where h is Planck’s constant

·         Note: the act of observing alters the thing observed.

 

Particles or Waves?

Are the fundamental constituents of the universe

·         Particles – which have a position and momentum, but we just can’t know it, or

·         Waves (or probability) – which do not completely determine the future, only make some outcome more likely than others

 

The Copenhagen Interpretation

·         Niels Bohr:

·         The underlying reality is more complex than either waves or particles.

·         We can think of nature in terms of either waves or particles when it is convenient to do so.

·         The two views complement each other. Neither is complete in itself.

 

Does Quantum Mechanics Describe Nature

·         Einstein said no.

·         “God does not play dice.”

 

Schrödinger’s Cat Paradox

·         Is there no reality until we look?

·         If quantum mechanics is complete, radioactive decay doesn’t happen or not happen until we measure it.

·         The cat is neither alive nor dead until we open the chamber.

 

Many Universes Interpretation

·         Hugh Everett (1950s)

·         Every outcome that is possible happens, in different universes