An Introduction to Quantum Mechanics

Part One - The Story of The Atom

In the essay on Relativity, I stated that the Theory of Relativity was one of the two most important ideas of 20th Century science. Relativity is a deviation from Newtonian Mechanics (also known as common sense!). The deviations were not discovered until this Century because they are only noticeable at high speeds and under very intense gravitational fields. There is another 20th Century idea that also violates Newtonian Mechanics. This is called Quantum Mechanics.

In this essay I will give a taste of the strange and fascinating world of the atom. I will try to keep it general and simple because these ideas are even more weird than Relativity (if that is possible).

The Ancient Greeks proposed that matter could not be divided indefinitely. They speculated that matter was made up of units called atoms. The word comes from a Greek word meaning single item or portion. They assumed that atoms were solid, different characteristics of substances being determined by the different shapes that atoms had. This atomic idea never really became popular.

During the 16th Century, chemists worked out that behaviour of gases. If they doubled the volume of a gas, its pressure halved. If they halved its volume, its temperature doubled. It was also found that chemical reactions always took place in fixed ratios. For example one volume of oxygen always combined with two volumes of hydrogen to produce water (assuming the gases were at the same temperature and pressure). Results like these lead to the idea of atoms. The Atomic Theory was by far the best way to explain these and other phenomena.

When the idea of elements came, it was assumed that different elements had different atoms. John Dalton showed that each element had an atom that differed in weight (correctly, mass) to other atoms. So now we say that a Carbon atom has a relative mass of 12, Oxygen has one of 16. The unit is the Hydrogen atom, the lightest of all the atoms.

During the middle of the 19th Century, James Maxwell explained the gas laws by applying statistics to the random motions of atoms. He showed that when you heat a gas you make its molecules go faster. These strike the surface of the container with more force, thus increasing the gas pressure. To keep the pressure the same the volume has to be increased. Atoms were now taken for granted and treated as featureless spheres (i.e. little balls).

At this point the idea that atoms were featureless spheres was overturned by several discoveries made towards the end of the 19th Century. Firstly, there were experiments in electricity and magnetism which indicated the existence of particles with less mass than the Hydrogen atom. The electron was the most famous of these. Secondly, atoms were found to be more complex that previously thought when radioactivity was discovered. Atoms were throwing out bits and changing to other atoms; atoms could take and give an electric charge.

From various observations and experiments it was eventually decided that an atom was made up of three particles:

• Protons - these were charged with electricity that was positive and contained most of the mass of atoms.

• Electrons - these were very light particles (1/1800th the mass of a Hydrogen atom!) with a negative electric charge exactly equal to the charge on a proton.

• Neutrons - neutral particles with a mass similar to protons but with no charge.

In an atom, the protons and neutrons were in the central regions of the atom (called the nucleus) while the electrons revolved around at high speed. It was the outer electrons that interacted when atoms reacted chemically with other atoms. It was these electrons that were involved in electrical effects. It was the number of protons that determined how many electrons there were (they had to be the same). This number (called the Atomic Number) determined how the atom behaved, i.e. what element it was. Hydrogen atoms have 1 proton and 1 electron, Oxygen has 8 of each, Uranium has 92 of each. The electrons were held in orbit by electric attraction (positive and negative attract), much as the planets were held in orbit around the sun by the attractive force of gravity.

Protons, neutron and electrons are discussed in more detail as Sub-Atomic Particles.

The above description of the atom is the Newtonian (or Classical) description. It is possible to picture it and it makes sense. Unfortunately, this description violates Maxwell's Laws of Electromagnetism. Maxwell's Laws of Electromagnetism were very powerful tools. However they could not explain how an atom could be stable. Under those laws, an electrically charged object (like an electron) that was changing direction (in orbit around the nucleus of an atom) should be radiating energy away until it spiralled into the nucleus! Clearly this does not happen. Atoms are stable. Furthermore, there were a few other observations about atoms that were not quite right.

Of course, atoms did absorb and radiate energy. The problem was that this process was strictly controlled. Atoms only absorbed specific wavelengths of energy. Sodium, for example, radiated a lot of yellow light (hence its use in street lamps), Potassium radiated lilac (hence the colour of most fireworks). This was a major flaw in the physics of the turn of the century. Physics had other problems - phenomena that didn't work as predicted: the way a hot, glowing body radiated energy at a given temperature (the Black Body Problem); the way metals produced electricity when light shone on them (the Photoelectric Effect); the way atoms decayed when they were radioactive. Something was wrong with the state of Physics. What was needed was a revolution in Physics. Unlike the onset of relativity which was the brainchild of one man, this new idea would spawn from many minds over a generation.

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Part Two - Quantum Mechanics

Isaac Newton thought that light was a stream of particles; Thomas Young thought it was a wave. Most people at the turn of the century thought of light as a wave. In 1900 Max Planck found that he could explain the way hot bodies radiate energy only if he assumed that energy occurred as packets. He assumed that his equations were simply tricks with the mathematics and called these packets of energy quanta. The equations were useful but the underlying ideas were not taken seriously.

In 1905, Albert Einstein published three scientific papers, any one of which was the mark of a genius.

The first was Part One of his Theory of Relativity.

The second proved the existence of atoms from direct observations (an effect called Brownian Motion).

The third paper is the relevant one for this essay. In this paper, he applied Planck's quantum idea of 1900 to explain the Photoelectric Effect. These quanta were now being utilised to explain two previously unexplainable phenomena. However, if quanta were real, was light a wave or a particle? It was as if in some experiments (refraction, diffraction) light was clearly a wave; in others (black body radiation, the photoelectric effect) it was a particle. This effect was strange and was known as wave-particle duality.

In 1912, Louise de Broglie, suggested that if energy could behave as both particles and waves, perhaps matter could also! He nearly didn't get his PhD for that ridiculous suggestion! He produced the mathematics and predicted that under the right conditions a beam of electrons (clearly matter made of particles) might show wave properties. Surprisingly, when the experiment was performed, a beam of electrons was found to diffract just like a wave would have done! That was it! It looked like energy and matter could both exhibit wave-particle duality. It appeared that a moving particle had a wavelength!

My readers should not worry - I cannot picture it either!

To continue: Neils Bohr decided to work out the wavelength of an electron moving around the nucleus of an atom. He found that for an electron to have a stable orbit, the orbit had to include a whole-number of the electron's wave. Orbits that include fractions of waves were impossible so the electron could not inhabit them. In other words, an electron could have a stable orbit, so that it would not lose energy and spiral in to the nucleus. If an electron absorbed or radiated energy, it would do so in discreet amounts so that it would move to another stable orbit. The analogy is a staircase. You can only stand on the steps, not in the region between steps.

So these quantum ideas explained two things. Why atoms were stable and why atoms absorbed or emitted energy in selected wavelengths. Bohr used his ideas to predict what energy could be radiated from different atoms. His theories corresponded with observation.

In 1925, Erwin Schrodinger and Werner Heisenberg separately worked out the mathematics of Quantum Mechanics. Using this new theory, scientists could understand the behaviour of atoms and subatomic particles. The wave-particle duality concept it true for both matter and energy. The 'position' of a particle like an electron is given by a probability. Electrons exist in energy states. When they absorb energy, they absorb a whole number of quanta, disappear, appearing at a different energy state. Gone is the idea of little ball-like particles. The orbit of an electron is a cloud of probability around the nucleus.

Another quantum effect is the famous Uncertainty Principle. This implies that there is a built-in uncertainty in the Universe. It is possible for something to be created out of nothing, given enough time! On a subatomic level it is impossible to pinpoint things down to an infinite precision. And not because of any technological failings: this is a constraint of the Universe itself. A zero energy is impossible since it would be a precise state. This is the reason that nothing can be cooled below -273 degrees C (Absolute Zero). An atom must retain at least one quantum of energy and this keeps it from cooling below Absolute Zero. This means that nothing can ever be at rest.

Quantum effects are not noticeable in the macro world. They only become important as one approaches the dimensions of the atom. Nevertheless, their effects are important in all branches of science. Quantum Mechanics is used to understand phenomena like radioactivity, chemical bonding, semi-conductors, solid-state micro-chips, electronics, sub-atomic physics, radiation from black holes, and many others.