- THE FIRST MILLENIUM
‘The notion of the indivisible particle’
Anaxagoras came from Ionia but settled in Athens, where he remained for thirty years and taught both Pericles and Euripides. Charged with impiety because of his theory that the Sun is a red-hot stone (such an explanation, denying the role of Helios the sun-god, was enough to warrant prosecution) he fled Athens before the trial and settled in Asia Minor.
What we know about Anaxagoras is based on references to him by later writers.
In the cosmology of Anaxagoras, the Universe began as a homogenous sea of identical basic particles. Nous gave this sea a stir, in the knowledge that in time the particles would so combine to arrange themselves such that everything would be as it is today.
Nous was a vital principle akin to the life force of vitalism – the nearest English words being ‘mind’ or ‘intellect’.
The range of the word ‘Nous’ is vastly greater, however, as it refers to the combination of insight and intuition which permits the apprehension of the fundamental principles of the cosmos – the concept is closer to the oriental idea of ‘seeing’ than the occidental notion of intelligence founded upon EUCLIDEAN LOGIC.
At the same time, Nous could be the creative, motive intelligence behind the cosmos, almost indistinguishable from the Christian concept of the will of God.
1927 – Germany
‘It is impossible to determine exactly both the position and momentum of a particle (such as an electron) simultaneously’
The principle excludes the existence of a particle that is stationary.
To measure both the position and momentum ( momentum = mass × velocity ) of a particle simultaneously requires two measurements: the act of performing the first measurement will disturb a particle and so create uncertainty in the second measurement.
Thus the more accurately a position is known; the less accurately can the momentum be determined.
The disturbance is so small it can be ignored in the macroscopic world, but is quite dramatic for particles in the microscopic world.
MAX BORN’S ‘probabilistic’ interpretation, expressed at about the same time, concerning the likelihood of finding a particle at any point through probability defined by the amplitude of its associated wave, led to similar conclusions.
The uncertainty principle also applies to energy and time. A particle’s kinetic energy cannot be measured with complete precision either.
Heisenberg suggested the model of the proton and neutron being held together in the nucleus of the atom after the work of JAMES CHADWICK who discovered the neutron in 1932.
Heisenberg decided to try to develop a new model of the atom, more fundamentally based on quantum theory that worked for all atoms. He believed the approach of trying to visualise a physical model of the atom was destined to fail because of the paradoxical wave-particle nature of electrons.
Every particle has an associated wave. The position of a particle can be precisely located where the wave’s undulations are most intense. But where the wave’s undulations are most intense, the wavelength is also at its most ill-defined, and the velocity of the associated particle is impossible to determine. Similarly, a particle with a well-defined wavelength has a precise velocity but a very ill-defined position.
Since the orbits of electrons could not be observed, he decided to ignore them and focus instead on what could be observed and measured; namely the energy they emitted and absorbed, as shown in the spectral lines. He tried to devise a mathematical way of representing the orbits of electrons, and to use this as a way of predicting the atomic features shown up in the spectral lines.
He showed that matrix mechanics could account for many of the properties of atoms, including those with more than one electron.
Together with PAUL DIRAC, Pascual Jordan created a new set of equations based on the rival theories of Schrödinger and Heisenberg, which they called ‘transformation theory’. Whilst studying these equations, Heisenberg noticed the paradox that measurements of position and velocity (speed and direction) of particles taken at the same time gave imprecise results. He believed that this uncertainty was a part of the nature of the sub-atomic world. The act of measuring the velocity of a subatomic particle will change it, making the simultaneous measurement of its position invalid.
An unobserved object is both a particle and a wave. If an experimenter chooses to measure the object’s velocity, the object will transform itself into a wave. If an experimenter chooses to measure its position, it will become a particle. By choosing to observe either one thing or the other, the observer is actually affecting the form the object takes.
The practical implication of this is that one can never predict where an electron will be at a precise moment, one can only predict the probability of its being there.
1928 – UK
‘Every fundamental particle has an antiparticle – a mirror twin with the same mass but opposite charge’
‘It appears that the simplest Hamiltonian for a point-charge electron satisfying the requirements of both relativity and the general transformation theory leads to an explanation of all duplexity phenomena without further assumption’
1931 – UK
‘A magnetic monopole is analogous to electric charge’
A magnetic monopole is a hypothetical particle that carries a basic magnetic charge – in effect, a single north or south magnetic pole acting as a free particle.
1913 – Denmark
‘Electrons in atoms are restricted to certain orbits but they can move from one orbit to another’
Bohr’s was the first quantum model for the internal structure of the atom.
Bohr worked with RUTHERFORD in Manchester and improved upon Rutherford’s model, which said that electrons were free to orbit the nucleus at random.
Classical physics insisted that electrons moving around the nucleus would eventually expire and collapse into the nucleus as they radiated energy. Bohr resolved the issue surrounding Rutherford’s atomic structure by applying the concept of quantum physics set out by MAX PLANCK in 1900.
He suggested that the electrons would have to exist in one of a number of specific orbits, each being defined by specific levels of energy. From the perspective of quantum theory, electrons only existed in these fixed orbits where they did not radiate energy. The electrons could move to higher-level orbits if energy was added, or fall to lower ones if they gave out energy. The innermost orbit contains up to two electrons. The next may contain up to eight electrons. If an inner orbit is not full, an electron from an outer orbit can jump into it. Energy is released as light (a photon) when this happens. The energy that is released is a fixed amount, a quantum.
Quanta of radiation would only ever be emitted as an atom made the transition between states and released energy. Electrons could not exist in between these definite steps. This quantised theory of the electrons’ orbits had the benefits of explaining why atoms always emitted or absorbed specific frequencies of electromagnetic radiation and of providing an understanding of why atoms are stable.
Bohr calculated the amount of radiation emitted during these transitions using Planck’s constant. It fitted physical observations and made sense of the spectral lines of a hydrogen atom, observed when the electromagnetic radiation (caused by the vibrations of electrons) of the element was passed through a prism. The prism breaks it up into spectral lines, which show the intensities and frequencies of the radiation – and therefore the energy emissions and absorptions of the electrons.
Each of the elements has an atomic number, starting with hydrogen, with an atomic number of one. The atomic number corresponds to the number of protons in the element’s atoms. Bohr had already shown that electrons inhabit fixed orbits around the nucleus of the atom.
Atoms strive to have a full outer shell (allowed orbit), which gives a stable structure. They may share, give away or receive extra electrons to achieve stability. The way that atoms will form bonds with others, and the ease with which they will do it, is determined by the configuration of electrons.
As elements are ordered in the periodic table by atomic number, it can be seen that their position in the table can be used to predict how they will react.
In addition to showing that electrons are restricted to orbits, Bohr’s model also suggested that
Bohr called the jump to another orbit a quantum leap.
Although it contained elements of quantum theory, the Bohr model had its flaws. It ignored the wave character of the electron. Work by WERNER KARL HEISENBERG later tackled these weaknesses.
Bohr’s theory of complementarity states that electrons may be both a wave and a particle, but that we can only experience them as one or the other at any given time. He showed that contradictory characteristics of an electron could be proved in separate experiments and none of the results can be accepted singly – we need to hold all the possibilities in mind at once. This requires a slight adjustment to the original model of atomic structure, we can no longer say that an electron occupies a particular orbit, but can only give the probability that it is there.
In 1939 he developed a theory of nuclear fission with Jon Archibald Wheeler (b.1911) and realised that the 235uranium isotope would be more susceptible to fission than the more commonly used 238uranium.
The element bohrium is named after him.
1914 – Manchester, England
‘Moseley’s law – the principle outlining the link between the X-ray frequency of an element and its atomic number’
Working with ERNEST RUTHERFORD’s team in Manchester trying to better understand radiation, particularly of radium, Moseley became interested in X-rays and learning new techniques to measure their frequencies.
A technique had been devised using crystals to diffract the emitted radiation, which had a wavelength specific to the element being experimented upon.
In 1913, Moseley recorded the frequencies of the X-ray spectra of over thirty metallic elements and deduced that the frequencies of the radiation emitted were related to the squares of certain incremental whole numbers. These integers were indicative of the atomic number of the element, and its position in the periodic table. This number was the same as the positive charge of the nucleus of the atom (and by implication also the number of electrons with corresponding negative charge).
By uniting the charge in the nucleus with an atomic number, a vital link had been found between the physical atomic make up of an element and its chemical properties, as indicated by where it sits in the periodic table.
This meant that the properties of an element could now be considered in terms of atomic number rather than atomic weight, as had previously been the case – certain inconsistencies in the MENDELEEV version of the periodic table could be ironed out. In addition, the atomic numbers and weights of several missing elements could be predicted and other properties deduced from their expected position in the table.
1925 – Austria
‘No two electrons in an atom can have the same quantum number’
A quantum number describes certain properties of a particle such as its charge and spin.
An orbital or energy level cannot hold more than two electrons, one spinning clockwise, the other anti-clockwise.
Electrons are grouped in shells, which contain orbitals. The shells are numbered ( n = 1,2,3 etc. ) outwards from the nucleus. These numbers are the ‘principle quantum numbers’.
An increase in n indicates an increase in energy associated with the shell, and an increase in the distance of the shell from the nucleus. The number of electrons allowed in a shell is 2n2. Each shell contains sub-shells or energy sub-levels. A shell can only have n sub-shells. A shell is given a number and a letter ( s,p,d,f,g,etc. ). For example, the electron shell structure of lithium is 1s22s1 (two electrons in ‘s’ sub-shell of the first shell, and one electron in ‘s’ sub-shell of the second shell; the superscript indicates the number of electrons in the shell).
The Pauli principle provided a theoretical basis for the modern periodic table.
1930 – Austria
‘The radioactive beta decay of an atomic nucleus in which a neutron turns into a proton and emits an electron does not seem to follow the law of conservation of energy. To account for the missing energy, Pauli postulated that a particle of zero charge and zero mass is released in such reactions’
A few years later ENRICO FERMI named the new particle a neutrino.
There are three known types of neutrino – muon, tau and electron.
1926 – Austria
‘The complex mathematical equation describing the changing wave pattern of a particle such as an electron in an atom. The solution of the equation gives the probability of finding the particle at a particular place’
This equation provides a mathematical description of the wave-like properties of particles.
Schrödinger developed what became known as ‘wave mechanics’, although like others, including EINSTEIN, he later became uncomfortable with the direction quantum theory took. His own proposal was built upon that of LOUIS DE BROGLIE – that particles could, in quantum theory, behave like waves. Schrödinger felt that de Broglie’s equations were too simplistic and did not offer a detailed enough analysis of the behaviour of matter, particularly at the sub-atomic level. He removed the idea of the particle completely and argued that everything is a form of wave.
PLANCK’s work had shown that light came in different colours because the photons had different amounts of energy. If you divided that energy by the frequency at which that colour of light was known to oscillate, you always arrived at the same value, the so-called Planck’s constant.
Between 1925 and 1926 Schrödinger calculated a ‘wave equation’ that mathematically underpinned his argument. When the theory was applied against known values for the hydrogen atom, for example in calculating the level of energy in an electron, it overcame some of the elements of earlier quantum theory developed by NIELS BOHR and addressed the weaknesses of de Broglie’s thesis.
Schrödinger stated that the quantum energies of electrons did not correspond to fixed orbits, as Bohr had stated, but to the vibration frequency of the ‘electron-wave’ around the nucleus. Just as a piano string has a fixed tone, so an electron wave has a fixed quantum of energy.
Having done away with particles, it was required that a physical explanation for the properties and nature of matter be found. The Austrian came up with the concept of ‘wave packets’ which would give the impression of the particle as seen in classical physics, but would actually be a wave.
The probabilistic interpretation of quantum theory based on the ideas of HEISENBERG and BORN proposed that matter did not exist in any particular place at all, being everywhere at the same time until one attempted to measure it. At that point, the equations offered the best ‘probability’ of finding the matter in a given location. Wave mechanics used much simpler mathematics than Heisenberg’s matrix mechanics, and was easier to visualise.
Schrödinger showed that in mathematical terms, both theories were the same and the rival theories together formed the basis for quantum mechanics.
Schrödinger joined Einstein and others in condemning the probabilistic view of physics where nothing was explainable for certain and cause and effect did not exist.
Ironically, PAUL ADRIAN MAURICE DIRAC went on to prove that Schrödinger’s wave thesis and the probabilistic interpretation were, mathematically at least, the equivalent of each other. Schrödinger shared a Nobel Prize for Physics with Dirac in 1933.