WERNER HEISENBERG (1901- 76)

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.

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NIELS BOHR (1885-1962)

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

  • the orbit closest to the nucleus is lowest in energy, with successively higher energies for more distant orbits.
  • when an electron jumps to a lower orbit it emits a photon.
  • when an electron absorbs energy, it jumps to a higher orbit.

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.

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LOUIS DE BROGLIE (1892-1987)

1924 – France

‘The wave-particle duality of matter.
Like photons, particles such as electrons also show wave-particle duality, that is, they also behave like light waves’

Einstein had suggested in one of his 1905 papers that the ‘photoelectric’ effect could be explained by an interpretation that included electromagnetic waves behaving like particles. De Broglie simply reversed the argument and asked: ‘if waves can behave like particles (a stream of quanta or photons), why should particles not behave like waves?’

Louis de Broglie (1892-1987), French physicist. De Broglie was instrumental in showing that waves and particles can behave like each other at a quantum level (wave-particle duality). He suggested that particles, such as electrons, could behave as waves. This was confirmed by Davisson and Germer in 1927. He was awarded the 1928 Nobel Prize for Physics for his work.

LOUIS DE BROGLIE

By applying quantum theory de Broglie was able to show that an electron could act as if it were a wave with its wavelength calculated by dividing PLANCK‘s constant by the electron’s momentum at any given instant. His proposal was found to be plausible by experimental evidence shortly afterwards.

BORN, SCHRODINGER and HEISENBERG offered arguments to the debate. NIELS BOHR provided some context in 1927 by pointing out that the equipment used in experiments to prove the case one way or another greatly influenced the outcome of the results. A principle of ‘complementarity’ had to be applied suggesting the experimental proof to be a series of partially correct answers, which have to be interpreted side by side for the most complete picture. Uncertainty and Complementarity together became known as the ‘Copenhagen interpretation’ of quantum mechanics.

Eventually, the ‘probabilistic’ theories of Heisenberg and Born largely won out. At this juncture, cause and effect had logically been removed from atomic physics and de Broglie, like Einstein and Schrödinger, began to question the direction quantum theory was taking and rejected many of its findings.

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ERWIN SCHRODINGER (1887-1961)

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’

the Schrodinger equation

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.

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ERWIN SCHRODINGER

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.

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