Fundamentals of Physics

A Brief History of Kinetic Atomic Theory

From about 600 BC Greek philosophers were speculating about the nature of the physical world and of matter itself. Thales at this time suggested that all matter originated from water (and that the earth was a flat disk floating in a sea of water). Anaxagoras, who died in 428 BC suggested that all matter consisted of infinite numbers of infinitely small particles he called ‘seeds’ and that all bodies are simply aggregations of these particles. Leucippus, who was aware that matter had three natural states, and has been credited with founding an atomic theory of matter, developed Anaxagoras’ ideas. However his writings on the subject did not survive like those of his pupil Democritus, who about 400 BC suggested that ‘matter consisted of minute hard particles moving as separate units in empty space’. This being the first suggestion of the ‘existence’ of the vacuum state.

But numerous questions remained, such as how these solid particles, even if moving, could remain suspended in empty space without falling and, as Aristotle (384-322 BC) subsequently asked; “How did these particles originally attain their velocity?” Aristotle also rejected the concept of an ‘empty space’ or a vacuum, clearly articulating that a vacuum could not exist, and also promoted the idea that the world was composed of just four elements, earth, air, fire and water and his ideas were generally accepted for two millenia, when Galileo’s pupil Torricelli’s experiments in 1643 were widely believed to have proven the ‘existence’ of the vacuum. This led to a re-evaluation of Aristotle’s four elements concept, and of the alternative ideas of Democritus. As a result, soon after in 1647, Pierre Gassendi resurrected atomic theory and wrote that ‘atoms (are) similar in substance, although different in size and form, (and) move in all directions through empty space and (are) devoid of all qualities except absolute rigidity’.

Bernoulli suggested in a 1738 publication that ‘the pressure of a gas on the walls of a vessel is the result of the innumerable collisions of its molecules with the walls’ and the fluctuations in pressure were explained by the suggestion that ‘heat applied to a gas results in an increase in the velocity of the molecules and a corresponding increase in collisions with the walls’. In the latter part of the 1700s two of Aristotle’s four elements, air and water, were separated into their constituent gases, which gases were identified and named, and the ‘four elements’ concept was finally proven to be false.

In 1808 Dalton published his theory of atoms (as solid, perfectly elastic, and indestructible spheres) based upon his observations of how different elements combine to form compounds, such as with the combination of Hydrogen and Oxygen to form Water. Dalton also presented in this publication his Laws of Multiple Proportions, (i.e. ‘when two elements combine in a series of compounds, the ratio of weights of one element combines with the fixed weight of the second element in a ratio of small whole numbers’). These laws together with Gay-Lussac’s Laws of Combining Volumes (i.e. when gases combine they do so in volumes that are in a ratio of small whole numbers) indicated that matter is divided into discrete, separate particles, which laws were seen as a confirmation of the atomic hypothesis.

In 1827 the British botanist Robert Brown discovered the phenomenon, later called Brownian Motion, which is the observed random movement of microscopic particles suspended in a gas or liquid. This motion of, for example, grains of pollen or smoke particles in air, appears to be completely random in both direction and dimension. This was later put forward as a visual manifestation of the effect of ‘kinetic’ atoms/molecules colliding with these particles. It was suggested that the inherent motion of the atoms/molecules in their collisions with the suspended particles induce their observed random motions.

In 1834 Émile Clapeyron introduced his equation of state for an ideal gas, which “is a good approximation to the behavior of many gases under many conditions, although it has several limitations”. The ideal gas law can also be derived from first principles using the kinetic theory of gases, in which several simplifying assumptions are made, chief among which are that the molecules, or atoms, of the gas are point masses, possessing mass but no significant volume, and undergo only elastic collisions with each other and the sides of the container in which both linear momentum and kinetic energy are conserved.” (Wikipedia)

Debate continued on the merits of one or the other theories of matter during the first half of the 1800’s but the next significant development came when Clerk Maxwell, following work by Krönig and Clausius, in 1859 put forward his ‘Law of Distribution of Velocities’ as a statistical or mathematical explanation of the distribution of kinetic molecular velocities in gases. The importance of the Maxwell distribution function, and of the later, more general Maxwell-Boltzmann distribution function ‘is that they contain all the information necessary to calculate any measurable variable of a gas’ such as the pressure, temperature, or volume. Clerk Maxwell based his statistics on the following assumptions.

1) Molecules are perfectly elastic balls of atomic dimensions that are in perpetual random motion.

2) The average kinetic energy of the molecules is proportional to the absolute temperature of the gas.

3) The molecules do not exert any appreciable attraction on each other.

4) The volume of the molecules is infinitesimal when compared to the volume of the gas.

5) The time spent in collisions is small compared with the time between collisions

(Inherent in assumption 4 is the concept of ‘empty space’, however Clerk Maxwell did not define this, either as a pure vacuum or as an ‘aether’, however he did not accept that a vacuum was a possible state)

Some principles of kinetic atomic theory are described as follows:–

Atoms in a gas, within a container, are ‘rushing around at different velocities and bouncing off each other and the walls like a three-dimensional game of billiards’ and ‘are moving in random directions, and because as many move in one direction as another, the average velocity of the molecules is zero’ – in other words the gas as a whole is not moving or producing unequal pressure on any inside surface of the container. ‘Pressure arises from the multiple collisions the atoms of a gas have with the walls that contain the gas’ and ‘heat applied to a gas results in an increase in the velocity of the atoms and a corresponding increase in collisions with the walls’. Also ‘when the fast moving atoms of a hot gas collide with slower moving atoms of a cooler gas, kinetic energy is transferred from the ‘hot’ to the ‘cold’ atoms’. ‘The collisions between atoms/molecules are completely elastic’, or in other words no energy of motion or ‘kinetic’ energy is lost as a result of any collision with other atoms/molecules of the gas or of the container.

‘The duration of collisions of atoms is about one thousandth of the time between collisions. Atoms spend the overwhelming part of their time in free motion, and collisions are a rare event in their life.’ In addition the theory suggests that the atoms of a gas only take up a minute proportion of the actual space the gas occupies. ‘An atom generally takes up only 1/1000th of the volume available to it and if we were to scale atoms to the size of human beings with a radius of 0.5 m, they would be spaced some 10m apart.’

In other words in any given volume of gas only about 0.1% is matter in the form of atoms. To put this in some sort of perspective 1000 cubic centimetres (one Litre) of gas contains a total volume of atomic matter that could be fitted into 1 cc while the remaining 999 cc is empty ‘space’. With this spacing the atoms, on average, have to go some distance before colliding with another and the theory states that ‘the mean free path of an atom is some 3000 times greater than the diameter of the atom itself’. Note: Quotations above are extracts from various University level textbooks.

In 1873 van der Waals introduced his equation of state, which was “an equation relating the density of gases and liquids to the pressure (p), volume (V), and temperature (T) conditions. It can be viewed as an adjustment to the ideal gas law that takes into account the non-zero volume of gas molecules, which are subject to a inter-particle attraction. It successfully approximates the behavior of real fluids above their critical temperatures and is qualitatively reasonable for their liquid and low-pressure gaseous states at low temperatures. However, near the transitions between gas and liquid, in the range of p, V, and T where the liquid phase and the gas phase are in equilibrium, the van der Waals equation fails to accurately model observed experimental behaviour, in particular that p is a constant function of V at given temperatures. As such, the van der Waals model is not useful only for calculations intended to predict real behavior in regions near the critical point. Empirical corrections to address these predictive deficiencies have been inserted into the van der Waals model, e.g., by Clerk Maxwell 1890 in his equal area rule, and related but distinct theoretical models, e.g., based on the principal of corresponding states, have been developed to achieve better fits to real fluid behaviour in equations of comparable complexity. (Wikipedia)

“It is quite clear from the (given) examples that this (the van der Waals) equation (of state) is only approximately true and is suitable only for rough quantitative assessments of the relationships between the parameters determining the state of a real substance.1(My emphases)

With respect to the atom itself, in 1884 J J Thompson relegated Dalton’s model to history and introduced a new structure, his ‘plum pudding atom’. “J.J. Thomson studied the conduction of electricity through gases, and experimented with cathode rays. He realised that he could deflect the cathode rays in an electric field produced by a pair of metal plates and argued that the cathode ray consisted of small charged particles, and by using different types of cathodes realised that the particles existed in many types of atoms. He concluded that the particles were a universal constituent of matter – they form part of all the atoms in the universe. We now know these particles as electrons.”2

To return to kinetic-atomic theory it necessary here to point out that it was not generally accepted at the turn of the century. Nobel Laureate Max Planck for example wrote that every attempt at elaborating the theory has not only not led to new physical results but has run into overwhelming difficulties”.3 Another Nobel winner, Wilhelm Ostwald, said that it is “a superficial habit to cover up rather than promote actual scientific tasks by arbitrary assumptions about atomic positions, motion and vibrations”.3

But in a 1905 paper on Brownian motion, Albert Einstein asserted ‘that Brownian motion, although random obeys a definite statistical law and is in accordance with statistics used by Boltzmann and Maxwell to describe the kinetic motion of molecules’. And then in 1908, Jean Perrin (who ‘was committed to the usefulness and the truth of molecular kinetic theory’) subjected Brownian motion to detailed microscopic analysis over a period of five years. The results of which work were generally accepted as confirming the existence of atoms and molecules and of their random kinetic motion. In his book ‘Les Atomes’ (an English translation of which was published in 1916) he states, that ‘each molecule of the air we breathe is moving with the velocity of a rifle bullet: travels in a straight line between two impacts for a distance of nearly one ten thousandth of a millimetre: is deflected from its course 5000 million times per second –. There are 30 milliard milliard (billion billion) molecules in a cubic centimetre of air, under normal conditions. 3000 million of them placed side-by-side in a straight line would be required to make up 1 millimetre. 20,000 million must be gathered together to make up 1000 millionth of a milligram’. He also subsequently states with respect to Brownian motion that ‘every granule suspended in a fluid (i.e. gas or liquid) is being struck continually by the molecules in its neighbourhood and receives impulses from them that do not in general exactly counterbalance each other; consequently it is tossed hither and thither in an irregular fashion.’

Further Perrin says that ‘the work developed by the stoppage of a molecule would be sufficient to raise a spherical drop of water 1 micron in diameter to a height of nearly 1 micron’.

The diagram below shows Perrin’s comparative dimensions with atoms increased to 2 mm diameter, and in this perspective the surface of the gamboge particle at this scale can only be shown as a straight line. Accordingly, at this perspective, he is suggesting that a single collision, out of untold billions of simultaneous collisions from every direction over the whole surface of the particle, could move this particle the equivalent of more than 600 metres.

With the subsequent elevation of Einstein to worldwide fame after the First World War, any doubts about the validity of the kinetic theory of gases dissipated.

Ernest Rutherford in 1909 set up an experiment that involved directing helium nuclei, which he called alpha particles, at sheets of gold foil of a thickness of 0.00004 cm. Most of the particles went straight through the foil, however a small number, 1 in 20,000, were deflected strongly at an average of 90° while some came directly back, which astonished Rutherford. Analysing these results led him to propose a completely different picture of the atom in 1911. The ‘Rutherford’ atom has a very small, (relative to the total suggested volume of the atom) unimaginably dense nucleus and is surrounded by one or more minute, and also very dense, electrons orbiting the nucleus at high speed. The nucleus consists of protons, which are particles with a positive electrical charge, and neutrons, which are electrically neutral, while the orbiting electrons have negative charge.

The mass of the electron is calculated to be about 0.0005 of the mass of the proton (the hydrogen nucleus) and they are extremely dense at 2 x 1017 Kg/M3. Rutherford calculated the diameter of the nucleus to be between 1/10,000 and 1/100,000 of that of the outer orbit of the electron/s. The outer orbit of the electrons is considered the extent of the atom, and the remaining space between the nucleus and the orbiting electrons is a “perfect vacuum”.4

The outer limits of these orbits, or the ‘shield’ of an atom are assumed to describe a sphere.
To put this in rough perspective, if a hydrogen nucleus was scaled up to the size of a pea then the orbit of its electron would be greater than the diameter of a football stadium and would be very difficult to see with a diameter of 3mm. The mass of the pea to scale would be 800 million tonnes while the electron would weigh about 400,000 tonnes (and would be invisible to the human eye with a diameter of .003 mm).

Thus the change in the hypothetical structure of the atom is dramatic, from the solid indestructible spheres of Dalton, via Thomson’s ‘plum pudding’ model, to an atom whose mass is concentrated in an almost insignificant volume.

But this new picture did not lead to any dramatic modification or adjustment to kinetic atomic theory in respect to the presumption of the perfect elasticity of molecules and atoms during their mutual collisions, or to the nature of the separating ’empty space’.

With respect to Kinetic Theory, Richard Feynman states in The Feynman Lectures in Physics 5 :- “It is obvious that this is a difficult subject, and we emphasize at the beginning that it is in fact an extremely difficult subject, and that we have to deal with it differently than we have dealt with the other subjects so far. In the case of mechanics and in the case of light, we were able to begin with a precise statement of some laws, like Newton’s laws, or the formula for the field produced by an accelerating charge, from which a whole host of phenomena could be essentially understood, and which would produce a basis for our understanding of mechanics and of light from that time on. – but we do not learn different physics, we only learn better methods of mathematical analysis to deal with the situation.

We cannot use this approach effectively in studying the properties of matter. We can discuss matter only in a most elementary way; it is much too complicated a subject to analyze directly from its specific basic laws, which are none other than the laws of mechanics and electricity. But these are a bit too far away from the properties we wish to study; it takes too many steps to get from Newton’s laws to the properties of matter, and these steps are, in themselves, fairly complicated. We will now start to take some of these steps, but while many of our analyses will be quite accurate, they will eventually get less and less accurate. We will have only a rough understanding of the properties of matter.”

(Note the emphasis ‘extremely‘ is Feynman’s own, the others are mine)

So today this, now very complex, theory remains firmly in place as the ultimate basis of all atomic physics, and from the core assumptions of this theory the hypothetical structures of the wider universe and of the sub-atomic arena today have been developed and are based. But the main, and by far the most important, problem with this theory of discontinuous atoms also remains firmly in place, as the transmission of gravity through and within this hypothetical structure is inexplicable.
It is an undeniable fact that it is impossible to transmit a force between two masses, of any dimension, through a non-resistive, non-interacting ’empty’ space of any hypothetical, speculative description. The transmission of any force is totally dependent on action and reaction, as defined by Newton’s Third Law, and there is no such thing as ‘action-at-a-distance’. As Newton wrote over 350 years ago :-

“That gravity should be innate, inherent and essential to matter, so that one body may act upon another at a distance through a vacuum without the mediation of any thing else by and through which their action or force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it.”

He also wrote that “Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things.” and today it is not only the kinetic theory of gases that is extremely complex it is all of current theoretical physics, from sub-atomic particle physics to astrophysics. The result of this complexity is that any two physicists, even those working in similar areas, will have different interpretations and opinions, and put four or more together they will argue for hours and still not come to any mutual agreement.

1) ‘Molecular Physics’ Kirkoin & Kirkoin, Mir Publishers
3) ‘Method and Appraisal in the Physical Sciences: The Critical Background to Modern Science’, 1800-1905, Colin Howson, CUP 1976.
4) Frank Close ‘The Void’ OUP 2007

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