None of these lines of evidence “proves” the existence of atoms individually.  However, what they do indicate is that nature behaves as if atoms existed.  So we can say with surety that the explanatory power of the idea of atoms far surpasses any competing idea both in its ability to explain observed phenomena, but to predict the behavior of phenomena accurately.

1. Behavior of Gases

Daniel Bernoulli – Swiss Physicist – 1700-1782.  Bernoulli was studying air pressure and thought about gases and the possibility of atoms.  He thought that if there were such a thing as atoms, they would have to have some amount of mass, and that they must be in motion, which means they must follow Newton’s Laws (particularly F=ma).  This means that they have some amount of kinetic energy (energy by virtue of motion).  So imagine a balloon filled with air.  The reason why the rubber balloon doesn’t collapse is because the air on the inside is made up of tiny little particles which are slamming into the inner surface of the balloon, pushing it outward.  The kinetic energy of these collisions exactly balances the tendency of the elastic tension in the rubber of the balloon to collapse.  If you put in twice as much air, then the pressure on the balloon will increase by 2 as well, because you have twice as many collisions with the side of the balloon, making the balloon expand. If you increase the temperature of the gas in the balloon, you increase their kinetic energy, thus making them hit the side of the balloon harder.  The result?  The balloon expands when heated. 

2. Ratios of Elements

John Dalton – English Meteorologist – 1766-1844.  Dalton made the first statement of atomic theory from a chemist’s point of view.  He said that “Having been long accustomed to making meteorological observations, and to speculate upon the nature and constitution of the atmosphere, it often struck me with wonder how a compound atmosphere of a mixture of 2 or more elastic fluids should constitute an apparently homogeneous mass.”  This question led Dalton to experiments where he noticed that two elements always combined in whole number ratios (by weight).  So you can discover that 1 pound of hydrogen will always combine with 8 pounds of oxygen.  This meant, to Dalton, that there may be a smallest unit of each element that would combine with other elements in whole number weight ratios.  This is because you could take ½ a pound of hydrogen and combine it with exactly 4 pounds of oxygen, or you could take ¼ a pound of hydrogen and combine it with exactly 2 pounds of oxygen.  The idea is that by continuing this process you would eventually come to tiny ‘bits’ or smallest units of hydrogen with a particular weight (which we can define as 1 since hydrogen is the lightest element) that would combine with an oxygen bit with a particular weight (in this case 16 because two hydrogen atoms combine with one oxygen atom to make water – so one atom of oxygen is 16 times heavier than one atom of hydrogen).  If you can combine elements in different ways, say for example, hydrogen and oxygen in a weight ratio of 1 to 16, then you know that in this case one hydrogen is combining with one oxygen.

3. Radioactivity

1896 – Discovery of radiation by Bequerel, who found that certain elements, when placed near photographic-type paper, would emit energy that was recorded by the paper as a flash of light.  This emission of something that showed up so discreetly and point-like on the photographic paper convinced even the most skeptical scientists that atoms existed and were like tiny tiny particles.

4. Brownian Motion

Einstein explained in 1905 the phenomenon of Brownian motion in a mathematical way by assuming atoms existed.  Brownian motion can be observed when looking at water in a microscope.  Tiny objects (like a dust particle for example) on the surface of the water are seen to be in constant motion, jiggling back and forth seemingly at random.  What makes the dust particle jiggle and vibrate?  If the dust particle is changing its motion, then there must be a force applied to it that causes this change.  The assumption that there are tiny particles of mass that are continually in motion which hit the dust particle and push it around explains this phenomenon.  Einstein’s paper on this subject showed that the force on the dust particle that caused the random motion was exactly what would be expected from the randomness of collisions of atoms in the water hitting the dust particle.   This mathematical discovery did more to convince the world of the existence of atoms than any other evidence that existed up to that point (1903).

5. Avagadro’s Number

If atoms are real, then there must be a large but finite number of them in any given material.  It must be possible to determine how many atoms are in a specific amount of substance.  Many different ways of determining this number of atoms were explored – for example evidence came from studies of Brownian motion, radioactivity and other methods.  What was unique was that every line of evidence came up with the same number of atoms for a given amount of substance.  This number is known as Avagadro’s Number, and is 6 x 1023 atoms per ‘mole’ (this is a HUGE number).  A mole of hydrogen weighs one gram, while a mole of oxygen weighs 16 grams (note that this is the atomic weight on the periodic table).  So in 16 grams of oxygen you have the exact same number of atoms as you would in 1 gram of hydrogen.  The weight difference is because one atom of oxygen weighs 16 times more than one atom of hydrogen.  This also gave evidence as to the size of atoms and the distance between them.

6. X-Ray Crystallography

X-rays are electromagnetic waves whose wavelength is about the size of a single atom.  When X-rays are fired at crystals, they diffract.  This type of diffraction cannot occur unless the object has hard points like spheres as well as spaces between the hard points.  The fact that X-ray diffraction occurs when passed through the center of a crystal confirms that there must be these hard points that are spaced apart from each other.  Indeed with X-ray crystallography we can quantitatively determine the structure of crystals at the atomic scale.

7. Atomic Microscopy

Technology has progressed to the point where we can actually take pictures of a sort of atoms.  In 1980 the first picture was taken of an individual atom.  The kind of microscope used is of course not a normal microscope, but it operates on exactly the same type of principles.  Today imaging atoms is routine.