reified abstract mathematical concepts.
In summary, electromagnetic radiation was found to have evidential wave-like properties, but also evidential particle properties.
Meanwhile, the construction of matter on its smallest scale was investigated in various laboratories. Ernest Rutherford did a 'golden' discovery.
Ernest Rutherford's model of the atom
During experiments with cathode rays in vacuum glass tubes, the precursors of the once ubiquitous but nowadays outdated TV display tube, John Joseph Thomson (1856-1940) sent these rays through an electric or a magnetic field - figure 4.4 - and noticed that they were deflected by those fields. He deduced from this deflection that these rays had to be composed of negatively charged particles. Thomson dubbed these particles electrons. He assumed that these electrons were normally positioned within the atoms that made up matter and that an atom was a positively charged solid little ball with the negative electrons scattered through it, like currants in a plum pudding.
Figure 4.4: Vacuum tube for cathode ray deflection by an electric field measurement. Plates D and E are electrically opposite charged.
Source: J.J. Thomson - Philosophical Magazine 1897.
Concerning his "plum pudding" model Thomson apparently did not realize that, because of their mutual repulsion, all electrons should be evenly distributed on the outside of the atom, each as far away as possible from the others. Also, the magnitude of the electric charge of the electron was still unknown at time of Thomson's discovery. The electron charge was later determined by Millikan [10] by measuring microscopically the velocities of charged slowly falling oil droplets, a beautiful sophisticated laboratory experiment.
However, experiments [11] conducted under supervision of Ernest Rutherford [12] (1871-1937) revealed that electrons probably formed the outer 'hard' shell of the atom with an almost totally empty void inside. The only exception to that emptiness inside was an utter tiny positive mass - the nucleus - positioned in the centre. The positive charge of this nucleus had to be equal to the sum of the negative electron charges in order to have a neutral atom.
In 1908 Rutherford's assistants Marsden and Geiger [13] directed positive charged and fast moving alpha particles, ejected at high velocity from a radioactive source (radium), at a gold foil. As Rutherford already suspected, these alpha particles turned out to be helium nuclei, consisting of two protons and two neutrons. Gold can be beaten to an ultrathin foil [14] of less than 1 nm thickness (1 nanometer = 0.000000001 m) but Marsden and Geiger used a gold foil of around 210 nm thick [15] in their experiment.
A gold atom has a diameter of 0.3 nm, so such an ultrathin gold foil will still be around 800 atoms thick when we assume closely packed spheres. From the perspective of these utter tiny alpha particles, the gold foil should therefore be experienced as an impressive solid 800 gold atoms thick wall. According to the "plum pudding" atom model from Thomson such a solid wall should present a major obstacle for the little alpha particles. However, the experimental result turned out quite contrary to expectations.
Figure 4.5: Shooting of alpha particles from a radioactive source through an ultrathin gold foil. Only 1:8,000 particles will be deflected.
Almost all alpha particles went straight through the foil as if that solid wall of 800 heavy gold atoms thick did not exist at all. Out of 8,000 alpha particles, an average of 1 was deflected and sometimes even fully bounced back over 180o. These numbers were measured by counting the little light flashes made by the alpha particles when hitting an along a circular rail movable, zinc-sulfide screen. Rutherford assumed that those rare deflections were actually near-collisions of positive alpha particles with the incredibly small positive atomic nuclei. He is said to have exclaimed:
"It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."
Rutherford concluded that the atom had to consist of negatively charged electrons orbiting around a very small and positive nucleus. The inside of an atom was a virtually empty space. He was able to calculate from the ratio of the deflected alpha particles against the not deflected ones - 1:7999 - that the ratio of the small nucleus to the size of the electron shell should measure approximately 1: 10,000 to 20,000. An image emerged of atoms as miniature solar systems with minuscule negatively charged electrons, orbiting at high speed around the positively charged nuclei like tiny satellites. To get an impression of the proportions: the ratio of the nucleus to electron shell can be compared with the ratio of a fruit fly of 2 to 4 mm to the dome of St. Peter's in Rome. Take a moment to visualize that image of a fruit fly circling in the middle of that dome. So, 99.999999999% of the atom is just empty space, nothing. The solidity of matter now really began to look like an illusion. But even still stranger views were soon to come.
The reason why we do not sink through a floor consisting of these ephemeral atoms, which we now know is mainly empty space, has to do with the Pauli exclusion principle [16], discovered by Wolfgang Pauli (1900-1958). This principle prohibits electrons from having the same position in space when all their quantum properties have equal values. These properties are connected to the four quantum numbers that describe the quantum state of the electron. One of them is the electron spin.
The electron spin is the quantum version of the north-south orientation of a magnet. It was discovered in 1925 by two Dutch PhD students - George Uhlenbeck (1900-1988) and Samuel Goudsmit (1902-1978). For their discovery of the electron spin they were awarded in 1964 the Max Planck medal. The electrons in the outer shells of the atoms of our hand repel the electrons from the outer shells of the atoms of the wall, and vice versa. Their absolute refusal to have the same position in space, when their quantum numbers are the same, prevents us putting our hand through a wall, where both hand and wall are in fact almost entirely made up of empty space. The electrons of these atoms repel each other, the nearer to each other the stronger. So, in fact, we don't even touch the wall even though we hit it really hard.
From Rutherford comes the parable of the two desks. One desk is solid and exists in the solid world of our daily experience, the other is mostly empty space, ghostly and exists in the world of physical ideas. Which desk would be the real one? What is your opinion?
The solar system model of the atom is impossible
The classic model of electrons as little charged balls circling around a positive core encountered serious problems:
Why are the orbits
