Atoms and Atomic Structure
Created | Updated Nov 20, 2007
From a practical point of view, everything in the universe is made of atoms. There are atoms in the air and in anything you can see or feel. Essentially, anything large enough to count as 'substance' of any kind is made up of atoms. Atoms are the smallest parts that 'substance' can be broken down into by chemical reactions.
It is easy to think that the atomic structure of matter is a relatively new theory. However, a surprisingly modern view of atoms was proposed in the 5th Century BC by the Greek philosopher Leucippus and was elaborated on some 30 years later by his student Democritus. They proposed that all matter consisted of tiny particles or atomos (Gk 'uncuttable', 'indivisible') between which was complete emptiness. The atoms of each substance had a different shape, and particles could combine in ways determined by their shapes.
This Greek insight stalled some years later when Aristotle extended an earlier idea of Empedocles': that all matter was composed of just four elements: earth, air, fire and water. Aristotle suggested that these four elements could be interconverted. The heavens were considered to be made up of 'aether'. Indeed, because of Aristotle's great influence, this erroneous idea held back our understanding of chemistry for over 1000 years, until the so-called 'golden age of Arabic Science' in the 8th - 11th Centuries.
Despite this, the Roman poet Lucretius was still suggesting that matter existed in the form of invisible particles in his poem 'On the Nature of the Universe', written in about 60 BC.
The Atomic Theory of Matter
It was not until the early 19th Century that anybody1 actually demonstrated that matter is composed of atoms. John Dalton also put forward the theory that chemical elements differ from each other because they consist of different types of atoms. He argued that the elements could not be broken down into anything simpler by chemical methods. Dalton also showed that different atoms differed in their masses: iron atoms are heavier than hydrogen atoms, oxygen atoms heavier than hydrogen, and so on.
Dalton had another important idea. He suggested that atoms of the same or different elements could combine to produce larger structures. Identical atoms combine to give an element and a combination of different atoms, in very precise ratios, produce 'compound atoms', later to be known as molecules and compounds. The properties of compounds are very different from those of the atoms from which they are formed.
Dalton also showed that it was possible to determine the relative masses of different atoms and by 1816, William Prout, a young physician and biochemist, had proposed that the masses of all atoms were whole numbers and, indeed, whole-number multiples of the mass of hydrogen — the simplest atom. Indeed, he thought that all atoms were aggregates of hydrogen. This model foundered somewhat when, as chemical techniques improved, the number of atoms with reliable non-integral atomic masses accumulated. For example, chlorine was discovered to have a mass of around 35.5, although the reason for this is now understood (see below).
A strength of Dalton's work was his emphasis on measurement2. His results match and explain the observations we make in practical chemistry today. Dalton's ideas, taken together, are known as the atomic theory of matter.
The Periodic Table of the Elements
In 1869, Dmitri Mendeleev published a short article called 'The Correlation Between Properties of Elements and their Atomic Weights'3. This documented how the properties of the known elements seemed to vary in a regular cycle in accordance with their relative atomic masses4. This arrangement was eventually developed into the modern 'Periodic Table of Elements' and was the first indication of an emerging pattern on the sub-atomic scale. How the sub-atomic particles are arranged within the atoms is the key to this.
Models of Atomic Structure
Once Dalton's model had been proposed, evidence began to accumulate that suggested that individual atoms have a sub-structure. Indeed, only a little over 100 years ago, scientists still believed that atoms were solid, indestructible particles, like microscopic billiard balls.
The Electron
Of peripheral relevance is Faraday's discovery of current electricity in the early 19th Century. After this, in 1874, GJ Stoney realised that Faraday's experiments could be explained in terms of tiny negatively charged particles, which make up an electric current. He suggested the name of 'electron' for these particles (from the Greek word elektron, meaning amber).
Eugen Goldstein
Following this, in 1876, the German physicist Eugen Goldstein was investigating what would happen if an electrical discharge is passed through a gas held at very low pressure in a sealed tube. He found that:
A beam (which he termed a 'cathode ray') was attracted towards the positive electrode (anode);
An object placed in the path of the cathode ray cast a shadow;
A magnetic field deflected the rays by an amount that depended on the strength of the magnetic field. (A magnetic field will only deflect particles if they have both mass and an electrical charge.)
From this basis, Goldstein was able to conclude that:
(a) The original gas particles were being split into smaller particles;
(b) These smaller particles had mass; and
(c) The particles in the ray were negatively charged.
Goldstein followed this up by placing a perforated cathode partway down the discharge tube and found that some rays, which he called 'canal rays', streamed through the holes in the cathode in a direction away from the anode. Compared to the cathode rays, these beams were less deflected by the magnetic field. From this, Goldstein was able to conclude that, as well as negatively-charged particles, the discharge also produced particles that were positively-charged and were more massive than the cathode ray particles.
Subsequent work on various gases showed that the values for the masses of the positive fragments varied from one gas to another, the smallest value being for hydrogen.
Goldstein naturally made the link between his negatively charged rays/particles and the electrons described by Stoney.
JJ Thomson (1897)
Firm evidence for the existence of electrons came in 1897 when JJ Thomson, working at the Cavendish Laboratory in Cambridge, repeated Goldstein's experiments, but using more sophisticated discharge tubes. Indeed, Thomson's equipment was the ancestor of the modern cathode ray tube. Thomson measured the deflections of the negatively-charged particles very accurately and worked out that they had almost negligible mass. Indeed, he later observed that these particles, which he also identified as electrons, were 1840 times lighter than hydrogen atoms.
Thomson obtained exactly the same results for a variety of gases, which suggested to him that electrons were a constituent of the atoms of all substances. This led him to propose a model of the atom (later known as the 'plum-pudding model') where the electrons were embedded in a sphere of dispersed positively-charged material that made up most of the atom's mass. This was the earliest model of atomic structure; since then the model has become more and more refined.
The Nucleus
Rutherford's Planetary Model, 1911
In the meantime, Ernest Rutherford had been working as one of Thomson's research students at Cambridge, where he was investigating X-rays. He had found two types of rays in X-radiation, which he named 'alpha' rays and 'beta' rays. He demonstrated that they had mass and therefore were particles. The alpha particles were exactly four times heavier than hydrogen and were positively charged. This suggested to him that they could be fundamental particles in atoms. The alpha particle later turned out to be helium nuclei: helium atoms that have lost their two electrons.
Rutherford moved on to Manchester University and there gathered evidence that Thomson's model of electrons embedded in a sphere of positive charge was not correct. He fired alpha particles at very thin sheets of gold foil which were only a few atoms thick and encased in an evacuated bulb. He had predicted that the high energy alpha particles would pass straight through the dispersed positive and negative charges of Thomson's 'plum-pudding' model with, perhaps, slight deflections as the alpha particles collided with individual positively charged particles in the foil atoms. To his astonishment, although most particles did pass straight through, about one in every 10,000 was reflected back from the foil. He later was to recall:
It was the most incredible event that has ever happened in my life. It was almost as incredible as if you fired a fifteen inch shell at a piece of tissue paper, and it came back and hit you.
Rutherford's explanation for this was that, rather than being like a plum pudding, the atom had all its positive charge densely concentrated in the centre (which he called the nucleus). The electrons circulated around the outside, kept apart by mutual repulsion of their negative charges. This was the 'planetary model', in which the positive charge was the 'sun' and the electrons orbited like 'planets' round the outside.
From the angles through which the alpha-particles were deflected, Rutherford calculated that the nucleus of a gold atom would have a radius of about 10-14m, whereas that of the whole atom is about 10-10m; ie the nucleus is about ten thousand times smaller than the atom itself. This led Rutherford and his co-workers to compare the ratio of the nucleus to the whole atom with the size of a fly in a cathedral, which provides an explanation of the fact that so few alpha particles rebounded from the gold foil.
Geiger and Marsden
Geiger and Marsden, working under Rutherford's guidance at Manchester University, explored the nuclei of atoms further by firing alpha particles at thin metal foils. They were able to show that the number of positive charges in the nucleus of an atom was about half its relative atomic mass. At about the same time, it was observed that the number of positive charges in the nucleus, which was given the symbol Z, was equal to the atom's numerical position in the periodic table. Thus, Z, which hitherto had been believed to have no more significance than being the atom's position in the periodic table, was found to be fundamental to the properties of the atom. Z is now known as the atomic number, representing:
- The number of protons in the nucleus
- The number of electrons in a neutral atom
- The element's position on the periodic table
The Discovery of the Neutron (1932)
Despite the successes of Rutherford's team, there was still a major problem to be explained: if the hydrogen atom contains one proton and the helium atom contains two protons, then why is the helium atom four times heavier than the hydrogen atom? In 1932, James Chadwick, another collaborator with Rutherford, was able to show that beryllium atoms contain uncharged particles, which he called neutrons. In fact, the existence of such particles had been predicted by Rutherford some years earlier.
The now-proven neutron provided a very useful particle for further probing the structure of the atomic nucleus. As it is a neutral particle, it would not be repelled by the positive charges within the nucleus, as protons were.
Albert Einstein — Direct Evidence for the Existence of Atoms
Incredible though it might seem to us now, at the end of the 19th Century, despite Dalton's work and all the evidence accumulating in favour of the sub-structure of atoms, there were still some eminent scientists who questioned whether atoms or molecules existed at all. Prominent among these were Wilhelm Ostwald and Ernst Mach. Although this disbelief is probably incomprehensible to us now, it has to be remembered that at this time there was not a single shred of direct evidence for the existence of atoms. Mach maintained that it was poor science if one could not directly perceive entities whose existence was postulated. Einstein, however, did believe in atoms and so set about obtaining some form of evidence 'which would guarantee as much as possible the existence of atoms of a finite size'.
Einstein saw that such evidence might be provided by Brownian motion, a phenomenon first described by the botanist Robert Brown in the 1820s.
Brown was carrying out a study of pollen grains, and believed that he would be able to observe them more effectively through his microscope if they were suspended in water. To his amazement (and annoyance!) he found that the grains darted erratically and randomly in the water. At first, Brown ascribed this to some manifestation of the 'vital force' with which many still believed all organic matter to be imbued. However, he soon discovered that 'dead' particles behaved in exactly the same manner.
His observations led to all kinds of theories invoking such influences as convection currents and electricity, yet none seemed entirely convincing.
Einstein's approach to solving the problem drew on his interest in molecular diffusion, which occurs as a result of the kinetic theory of gases. A central assumption of the kinetic theory, incidentally, is that matter is made up of atoms and molecules; it assumes that heat is the result of random molecular motions. It had previously been argued that, even thought these motions involved very high velocities, suspended particles such as dust or pollen were sufficiently massive that impact by an individual molecule would be totally insignificant, much like trying to deflect the path of the Earth with a meteorite.
However, Einstein was able to calculate that a statistical imbalance in the number of molecules striking a micrometre-sized particle from different directions would indeed make the particle move. Thus, the erratic movements of pollen grains could be due to the thermal motion of water molecules. Einstein argued that, if one tracked the random motion of a particle over a period of time, the particle would end up somewhere different than where it started. He calculated a 'mean square displacement' as a function of time and was thus able to predict that a one-micron particle would travel about six microns in one minute.
If it could be shown that this quantitative prediction was borne out experimentally, then this would be irrefutable evidence for the existence of molecules.
Many researchers attempted to perform this experiment, but a major constraint was in trying to ensure a constant uniform temperature throughout the liquid. After several years, people began to despair of it being possible to measure Brownian motion so precisely. However, in 1908, the French physicist Jean-Baptiste Perrin was successful, thus confirming Einstein's theory and providing direct proof of the existence of atoms and molecules. For this work, Perrin received the 1926 Nobel Prize for Physics.
The Rutherford-Bohr Model
Returning to the electronic structure of atoms, there were a number of problems with Rutherford's planetary model. Classical mechanics predicted that, in such a model, orbital electrons would gradually spiral into the nucleus, emitting 'white radiation', unless energy was supplied. Such an atom would be intrinsically unstable — and is not what is observed.
A further observation was that, if light from a hydrogen discharge tube is passed through a prism spectrometer, the spectrum is seen to consist of only four lines, meaning that the light consists of only four discrete wavelengths. This cannot really be explained by a model in which the electron gradually spirals into the nucleus.
In 1913, Niels Bohr modified Rutherford's model by integrating the newly emerging 'quantum theory' of Max Planck . Bohr suggested, therefore, that the orbital electrons could possess only certain energies. In other words, the energy of the electron is quantised.
A number of key features characterised this model:
The extranuclear electrons could only occupy certain energy levels (known as orbits) or shells. The electrons in each shell all have the same level of energy. These shells are all at fixed distances, known as the Bohr radius.
Only certain values of Bohr radii are permitted. This means that only certain energy levels are allowed. In such energy levels, an electron can have acceleration and yet not radiate energy. By allowing only certain orbits to contain electrons, Bohr was able to sidestep the classical view that electrons would lose energy and spiral inwards. Instead, radiation with a specific energy would be lost or gained when the orbit changed.
Each shell is assigned a principal quantum number, n. For example, for the shell closest to the nucleus, n=1, for the next, n=2, for the third, n=3 and so on. The higher the value of n, the higher the energy of the electron.
In order to change from one orbit E1 to another E2, the electron must gain or lose an amount of energy which is precisely equal to the difference in energy (symbolised by (ΔE) between the two levels:
ΔE = E2 - E1
and ΔE = hv (where h = Planck's constant and v = frequency of EM radiation).
Each shell can only accommodate a fixed number of electrons. For example, the first shell can contain a maximum of two electrons; the second, a maximum of eight. The total number of electrons permitted in each shell is 2n2.
Electrons occupy the lowest possible energy levels. This means that, as electrons are added to an atom, the lowest-energy level shells are filled first.
Later, further quantum numbers were proposed, principally by Arnold Sommerfeld, to explain the details observed in the spectra of the known elements. These were 'l', which could take any value between 0 and n-1, and 'm', which could take any value from +l to -l. These correspond to the various possible shapes of non-spherical orbits around the atom. Finally, each electron had a 'spin', which represented the two directions in which an electron could be spinning around its own axis5.
The various combinations of these quantum numbers can be used to explain a great deal about the periodic table and the properties of the elements. For example, when n=1, l and m can only be 0 and the spin can be up or down, so there are only two possibilities. These correspond to the two elements in the first period of the periodic table — hydrogen with one electron and helium with two.
The question still remained, however: why do these electrons stay in their discrete orbits rather than spiralling inwards? The answer to this came in 1923, when de Broglie suggested that electrons could show wave particle duality, like light. Within a few years, wave mechanics had been developed, principally by the Austrian physicist Irwin Schrödinger. This described the various 'orbits' of the electrons as solutions to a wave-equation. Each orbital, as they are known, was a solution giving a stationary 'wave' of electrons around the nucleus. These orbitals confined the electrons into various regions without requiring them to move and so removed the conflict. One solution to this wave equation was provided by each combination of quantum numbers giving various shells of orbitals6.
The Size of Atoms
Like many other things in science, we don't exactly know what an atom is like; even the most powerful electron microscopes cannot see things of atomic size. The best science can usually do is say, 'Well, here is a model of how we think it is — it predicts many of the properties we observe; but who knows, there may be details we don't yet understand'. Some of the models that have been proposed have been reviewed above, but our understanding will continue to evolve.
The key thing about atoms is that they are very, very small. So small, in fact, that a line of hydrogen atoms one centimetre long would contain about 333 million atoms. Unlike Democritus, we now believe that there are several hundred types of atom7, forming the 110 currently-known chemical elements. Because atoms are so small, a massive number of them would be required in order to make anything useful. Indeed, a glass of water (360cm3) contains some 12.0 x 1024 oxygen atoms and twice that number of hydrogen atoms!
Fast-forward to the 20th Century, when the Scanning Probe Microscope was invented, which enables us to 'see' and measure individual atoms.
What are atoms made of?
We now know that atoms themselves are made up of three simpler sub-atomic particles: protons, neutrons and electrons. Their properties are summarised in the table below:
| Particle | Relative Mass | Relative Charge |
|---|---|---|
| Proton | 1 | +1 |
| Neutron | 1 | 0 |
| Electron | 1/1846 | -1 |
As can be seen, the mass of an atom resides almost entirely in the nucleus, which consists of protons and neutrons, known collectively as nucleons.
In a normal, stable atom, the number of electrons is equal to the number of protons and so the charges balance out. The net charge on the atom is zero, and so the atom is electrically neutral. Furthermore, the number and arrangement of the electrons in an atom determines its chemical properties.
The number of protons in an atom is called its 'atomic number', Z, and the total of the protons and neutrons together is called the 'atomic mass' or 'mass number', A.
A grouping of atoms of a specific atomic number is known as an element. The name 'element' derives from the fact that atoms were thought to be the elementary building blocks of matter.
The Role of the Neutrons
Clearly, it is possible to have an element containing a specific number of protons but a variable number of neutrons. This would create the same element, but its atoms would be heavier or lighter (same atomic number, different atomic mass).
The neutrons act as a kind of 'nuclear glue' to bind the positively-charged, and therefore mutually repelling, protons together. If it were not for the neutrons, atoms would be intrinsically unstable and would spontaneously fly apart, even if they were formed. For the lighter elements, it is seen that the protons and neutrons of the stable elements are in the ratio 1:1, but as the atoms get heavier progressively more neutrons are required to maintain stability.
Isotopes
Atoms having the same numbers of protons but different numbers of neutrons are said to be 'isotopes'. Isotopes may also be described as atoms having the same atomic number but different mass numbers.
For reasons that are somewhat complicated, only a certain proportion of neutrons to protons tends to be stable and so there are only a few stable isotopes of each element. The less stable ones are radioactive and break up (decay) into smaller particles. Atoms that are really unstable just don't stick around long enough to be measured.
Now consider hydrogen. This exists as three isotopes: 1H (protium), 2H (deuterium) and 3H (tritium). The most abundant isotope is protium (1H), and this makes up 99% of the natural hydrogen on earth. It has one proton and no neutrons and so its relative atomic mass is 1 (from the table above).
Let's return to the problem of chlorine. Recall that this element was found to have a relative atomic mass of 35.5, and yet, according to Prout, its mass should be a simple multiple of the mass of the hydrogen atom (=1). The anomaly is due to the fact that natural chlorine is a mixture of two isotopes, one with 18 neutrons and one with 20 neutrons. (Both isotopes, of course, have an equal number of protons, 17, and so the mass numbers are 35 and 37 respectively). There is approximately three times as much chlorine-35 as there is chlorine-37, so the average mass of a natural sample turns out to be 35.5.
Most elements have isotopes, and the proportion of isotopes in a particular element is always the same. For example, chlorine consists of 75.4% of 35Cl and 24.6% of 37Cl, thus giving a relative atomic mass of 35.5. It is the existence of isotopes which accounts for the fact that relative atomic masses are rarely whole numbers.
The relative atomic mass of an element is the 'weighted mean' of the mass numbers of its isotopes. Thus, for chlorine:
Relative Atomic Mass = (75.4 x 35 + 24.6 x 37)/100
= 35.49
The Structure of the Nucleus
Nuclear Forces
The largest element known to date is element 111 (roentgenium), reported in 1994. How does the nucleus of an atom containing around 100 positive charges hold itself together8? Why does the electrical repulsion among all those positive charges not cause the nucleus to fly apart? The answer is that there must be some sort of attractive force which is strong enough to overcome the enormous repulsive coulombic forces acting between protons. This attractive force is over a hundred times greater than the repulsive force acting between any pair of nucleons (protons or neutrons). This attractive force, unique to the nucleus, acts only at very short range (not more than 10-15 metres).
The operation of the attractive force between nucleons is explained in terms of particles called mesons. The theory, first suggested in 1935 by the Japanese physicist Yukawa, proposes that the interacting protons and neutrons are linked by passing the mesons to and fro between them.
So, how big are the nuclear forces?
A measure of the strength of the nuclear forces is given by the 'nuclear binding energy', which is the amount of energy that would be needed to break the nucleus up into its constituent particles. This can be calculated from what is called the 'mass defect' of the nucleus. (The rest mass of the nucleus is always slightly less than the sum of the masses of its constituent nucleons.) The loss of mass is accounted for by the concept of mass-energy equivalence — part of Einstein's Theory of Relativity. Thus, the mass defect corresponds to the energy which would be liberated if a nucleus were formed from protons and neutrons and which would have to be supplied to break the nucleus up into these particles. The quantity of binding energy is given by multiplying the mass defect by the square of the speed of light, which is an enormous figure!
Models of the Nucleus
A detailed description of nuclear structure is beyond the scope of this entry. Suffice it to say that there are four major models that attempt to account for the properties of the nucleus and each model is quite good at describing certain specific behaviours of the atomic nucleus, but none describes all of them adequately. The models include:
- The Liquid Drop Model
- The Shell Model, which emphasizes the orbits of individual nucleons in the nucleus
- The Collective Model, which complements the shell model by including motions of the whole nucleus, such as rotations and vibrations
- The Face-Centred Cubic Model
The Liquid Drop Model treats the nucleus as a liquid. Although the nucleons are held so closely, they are continuously moving around as though in a drop of liquid. The nucleus is considered to have such properties as surface tension and compressibility, which are normally associated with liquids. This model has found success in describing how a nucleus can deform and undergo fission9.
The Nuclear Shell Model is based on the electronic shell model, where electrons arrange themselves into shells around the nucleus. Here, the least-tightly-bound electrons (those in the incomplete shells) are known as valence electrons because they can participate in exchange or rearrangement — that is, chemical reactions. Electrons, protons and neutrons are a type of particle known as fermions and can occupy particular energy levels as further nucleons are added to the nucleus. Protons and neutrons occupy different energy levels. This model has been very successful in explaining the basic nuclear properties such as angular momentum, magnetic moment and shape. As with the electronic shell model of the whole atom, these properties are dictated by the last filled or unfilled energy level.
The Collective Model emphasises the collective, coherent behaviour of all of the nucleons, such as rotations or vibrations that involve the entire nucleus. Hence, the nuclear properties can be analysed in the same way that the properties of a charged drop of liquid suspended in space can be investigated. This model is therefore an extension of the Liquid Drop Model and is very useful for describing nuclear fission.
In addition to fission, the Collective Model has been successful in describing the properties of nuclei containing even numbers of protons and neutrons. Such even nuclei can often be treated as having no valence particles, to which the Shell Model is not applicable.
The nuclear models described so far have the nucleus assume either a gas phase or a liquid phase. Although each of these models is able to successfully describe certain selected properties of the nuclei, none of them is able to give a comprehensive description. Hence, researchers turned to the last remaining phase of matter — the solid — in the hope that this would give a more complete description of the nucleus.
The Face-Centred Crystal (FCC) Model — The common assumptions regarding the solid phase models developed so far are that the protons and the neutrons have the same size and are arranged alternately in a close-packing crystal structure. These assumptions are reasonable, as the radii of protons and neutrons differ only slightly and the equal diameter spheres would most likely utilise the available space in the most efficient manner, which is a close-packing arrangement.
Of the various possibilities, the FCC arrangement has been found to give the best correspondence between the nuclear properties and the lattice parameters and is consistent with the various shell, liquid-drop and collective properties. Phenomena such as asymmetric nuclear fission, which the traditional models of nuclear structure theory cannot explain, can also be reproduced by the FCC lattice model.
Endpiece
The author discovered the following poem while doing a piece of work at the RISØ National Laboratory, Roskilde, Denmark. It was in a publication called Faust and Journal of Jocular Physics, Vols I, II and III, which stated that it had been reprinted on the occasion of Niels Bohr's centenary on 7 October, 1985. This seemed to be the Danish equivalent of a student 'rag magazine', but this Researcher feels that it deserves a wider audience:
The Atom that Bohr Built
With apologies to 'Jack' from Bohr's colleague, Professor Sir Rudolph E Peierls, FRS, CBE (1907 - 1995), who prepared this verse for the occasion of Bohr's 70th birthday celebration.
This is the atom that Bohr built
This is the nucleus
That sits in the atom
That Bohr built
This is the drop10
That looks like the nucleus
That sits in the atom
That Bohr built
These are the nodes
That belong to the drop
That looks like the nucleus
That sits in the atom
That Bohr built
This is the spectrum
That's due to the nodes
That belong to the drop
That looks like the nucleus
That sits in the atom
That Bohr built
These are the compound levels11 galore
That make up the spectrum
That's due to the nodes
That belong to the drop
That looks like the nucleus
That sits in the atom
That Bohr built
This is the shell and this is the core
That possess the compound levels galore
That make up the spectrum
That's due to the nodes
That belong to the drop
That looks like the nucleus
That sits in the atom
That Bohr built
This is correspondence (as Bohr said before)
That holds in the shell, as well as the core
That possesses the compound levels galore
That make up the spectrum
That's due to the nodes
That belong to the drop
That looks like the nucleus
That sits in the atom
That Bohr built
This is the complementarity law12
That gives correspondence (as Bohr said before)
That holds in the shell, as well as the core
That possesses the compound levels galore
That make up the spectrum
That's due to the nodes
That belong to the drop
That looks like the nucleus
That sits in the atom
That Bohr built
This is the day we celebrate Bohr
Who gave us the complementarity law
That gives correspondence (as Bohr said before)
That holds in the shell, as well as the core
That possesses the compound levels galore
That make up the spectrum
That's due to the nodes
That belong to the drop
That looks like the nucleus
That sits in the atom
That Bohr built
