How Do We See the Hidden Structure of Atoms?

Structure of the atom

History and discovery of the atom

Everything we see is made up of atoms, lots of atoms from the Greek word "atomos" (indivisible). Long ago, in the 4th century BC, the Greek philosophers Leucippus and Democritus put forward the hypothesis that all matter is composed of tiny particles in perpetual motion, very solid and eternal. Today we have a slightly more precise idea of the atom, because it is not indivisible.

Its approximate size has been known since 1811, when Amedeo Avogadro estimated the size of atoms to be 10^-10 metre. In 1911, Ernest Rutherford refined the structure of the atom and gave the atomic nucleus a size of around 10^-14 metre.

Size, mass and composition of the atom

As for the size of atoms, we speak of atomic orbitals, i.e. the electron cloud surrounding the nucleus. This cloud has a theoretical diameter ranging from 62 pm (picometres) for the helium atom to 596 pm for the caesium atom. Nothing is simple in the nature of matter, and this tiny distance varies according to the chemical nature of the surrounding atoms.

Although the nucleus contains most of the mass of the atom (99.99%), its mass is also known; for stable atoms, it ranges from 1.674×10^-24 g for hydrogen to 3.953×10^-22 g for uranium.

Its composition is also known: inside we see a nucleus and an electron cloud that occupies the entire spatial extent of the atom, since it is about 100,000 times larger than its nucleus. Even more astonishing, we even know, to an order of magnitude, the number of atoms in the observable universe: it is estimated at about 10⁸⁰, i.e. a 1 followed by 80 zeros — a value obtained by combining the estimated number of stars (about 10²³) and their average mass converted into an equivalent number of hydrogen atoms.

The stability of atoms

The paradox of classical physics

The stability of the atom cannot be explained by classical physics, because in classical physics, the electron particle, negatively charged, and the proton, positively charged, raise a paradox.

In classical physics, matter should disappear, annihilate itself, because an electron radiating around a nucleus loses energy (Maxwell's theory) and should therefore fall onto the nucleus. This means that the stability of an atom is incomprehensible within the framework of classical theory.

The solution of quantum mechanics

The scientific geniuses of the 20th century resolved this paradox in 1924, thanks to the wave mechanics of Louis de Broglie (1892-1987), generalised in 1926 by Erwin Schrödinger (1887-1961), Nobel Prize in Physics in 1933 with Paul Dirac (1902-1984), for the wave equation called the Schrödinger equation.

In quantum mechanics, it is not possible to know exactly the value of a parameter without measuring it. The mathematical theory describes a state not by a precise pair of velocity and position, but by a wave function (state vector), which allows the probability of finding the particle at a given point to be calculated. Hence the probabilistic nature of quantum mechanics, which predicts that particles are also waves and no longer just material points.

Orbitals and chemical bonds

Electrons occupy atomic orbitals in interaction with the nucleus via the electromagnetic force, while nucleons are held together within the nucleus by the nuclear bond.

The electron cloud is stratified into quantised energy levels around the nucleus, defining electron shells and subshells. Nucleons are also distributed in nuclear shells, although a fairly convenient model popularises the nuclear structure based on the liquid drop model.

Several atoms can form chemical bonds with each other through their electrons, and in general, the chemical properties of atoms are determined by their electronic configuration, which follows from the number of protons in their nucleus. This number, called the atomic number, defines a chemical element.

Visible gold atoms

Observation of gold atoms by scanning tunnelling microscope

At the closest to matter, the surface of a sheet of pure gold (Au 100) is detailed here by a scanning tunnelling microscope. The gold atoms visible in this image are regularly spaced on the crystalline structure of gold. This atomic image was obtained with a low-temperature Omicron STM by Erwin Rossen, Eindhoven University of Technology, in 2006.

IBM's historic feat: writing with atoms

Seeing atoms is one thing; moving them one by one is another. This is what physicists Donald Eigler and Erhard Schweizer from the IBM Almaden Research Center in California demonstrated in November 1989. Using the tip of a scanning tunnelling microscope as an atomic tweezer, they moved one by one 35 xenon atoms on a nickel surface cooled to 4 kelvins (i.e. -269°C) to form the three letters "IBM". The painstaking operation took about 22 hours. The logo obtained measured only 5 nanometres high by 17 nanometres wide — about 500,000 times smaller than ordinary printed letters. Published in 1990 in the journal Nature, this image has become emblematic of the birth of nanoscience: it proved that the scanning tunnelling microscope could not only observe atoms, but also manipulate them and literally build with the most elementary matter there is. This atom-by-atom manipulation technique remains a laboratory tool rather than an industrial manufacturing process, because the required conditions (high vacuum, near absolute zero temperature) are too restrictive for mass production.

Beyond STM: atomic force microscopy and recent advances

The scanning tunnelling microscope (STM) has a limitation: it requires a conductive surface, because it measures a current of electrons that "tunnel" between the tip and the sample. To study insulating materials or individual molecules, researchers use a complementary technique developed in 1986: atomic force microscopy (AFM), which measures not a current but the interaction force between an ultrafine tip and the atoms on the surface, allowing virtually any material to be probed.

Since the mid-2010s, these techniques have made a leap forward. In 2023, a research team used AFM to directly observe the signature of electron orbitals of single metal atoms within organic molecules, a feat that confirms, at the scale of a single atom, the shapes predicted for a century by the Schrödinger equation. The same year, another team developed a technique based on scanning transmission electron microscopy (STEM) capable of mapping electron density at the atomic scale in two-dimensional materials. These measurements remain indirect — we do not "photograph" an electron as an ordinary object — but they bring theoretical quantum physics a little closer to direct observation every year.

Size of atoms

Atomic radii of elements

Theoretical (calculated) atomic radius of some atoms (size in picometres (10^-12 metre). The atomic radius is half the distance between the nuclei of two adjacent atoms. The values given in this table are indicative only.