Lecture

What does atomic physics study?

All matter — air, water, the human body, the stars — is made of atoms. Why are atoms stable? Why does each element emit light only of its own characteristic colours? Why does copper conduct electric current well while glass does not? The science that answers these questions is atomic physics.

Atomic physics is the branch of physics that studies the structure and properties of atoms and molecules, their interaction with electromagnetic radiation and with each other, and the quantum laws that govern these phenomena.

Atomic physics is the birthplace of quantum mechanics and the theoretical basis of chemistry, solid-state physics, astrophysics, laser technology and electronics. Nuclear physics (the nucleus at the centre of the atom) and particle physics grew out of it.

Stages in the development of atomism

1. Natural-philosophical atomism

In the 5th century BC Leucippus and Democritus put forward the idea that matter consists of indivisible particles — atoms (Greek "atomos", indivisible) — and void. Epicurus and Lucretius developed this doctrine. Scholars of Central Asia, including Abu Rayhan Biruni in his correspondence with Ibn Sina, discussed the divisibility of matter. However, at that time ideas did not rely on experiment.

2. Chemical and kinetic atomism (18th–19th centuries)

• J. Dalton (1808) — using the law of multiple proportions, showed that each element consists of atoms of a definite mass.
• A. Avogadro (1811) — equal volumes of gases under the same conditions contain equal numbers of molecules.
• D. I. Mendeleev (1869) — the periodic law of the elements.
• Clausius, Maxwell, Boltzmann — the molecular-kinetic theory; Einstein (1905) and Perrin (1908) measured $N_A$ from Brownian motion and rigorously proved the existence of atoms.
• M. Faraday (1833) — the laws of electrolysis pointed to the discreteness of electric charge: $F = N_A e$.

3. Discovery of the internal structure of the atom (1895–1913)

• 1895 — X-rays; 1896 — Becquerel discovered radioactivity.
• 1897 — J. J. Thomson measured the specific charge $e/m$ of cathode rays and discovered the electron.
• 1900 — M. Planck introduced the energy quantum $\varepsilon = h\nu$ to explain thermal radiation.
• 1905 — A. Einstein explained the photoelectric effect using light quanta (photons).
• 1909–1913 — R. Millikan measured the elementary charge $e$ accurately by the oil-drop method.
• 1911 — E. Rutherford proposed the nuclear model of the atom from alpha-particle scattering.
• 1913 — N. Bohr created the quantum theory of the hydrogen atom.

4. The era of quantum mechanics (1924 to the present)

De Broglie (1924) proposed the wave properties of particles; Heisenberg (1925) and Schrödinger (1926) created quantum mechanics; the Pauli principle (1925) and electron spin (Uhlenbeck and Goudsmit, 1925) explained the periodic table; Dirac (1928) found the relativistic equation. From the mid-20th century came quantum electrodynamics, lasers (1960), atomic clocks, laser cooling and the Bose–Einstein condensate (1995).

Scales of the microworld

To describe microworld phenomena one must first know the orders of magnitude. The size of an atom can be estimated from the density $\rho$, the molar mass $M$ and the Avogadro number $N_A$: the volume per atom is

$$V_1 = \frac{M}{\rho N_A},\qquad d \approx \sqrt[3]{V_1}.$$

An atom is about $10^4$–$10^5$ times larger than its nucleus, yet more than 99.9 % of the atom's mass is concentrated in the nucleus. Therefore the density of nuclear matter is enormous: $\rho_{\text{n}} \approx 2\cdot10^{17}\ \text{kg/m}^3$.

The unit of energy — the electronvolt

1 electronvolt is the energy gained by an electron passing through a potential difference of 1 V: $1\ \text{eV} = 1.602\cdot10^{-19}\ \text{J}$.

A convenient relation between photon energy and wavelength: $E\,[\text{eV}] = \dfrac{hc}{\lambda} = \dfrac{1239.8}{\lambda\,[\text{nm}]}$. The thermal energy at room temperature is $kT \approx 0.026$ eV — not enough to excite an atom, so under ordinary conditions atoms are in their ground state.

Fundamental constants

All formulas of atomic physics contain a few fundamental constants (since 2019 $h$, $e$, $k$, $N_A$ have exact values in SI):

The natural scales of atomic physics follow from them. For example, the Bohr radius and the fine-structure constant:

$$a_0 = \frac{4\pi\varepsilon_0\hbar^2}{m_e e^2} = 0.529\cdot10^{-10}\ \text{m},\qquad \alpha = \frac{e^2}{4\pi\varepsilon_0\hbar c} \approx \frac{1}{137}.$$

Here $a_0$ is the characteristic size of the hydrogen atom and $\alpha$ is the dimensionless number that sets the strength of the electromagnetic interaction.

Example

Problem. Estimate the size of a water molecule ($M = 18$ g/mol, $\rho = 1000$ kg/m³).

Solution. The volume per molecule: $V_1 = \dfrac{M}{\rho N_A} = \dfrac{0.018}{1000\cdot 6.022\cdot10^{23}} = 2.99\cdot10^{-29}\ \text{m}^3$. Size: $d \approx \sqrt[3]{V_1} = 3.1\cdot10^{-10}\ \text{m} = 0.31\ \text{nm}$.

Answer: $d \approx 0.3$ nm, which confirms that atomic sizes are of the order of $10^{-10}$ m.

Modern atomism

Today atoms are not only a theoretical object but also an object of direct observation and control. The scanning tunnelling microscope (Binnig and Rohrer, 1981) shows individual atoms on a surface and makes it possible to move them one by one. Laser cooling made it possible to cool atoms to microkelvins and to obtain a Bose–Einstein condensate. Optical atomic clocks have reached a relative accuracy of $10^{-18}$. In quantum computers individual ions and atoms are used as qubits.

In the interactive timeline model on the lecture page, step through the main discoveries of atomic physics; in the scale model, zoom from the nucleus to the Universe and compare the sizes of an atom and a nucleus.