There is no exact size to an atom because electrons are modeled as existing in blurry probability clouds—an inherent property of the quantum scale.

The quantum model of the atom resulted from over two millennia of scientific thinking

In 440 BCE, Democritus proposed that everything was made up of tiny particles surrounded by empty space, which varied in size and shape based on the substance's properties. It was not until the 20th century that experimental evidence validated elements of Democritus' model.

View the quantum mechanical depiction of electrons as waves around the atomic nucleus

Unlike Bohr's fixed paths, the quantum model describes electrons as exhibiting behavior resembling standing waves—waves that have fixed points at the end while vibrating, like a plucked guitar string. Rather than determining their exact positions, only the probabilities of electrons being in a specific region can be determined.

View the evolution of atomic models, with four successively overturned between 1900 and 1926

Originally thought to be indivisible spheres unique to each element, the discovery of the electron by J.J. Thomson revealed them to be made of smaller particles. Ernest Rutherford's gold foil experiment uncovered the existence of nuclei, which Niels Bohr suggested were surrounded by electrons in fixed orbits. By applying quantum mechanics, Erwin Schrödinger replaced orbits with probability clouds.

In quantum mechanics, matter is not in one location until it's measured

The probability that a particle is located at a given point is described by a wave function, in which peaks correspond to high probability and valleys to low probability. The wave nature of matter introduces uncertainty, allows it to exhibit complex behavior, such as interfering with itself, and also explains the observed structure of atoms.

An overview of atomic composition, scale, and structure, which is almost all 'empty' space

It takes about 500,000 carbon atoms lined up next to one another to span the thickness of human hair, and over 99.9994% of the mass of each is contained in the nucleus. About 99.999999999999% of an atom's volume lies outside this nucleus, where electrons exist in clouds of probability. Removing these clouds, the Empire State Building would be the size of a rice grain.

How atomic clocks have been used to measure the universe's fundamental constants

Atoms behave according to a set of parameters that scientists have determined give reality its properties. For example, the fine-structure constant, α, quantifies the strength of interactions between charged particles. Since the light emitted by atoms as they move between energy levels is affected by α, analyzing these emissions—the basis of atomic clocks—using different atoms helps calculate α.

Quantum mechanics explains how particles behave like both matter and waves

In the quantum world, particles such as electrons are “quantized,” meaning they can only hold specific values of energy or momentum. These particles also behave like waves, with their wave function predicting where they might be found at any moment as probability clouds called orbitals.

Quantum field theory, which has made predictions accurate to 12 decimal places, explained

Instead of being made of indivisible particles, all visible matter in the universe is built from underlying quantum fields—smooth, invisible entities that behave like waves and extend throughout space and time. The theory suggests these fields are fundamental, and particles are disturbances that move through them.

Smaller than atoms—what are quarks?

One of humanity’s eternal questions surrounds what we are fundamentally made of. Many ancient philosophies believed in a set of classical elements: from water, air, fire and earth of ancient Greeks; to…

Measurements of an electron’s magnetic moment help test the Standard Model

A particle’s magnetic moment quantifies how it responds to the presence of an external magnetic field. An electron’s value can be measured down to 14 decimal places, with certainties in the first 12 allowing it to be used to assess the accuracy of predictive models.

Why most atoms do not spontaneously break apart, despite protons repelling one another

At small scales, the strong nuclear force overwhelms electromagnetic repulsion between positively charged particles, keeping the nucleus intact. However, because the force's range is limited, it cannot provide the attraction needed to hold onto protons that are spread out across very large atomic nuclei.

Within quantum mechanics, the Heisenberg uncertainty principle limits how precisely one can simultaneously know the values of pairs of complementary properties for an object, such as position and momentum.

The simple grandeur of atomic theory

Is the universe made up of a continuous substance, or a finite amount of tiny, indivisible atoms? The atomic hypothesis, largely vindicated in the 20th century, was forgotten for nearly 2,000 years after first being formulated by the Greek philosopher Democritus. Learn more about the theory and its implications for science and human life with this reflective essay.

Probability waves govern particles like electrons in the quantum space

Just as waves are extended objects whose heights change across space, quantum waves dictate that the probability of an object existing in different locations across space varies. Like water waves, the probability waves can combine, changing the heights—and therefore probabilities—in different locations.

View 3D renderings of atomic orbitals created with quantum mechanics

Scientists use the Schrödinger equation to determine how a system governed by a wavefunction—an equation that predicts the probability of certain outcomes—evolves with time. Computers can animate atomic structure and behavior by depicting the wavefunction as a fluid that guides a particle, like water moving a speck of dust.

Quantum field theory reveals that particles are ripples in universal fields

Instead of being made of indivisible particles, all visible matter in the universe is built from underlying quantum fields—smooth, invisible entities that behave like waves. The theory suggests these fields are fundamental, and particles are disturbances that move through them.

How the nuclear shell model explains the stability or radioactivity of atomic nuclei

When the number of protons and neutrons completely fills shells within the nucleus, the binding energy that prevents these particles from being pulled apart increases. These are called "magic numbers," and they produce atoms with exceptionally stable nuclear configurations.

Uncertainties in measurements make finding gravity's Newtonian limit unclear

Although Newton's "universal" law is unreliable in strong gravitational fields when compared with the field equations of general relativity, it is still taught for its accuracy on everyday scales. However, gravity's effect on small scales is too weak to be measured reliably, its accuracy at atomic scales remains unknown.

Cooling silica nanoparticles lets physicists push the boundary of how large an object can still behave quantum mechanically.

The one-electron theory describes the universe as having only one electron

The thought experiment explains why every electron has the same charge and mass as every other electron, and describes every positron—the antimatter version of the electron—as that same electron traveling backwards in time. Among other foundational challenges, the model suggests that the universe contains equal numbers of electrons and positrons, yet normal matter is much more common than antimatter.

Ernest Rutherford's gold foil and nitrogen experiments revealed nuclear structure

Observing high-angle deflections when alpha particles were fired at gold foil led to an atomic model with a dense, positively charged nucleus. Firing those particles at nitrogen resulted in the emission of hydrogen nuclei—protons—leading to the discovery of the subatomic particle.

Because some models of the universe do not incorporate time, it may be an emergent property born from our limited perception of the universe, rather than a fundamental property of reality.

The Standard Model reveals an underlying organization to the universe

Using the framework of quantum field theory, it structures all known particles into 12 matter particles, alongside five particles that carry three of the four fundamental forces. Although remarkably precise and predictive, it cannot yet explain gravity, dark matter, or dark energy.

Quantum mechanical principles are responsible for chemical properties

Besides quantization, the wave-particle duality, and probabilistic features, quantum theory's mathematics introduces the exclusion principle, quantum tunneling, quantum entanglement, and other phenomena foreign to our everyday experiences. Some suggest that all possibilities for a quantum system may also occur across the multiverse.

A scale of the universe, from atoms to cosmos

Can you really appreciate just how small protons are, or how massive the universe is? To attempt to grasp it, watch this short video which zooms out from a young woman in California to the very limits of the cosmos using established scales. Then, dive deep into the atoms of her white blood cells for a fully-rounded effect.

Particle interactions follow rules related to specific quantum properties

Like a business whose purchased inventory matches sold inventory, physicists identified specific patterns across decades of particle accelerator data, which became new conservation laws for elementary particles. These laws help identify which particle decays are expected or forbidden.

Why atoms are used to keep track of time and define the meaning of a second

Small variations in the production of human-made devices, such as mechanical watches and pendulums, make them unreliable for the ultraprecise timekeeping required by modern technology, including financial transaction timestamping and GPS. Because atoms obey fundamental laws of nature and never wear out, their light emissions when energized provide a consistent timekeeping signal.

Build atomic nuclei to explore their instability and resulting radioactive decay

In this simulation, users can add protons and neutrons to create an atomic nucleus, view its half-life and decay options, and identify patterns in how specific combinations of particles create extremely stable nuclei, from which the nuclear shell model of stability emerged.

Virtual particles are bookkeeping tools used to describe force interactions

Physicists mathematically describe the electromagnetic, weak nuclear, and strong nuclear forces as the result of these particles being exchanged between particles of matter. Despite not being real, observable particles, this method has provided experimental predictions with an accuracy of over 12 decimal places.

The outermost shell of electrons in an atom dictates how it bonds to other atoms, including those of the same element, and the properties of the materials composed of those atoms.

Understanding how gravity works at the quantum scale is physics's greatest challenge

While the theory of general relativity explains how gravity works and quantum mechanics explains interactions at the subatomic scale, the two frameworks contradict one another. Developing a model of gravity mediated by particles can help complete the Standard Model.

How string theory explains gravity on the quantum scale, but may be untestable

Combining the general theory of relativity with quantum field theory creates nonsensical mathematical outcomes, such as probabilities of infinity. These are resolved by treating particles as vibrating strings rather than points of matter. However, probing the scale of these strings to validate the theory requires technology equivalent to a particle accelerator the size of the solar system.

Although among the most comprehensive frameworks in science, the Standard Model has numerous gaps, including its inability to explain dark matter, dark energy, or why normal matter is so much more abundant than antimatter.

An explanation of isotopes, which can help scientists trace food, water, and farming choices

Atoms of the same element have the same number of protons, but experiments showed that atoms of the same element can move through electromagnetic fields as if they had different masses. These differences in mass come from variations in the number of neutrons, which contribute to the stability of atoms by providing a buffer to the repulsion between protons.

Scientists can map Earth's shape and structure by measuring the ratios of certain particles arriving from different directions in space, as these ratios change with the density of the material particles travel through.

Once called 'aces,' quarks are fundamental pieces of matter that combine to create over 100 known composite particles, including the proton and neutron.

The Planck time, equal to 5.39 × 10⁻⁴³ seconds or less than a millionth of a trillionth of a trillionth of a trillionth of a second, is the smallest unit of time that could ever be theoretically measured.

Build atoms to learn about atomic number, mass number, and charge notations

In this simulation, users can add protons, neutrons, and electrons to create atoms, view their stability and atomic configurations, and identify how the amounts of these subatomic particles are detailed around the abbreviation for the resulting element using AZE notation.

Even in a perfect vacuum, empty space is full of quantum activity

Scientists have tried to create “nothing” by removing all matter, energy, and heat from a container, but the uncertainty principle and relativity prevent such conditions within any period of time. This means the universe is full of quantum foam, which can produce forces from nothingness.

View a ranking of the masses of fundamental particles, from the massless photon to the top quark, and a timeline of their discoveries.

While atoms are normally made of protons, neutrons, and electrons, exotic ones have been built with antimatter—alternate versions of normal matter that live for fractions of a second.

Watch how the machine at the heart of NASA's Cold Atom Lab produces atoms near absolute zero—the coldest theoretical temperature in the universe—for experiments involving quantum phenomena.

Explaining the unified atomic mass units, which quantifies the mass of atoms and molecules

Until 1961, the atomic mass unit was defined based on oxygen-16, but it was later replaced by the unified atomic mass unit, defined as 1/12th the mass of a carbon-12 atom. Today, the term "atomic mass unit" often refers to the "unified atomic mass unit," denoted by the symbol u.

Nanotechnology refers to the study of objects measuring 1 to 100 billionths of a meter, which has produced materials with unique properties by manipulating the arrangement of atoms.

The hypothetical matter that neutron stars' cores may contain, including strange quarks

Models of the extreme pressures and energies in neutron stars suggest conditions resembling those believed to have existed within a fraction of a second after the Big Bang. In these environments, the quarks that make up protons and neutrons in trios may instead form pairs that combine to form one quantum object. (Some readers may experience a paywall.)

Unlike quantum mechanics, classical physics suggests free will does not exist

Models based on Newton's laws of motion suggest all actions are predetermined and must follow specific trajectories and outcomes, such that everything that will ever occur in the future has already been set in motion by past causes. However, quantum mechanics challenges determinism because it is based on probability, where no outcome is certain.

Quantum computers can simulate nature more effectively than classical computers

Ordinary computers struggle to simulate quantum fields due to entanglement, but systems built from those elements can model the complexity. Systems using particle in more than two states—qudits—have successfully modeled 2D electromagnetic fields and done so more efficiently.

Neural networks mimic the structure and behavior of real physical systems

Early generative AI systems were inspired by scientific models such as the Ising model, which explains how atoms interact with one another and align in magnets. As these networks have expanded, their behavior has more closely resembled that of quantum fields, enabling them to be used in exploring complex particle physics interactions.

Quantum mechanics and general relativity—two of the most successful explanations of the physics seen across the universe—are logically incompatible with one another because they use contradictory models for space and time.

Rather than measuring the rising and falling of the sun or pendulum swings, optical clocks track the passage of time using the vibrations of atoms.