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

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.

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.

An explanation of the weak nuclear force, which can induce some forms of radioactive decay

While the strong nuclear force holds the protons and neutrons together in an atomic nucleus, despite the electromagnetic force pushing protons apart, the weak nuclear force can change the identity, or flavor, of the quarks that make up these particles. In doing so, protons can be converted into neutrons, and vice versa, altering the stability of atomic nuclei.

Unusually stable, undiscovered elements may exist near atomic number 126

While heavier elements like uranium and plutonium are unstable and decay quickly, simulations suggest a pocket of stability exists for elements with approximately 126 protons and 184 neutrons. Such elements may have practical applications, such as americium, a synthetic element used in smoke detectors.

An overview of radioactivity, which can spontaneously change one element into another

Unstable atomic nuclei can transmute into a new element—an atom with a different number of protons—by emitting an alpha particle (two protons and two neutrons) or a beta particle (an electron). The electron can emerge from the nucleus when a neutron, which has no charge, suddenly transforms into a proton and an electron, thereby maintaining zero charge before and after the transformation, but altering the original element.

Visualize what happens to atoms during nuclear fission and how the process produces energy

Nuclear fission occurs when an unstable, often massive, atomic nucleus splits into smaller ones—daughter atoms—and releases energy. Within a nuclear reactor, these daughter atoms can collide and combine with neighboring atoms, destabilizing them and triggering a chain reaction of atomic splitting.

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.

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.

The discovery of the neutron paved the way for nuclear weapons

In 1932, James Chadwick discovered the subatomic particle when trying to explain the radiation emitted by beryllium after it was bombarded with alpha particles. The radiation’s ability to eject protons from a target suggested a chargeless particle with slightly more mass than a proton.

A look inside neutron stars, which are thought to contain nuclear pasta

Simulations show that beneath the outer crust of these objects, the gravitational force is so extreme that atomic nuclei link together into chains of primarily neutrons and some protons called nuclear spaghetti. Deeper in the star, these links combine to form sheets—nuclear lasagna—a quintillion times stronger than steel, making it the strongest material in the universe.

Why quantum mechanics causes disagreement on where the edge of an atom is located

The quantum model of the atom describes it as having a dense nucleus at its center, surrounded by electrons in probability clouds where they are most likely to be found. The fundamental uncertainty of these clouds has led to various methods and resulting measurements of the atomic radius. (Some readers may experience a paywall.)

Understanding how atomic structure contributes to each element's properties

The outermost layer of electrons in an atom dictates how it will bond to other atoms. These bonds determine whether elements exist as solids, liquids, or gases in the environment and other characteristics. For example, electrons are freely shared between atoms in metallic bonds, allowing them to immediately re-emit light that strikes them, thus making most metals shiny.

How fusion—which releases energy when two lighter atoms combine to form a heavier atom—differs from fission

Helium formation, from radioactive decay inside Earth to nuclear fusion within stellar cores

Over the course of billions of years, uranium and thorium undergo alpha decay, producing helium nuclei—two protons and two neutrons—which become helium atoms after gaining two electrons. This helium becomes trapped in underground reservoirs along with other gases and can be recovered during natural gas extraction.

Water acts as a coolant and a moderator of nuclear reactions in reactors

Nuclear reactions within a containment structure boil water into steam, which drives a turbine that generates electricity. This water is then recirculated via pumps back into the containment structure to repeat the process, with reaction rates lowered by the insertion of control rods that absorb neutrons, which trigger reactions.

Nuclear batteries generate electrical currents using radioactive materials

Rather than using electrochemical reactions to produce the electrons that flow through a circuit, isotopes like nickel-63 undergo beta decay—emitting electrons—which a semiconducting material can absorb to establish a charge imbalance that generates current. Such batteries could provide low-power energy for decades.

How Robert Oppenheimer determined when neutron stars become black holes

Building on the work of Richard Tolman and George Volkoff, Oppenheimer reasoned that, once massive enough, a hypothetical, star-sized atomic nucleus would be unable to stave off gravitational collapse with neutron degeneracy—quantum pressure—alone. The mathematical model estimated the maximum mass of a non-rotating neutron star, known as the Tolman-Oppenheimer-Volkoff limit.

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.

Explaining why solving the solar neutrino problem revealed that neutrinos could transform

Electron neutrinos are byproducts of the nuclear reactions within the sun's core. Based on the sun's energy output, scientists modeled reaction rates and predicted neutrino production, but the observed values were consistently one-third the predicted values. Experiments later showed that these neutrinos could change into other types on their way to Earth, causing the discrepancy.

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 and are about a billion times as rare.

Nuclear-powered missiles replace chemical combustion with energy from nuclear fission

In these systems, energy is added to an airstream, which passes through a nozzle to generate thrust. Because the amount of energy released per unit mass of nuclear fuel is millions of times larger than that of chemical propellants, nuclear missiles can travel faster and farther with less fuel.

Neutron stars, the remains of some massive stars after they explode in a supernova, are the densest directly observable objects in the universe.

How a quantum quirk allowed neutral atoms to form soon after the Big Bang

At the beginning of the universe, high-energy photons prevented atomic nuclei from combining with electrons to form neutral atoms. Rather than waiting for the universe to expand and cool completely, a rare quantum phenomenon—a two-photon transition—allowed neutral hydrogen atoms to form sooner, expediting the formation of stars, planets, and life.

As of 2025, the Standard Model has at least five unresolved problems

Among the issues with the most successful theory of the universe at subatomic scales is its inability to explain the extreme imbalance observed between visible matter and antimatter, since both should be roughly equal. The Standard Model also omits gravity and cannot account for the observed rate of cosmic expansion.

86% of the world's 12,321 nuclear warheads are held by just two countries

As of early 2026, the US and Russia together control about 86% of the world's more than 12,000 nuclear warheads—over 9,600 in military stockpiles. None of the seven other nuclear nations holds more than 600.

Radioactive elements can introduce software errors because the ionizing radiation they produce can detach electrons from atoms, and computer code relies on the distribution of electrons.

Study pinpoints where to hide during a nuclear blast

There’s no surviving the fireball of a nuclear bomb, but beyond that, there are certain spots indoors where you can try avoid the destructive shockwave.

A primer on the president's nuclear football

During the Cold War, the United States and the USSR were forced to prepare for a nuclear strike at a moment's notice, leading to a new innovation: the so-called "football" (known as the chemodanchik in Russia), a bag containing nuclear strike plans, authentication codes, and likely a communication device, which attended the country's leader wherever they went. This easy-to-read piece breaks down the history and lore around the high-stakes quirk in nuclear governance.

Explore the chemical compounds found in fireworks

Besides the various salts and metals used to produce fireworks colors, shells are also filled with gunpowder and oxidizers to help fuel and accelerate reactions. Chlorates help strengthen colors, while dextrin, a starch, helps hold mixtures together.

While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.

Fireworks make a loud booming sound after exploding due to air expanding faster than the speed of sound.

Sunflowers have long been a symbol of nuclear disarmament because they can extract large amounts of radioactive cesium from soil.

In 1984, Operation Smash Hit intentionally crashed a 239-ton train into a nuclear waste canister at 100 miles per hour to prove the canister's safety, which remained completely intact and lost just 0.29 of its 100 pounds of pressure.

Volcanoes 'die' when their supply of magma runs out, if they are shifted away from their underlying magma reservoir, or if they get clogged by collapsing or their magma cooling back into rock.

Planeterrellas create artificial auroras that mimic the atmospheric displays of light by setting up an electric field between two metal balls in a jar filled with a small amount of air.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

When caught in the mouths of cardinal fish, seed shrimp release glowing, bioluminescent chemicals, which alert predators of the cardinal fish, prompting the shrimp's ejection.

Pure water does not conduct electricity because this flow of energy requires the movement of charged particles, and water is a neutral molecule.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

The power and influence of the American presidency have expanded significantly over time—far beyond what the founders envisioned.

The United States has had a tumultuous relationship with Cuba since its 1959 revolution, highlighted by a nuclear crisis and a decades-long trade embargo.

Indefinite cloning of some endangered species may not sustain their longevity because cloning success rates decrease as genetic mutations accumulate.

Sony set the standard for cylinder-shaped batteries when it repurposed manufacturing equipment used to make rolls of magnetic recording tape.

Bone marrow (soft tissue found inside certain bones) generates roughly 500 billion new blood cells each day

In recent years a child anxiety expert has created and tested a novel phobia and anxiety treatment approach for children, focused on changing how parents respond to the fears.

Existentialist writer Jean-Paul Sartre coined the famous phrase 'Hell is—other people' in his play 'No Exit'

The Nasdaq's 'Magnificent 7' companies are responsible for roughly 40% of the Nasdaq 100 index's gains, while the remaining 93 companies account for the other 60%.

Recent research found that the brain doesn't seem to massively rewire following amputation—upending earlier beliefs about the cause of phantom limb pain.

In 2026, Finland was named the world's happiest country for the ninth consecutive year based on its wealth, social safety network, and high life expectancy, among other factors.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.