/posts/til/til-researchwhy-solid-matter-is-mostly-empty-space-inside-atoms
Why ‘Solid’ Matter Is Mostly Empty Space Inside Atoms
When Empty Space Feels Solid I’d heard the line “atoms are mostly empty space” for years, but I’d never really internalized what that meant for the chair I’m sitting on or the h...
When Empty Space Feels Solid
I’d heard the line “atoms are mostly empty space” for years, but I’d never really internalized what that meant for the chair I’m sitting on or the hand I’m typing with. Today I dug into the actual numbers and mechanisms and realized how violently this clashes with the everyday intuition that solid things are full of stuff. Understanding how something can be both mostly empty and stubbornly solid at the same time is a surprisingly useful mental model for thinking about scale, structure, and why our senses are such unreliable guides at the microscopic level.
Background
Modern atomic theory describes matter at scales from about 10^-10 meters (the size of atoms) down to 10^-15 meters (the size of atomic nuclei). The key experiments that revealed atomic emptiness—like Rutherford’s gold foil experiment—were done in the early 1900s in labs in the UK and elsewhere. Today, particle accelerators and electron microscopes routinely probe these scales, confirming that what we call “solid” is mostly structured emptiness held together by fields and forces.
How Rutherford’s Gold Foil Broke the Atom
For a long time, people pictured atoms as more or less uniform blobs of positive charge with electrons sprinkled inside, like raisins in a pudding. When Ernest Rutherford’s team fired alpha particles (heavy, positively charged particles) at thin gold foil in 1909, they expected most to pass through with only tiny deflections, because the charge was thought to be smeared out. Most did pass through—but a tiny fraction bounced almost straight back, as if they’d hit something incredibly dense and tiny.
The only way to explain those wild deflections was to put almost all the atom’s mass and positive charge into a tiny central nucleus, with electrons somewhere around it. If the nucleus were even moderately big compared to the atom, more alpha particles would have bounced; the fact that almost all sailed through told us the nucleus is minuscule and the rest is effectively empty. Quantitatively, a typical atom is about 10^-10 meters across, while its nucleus is about 10^-15 meters—roughly a factor of 100,000 smaller in radius.
Quantum Mechanics and the Electron Cloud
Classical orbits would make electrons radiate energy and spiral into the nucleus, so quantum mechanics replaces orbits with orbitals—standing wave patterns of probability. An electron in an atom isn’t a point whizzing on a track; it’s a spread-out wavefunction with regions where it’s likely or unlikely to be detected. The “size” of an atom is basically the region where the electron’s probability density is significant, and that region is huge compared to the nucleus.
Between the nucleus and the most probable electron distances, there is no lattice of little balls filling the gap. Instead, there’s a low-density probability cloud and electromagnetic fields extending through space. The trade-off is stark: concentrating mass and charge in a tiny nucleus allows strong nuclear forces to bind protons and neutrons tightly, but it also means the atom’s overall footprint is set by much weaker electromagnetic and quantum effects, which naturally operate on much larger length scales.
Why ‘Mostly Empty’ Still Feels Solid
If atoms are mostly empty, why don’t we fall through floors? The answer is that forces and quantum rules, not physical contact of hard spheres, set the limits. When you press your hand on a table, the negatively charged electrons in your skin get close to the electrons in the table. The electromagnetic repulsion between like charges skyrockets as distance shrinks, and the Pauli exclusion principle prevents electrons from occupying the same quantum states, effectively creating a powerful “do not overlap” barrier.
So the emptiness is structured: fields permeate it, and quantum mechanics dictates how particles can inhabit it. The trade-off is that matter can be both incredibly light for its size (because it’s mostly space) and incredibly resistant to compression (because those quantum rules get brutally stiff at short distances). The phrase “atoms are nearly empty space” is less a fun fact and more a reminder that what we experience as solid is really a set of invisible constraints playing out in a mostly vacant arena.
💡 Did you know: If the nucleus of a hydrogen atom were the size of a pea, the electron’s most likely distance would be roughly a few hundred meters away, and everything in between would be vacuum shaped by electric fields.
Watching Empty Space Deflect Particles
Thought experiment: Rutherford scattering
1. Fire a beam of alpha particles (helium nuclei) at a very thin gold foil.
2. Surround the foil with a fluorescent screen that flashes when hit.
3. Count how many alpha particles:
- go straight through,
- are slightly deflected,
- are strongly deflected (large angles),
- bounce almost straight back.
Observed pattern:
- ~99% go straight through → most of the atom offers no hard obstacle.
- A small fraction deflect at moderate angles → they passed near something concentrated and charged.
- A tiny fraction (~1 in 8,000) bounce back → they hit a very dense, very small nucleus.
Scale analogy:
- Imagine the nucleus as a pea in the center of a sports stadium.
- The electron cloud that defines the atom’s size would extend roughly to the outer seats.
- Everything between the pea and the seats is effectively empty of matter, yet fields fill that space.
The Insight
Atoms are not tiny packed balls of matter but dense pinprick nuclei surrounded by vast regions where particles are almost never found, with solidity coming from quantum rules and electromagnetic forces, not from matter filling that space. In other words, what feels solid under your hand is mostly structured emptiness enforced by invisible constraints.
🧠 Bonus: The stiffness of solids comes less from particles physically touching and more from the Pauli exclusion principle, which forbids electrons from piling into the same quantum state and effectively creates a powerful ‘do not overlap’ rule.
Gotchas
- “Empty space” inside atoms is not a literal nothingness; it’s a region where the probability of finding particles is extremely low but where fields (like the electromagnetic field) are very much present, so forces still act there.
- Electron “orbits” are not tiny planets circling a sun; treating them that way makes the atom look like a miniature solar system, but quantum mechanically electrons are spread-out wavefunctions with fuzzy boundaries.
- Saying atoms are “99.9999% empty” can mislead people into thinking you could walk through walls; in reality, quantum rules and electromagnetic repulsion make that vanishingly improbable on human timescales.
- Visual models that draw nuclei and electrons almost touching are for pedagogy, not scale; taking those diagrams literally hides just how extreme the size difference really is.
Takeaways
- Use the nucleus-to-atom size ratio (10^-15 m vs 10^-10 m) as your mental yardstick for how extreme atomic emptiness really is.
- When explaining solidity, emphasize electromagnetic repulsion and the Pauli exclusion principle, not tiny billiard balls touching.
- Treat electron orbitals as probability clouds, not miniature planetary orbits, whenever you visualize or sketch atoms.
- Remember that ‘empty’ atomic space is still full of fields and quantum rules, so forces can act strongly even where there are almost no particles.
- Reach for the stadium-and-pea analogy (or similar) when you need an intuitive picture that preserves the actual scale difference.
🔥 One more thing: Neutron stars are what you get when you mostly remove that emptiness: a teaspoon of neutron star material would weigh billions of tons on Earth because the space between nuclei has been almost completely crushed out.
References
- Rutherford’s 1911 paper on the scattering of alpha and beta particles (article)
- Feynman Lectures on Physics, Vol. I, Chapter 2: Basic Physics (book)
- HyperPhysics: Rutherford Scattering and the Nuclear Atom (article)
- MIT OpenCourseWare: 8.04 Quantum Physics I – Atomic structure lectures (video)