Our Solar System

Quantum physics

At the scale of atoms, energy comes in fixed packets, particles travel as waves and a rule about electrons holds up dead stars. Move the sliders and watch a star change colour, an atom give out light and an electron pass through a wall.

Start with a glowing star Explore relativity

Above is one hydrogen atom, drawn from Schrödinger's equation. Its electron is in two states at once, and the beat between them turns the cloud round: in a real atom it goes round 457 million million times a second, the frequency of hydrogen's red light1. Every scene below runs on the real equations.

Light comes in packets

The idea

Everything warm glows, and the hotter it is, the bluer its light. In 1900 the physics of the day could not explain the colour of that glow. Max Planck could, by assuming that light's energy is handed out in packets, each worth a constant h times the light's frequency2.

In plain words

Classical physics shared heat out equally among all the ways light can wave. Short waves have far more ways to fit, so it predicted that anything warm should pour out endless ultraviolet light, the "ultraviolet catastrophe"3. With Planck's packets a packet of blue light costs more energy than a packet of red, a warm body can only make a few of the costliest, and the curve turns over.

The numbers

Planck's constant h is 6.62607015 × 10⁻³⁴ joule seconds, exact by definition since 20 May 2019, when it became the basis of the kilogram45. The peak's wavelength is 2.898 millimetre kelvins divided by the temperature6: 502 nm for the Sun's surface at 5,772 K7, counted per unit of wavelength. Double the temperature and each square metre gives out 16 times the light.

In the sky

A star's colour is its temperature. Betelgeuse, at 3,600 K8, peaks at 805 nm, just past red, and looks orange. Sirius at 9,940 K9 and Rigel at 12,000 K10 peak in the ultraviolet and look blue-white. ζ Puppis, at 40,000 K, sends out most of its light at about 72 nm, far into the ultraviolet11.

Try it

Press Physics before Planck and the dashed curve climbs out of the picture toward the ultraviolet. Slide down toward Betelgeuse and the peak leaves the colours we see on the red side.

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An atom's energy comes in steps

The idea

In 1913 Niels Bohr proposed that the electron in a hydrogen atom can only have certain energies12. When it drops from one level to a lower one, the atom gives out one packet of light carrying exactly the difference, so glowing hydrogen shines in a few sharp colours.

The numbers

The levels sit at −13.6 eV divided by n², where 13.598 eV is the energy it takes to pull the electron free1. A drop from level 3 to 2 releases 1.89 eV, a red photon of 656.28 nm, hydrogen's H-alpha line. Drops to level 2 from 4, 5 and 6 give blue-green 486.13 nm, blue 434.05 nm and violet 410.17 nm. Drops to level 1 carry far more, 10.2 eV for the first, and land in the ultraviolet at 121.567 nm13.

In plain words

During the change the electron is in both levels at once, and the two beat against each other, so its charge swings up and down at the light's own frequency: 457 million million times a second for the red line. That swinging charge is what sends the light out. Here it is slowed to twice a second.

How we know

Pass the light of a glowing hydrogen tube through a prism and only these four colours appear. Bohr's levels give all of them from one number, the Rydberg constant, now measured to about one part in a million million14.

Try it

Slide to n = 6 for the violet line, then switch to Taking in light: only a photon of that exact colour can lift the electron back up.

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Sunlight carries fingerprints

The idea

Spread sunlight into its colours and it is crossed by dark lines. Each one is a colour taken out by atoms in the Sun's outer layers, at an energy step all their own, so the lines tell us what the Sun is made of.

How we know

Joseph Fraunhofer saw the lines in 1814, lettered the strongest A to H and counted 574 between B and H1516. In 1859 Gustav Kirchhoff and Robert Bunsen found that elements heated in a flame give bright lines at the places of dark ones, and that the D lines are sodium in the Sun1718.

The lines drawn

Hydrogen at 656.28, 486.13, 434.05 and 410.17 nm13, sodium's D pair at 588.995 and 589.592 nm19, magnesium's b lines from 516.73 to 518.36 nm20, iron's E at 527.04 nm21 and ionised calcium's H and K at 396.847 and 393.366 nm22. A and B are oxygen in our own air, taken out on the way down23.

A new element

In 1868, during a total eclipse, Pierre Janssen saw a yellow line in the Sun's light that matched no known element, and Norman Lockyer named its source helium24. The line sits at 587.56 nm25. Helium was found on Earth in 1895 by William Ramsay and, independently, by Per Teodor Cleve and Nils Langlet2624.

Try it

Switch to With the elements: every lamp's bright lines fall exactly under dark lines in the sunlight above.

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Electrons travel as waves

The idea

In 1924 Louis de Broglie proposed that electrons, and every other particle, travel as waves27. Fire electrons one at a time at two slits and each lands as a single dot, yet the dots build up stripes that only a wave passing through both slits can make.

In plain words

Each electron's wave goes through both slits, and the two halves add up beyond them: where crests meet crests the chance of landing is high, and where crests meet troughs it is zero. Where any one electron lands is pure chance, weighted by the wave. Watch which slit each one takes and the stripes fade away28, because an electron seen at one slit carries on with that slit's wave alone.

The numbers

An electron's wavelength is Planck's constant divided by its momentum27. Accelerated through 50,000 volts it is 5.36 picometres, about a twentieth of the width of a hydrogen atom29. With slits 1 µm apart and a screen 1 m away, the stripes land 5.36 µm apart.

How we know

In 1927 Davisson and Germer saw electrons scatter off a nickel crystal the way X-rays do3031, and de Broglie and Davisson both won Nobel Prizes for it3233. In 1989 Akira Tonomura and colleagues sent about 1,000 electrons a second through an electron version of two slits and watched 70,000 dots build the stripes over about 20 minutes34.

Try it

Turn on Watch which slit and the run starts again: this time the stripes never form.

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Particles pass through walls

The idea

A ball rolled at a hill too high for it always rolls back. An electron's wave meeting a wall higher than its energy leaks into it, fading as it goes, and if the wall is thin enough part of the wave comes out the far side. That part is the chance the electron gets through.

In plain words

Inside the wall the wave stops swinging and dies away, faster the higher the wall. Whatever is left at the far side carries on as an ordinary wave. Each electron either bounces back or gets through whole: the wave only sets the odds.

The numbers

The electron here has 2 eV of energy, a wavelength of 0.87 nm. Against a wall 1.3 times higher and 0.3 nm thick, 24% gets through. Each extra 0.3 nm cuts that about tenfold: 2.4% at 0.6 nm, 0.22% at 0.9 nm. Make the wall lower than the electron's energy and some of it still bounces back, which a ball never would.

Why the Sun shines

The Sun's core is about 15 million °C35, which gives its protons about 1.3 keV each, while the electric push between two protons a femtometre apart is about 1.44 MeV, a thousand times more36. Without tunnelling, fusing them would take billions of degrees3637. George Gamow brought tunnelling to the atomic nucleus in 192838, and in 1929 Atkinson and Houtermans used it to show how stars could build up elements39.

Try it

Make the wall thicker than 0.6 nm and the part that gets through all but disappears. Drop its height below 1× and watch part of the wave bounce back anyway.

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Dead stars held up by a rule

The idea

No two electrons can be in the same quantum state, Wolfgang Pauli's exclusion principle of 192540. Squeeze electrons together and they are forced into ever faster motion, a push that holds up a dead star however cold it gets.

The numbers

Sirius B packs 1.02 Suns into 0.0081 of the Sun's radius, about 5,600 km41, smaller than the Earth's 6,371 km42. A teaspoon of Sirius B would weigh about 13 tonnes.

Heavier means smaller

A heavier dwarf needs more push, so it is squeezed smaller, and its electrons move faster. As they near the speed of light their push stops keeping up, and past about 1.4 Suns no size is small enough43. Neutron stars are smaller still: NICER measured one holding 1.34 Suns in a radius of just 12.7 km44.

How we know

Subrahmanyan Chandrasekhar found the limit in 1930. His 1931 paper put it at 0.91 Suns for the makeup he assumed; for white dwarfs of helium, carbon or oxygen, with two nucleons to each electron, the same physics gives about 1.45 Suns4543. He shared the 1983 Nobel Prize in Physics46.

Try it

Slide the mass toward 1.44 Suns and the dwarf shrinks faster and faster, to nothing at the limit.

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The rules every atom follows

Quantum physics began as a fix for the colour of hot things2 and became the rulebook for atoms, light and stars. The same few ideas explain why the Sun shines36, what it is made of17 and what holds up a dead star40.

RelativityMoving clocks that slow, GPS, bent starlight and Mercury's turning orbit. Black holesRay traced live: bent light, a slow clock at the edge, a star torn apart and the first photograph. LessonsLessons for the classroom, each with its live scene and questions. The 3D viewerThe solar system on its real orbits, at any date.

Questions

What is quantum physics, in simple terms?

The physics of very small things. At the scale of atoms, energy comes in fixed amounts, particles travel as waves, and what a measurement finds is a matter of chance with odds the wave sets. It began with Planck's packets of energy in 19002, which won him the 1918 Nobel Prize47.

What is a photon?

A packet of light. In 1905 Einstein proposed that light itself travels in packets, each with energy h times its frequency, which explained how light knocks electrons out of metal, the photoelectric effect48. It won him the 1921 Nobel Prize in Physics49.

What is the 21 cm line?

The electron and the proton in a hydrogen atom each act like a tiny magnet. When they flip from lined up to opposed, the atom gives out a radio wave of 1,420.405751768 MHz, 21.1 cm long50. Any one atom does it about once in 11 million years51, but space holds so much hydrogen that radio telescopes pick it up everywhere. Hendrik van de Hulst predicted it in 194452, Ewen and Purcell detected it in 195153, and it mapped the Milky Way's spiral arms5455.

What is Hawking radiation?

In 1974 Stephen Hawking showed that quantum effects make a black hole glow, as if it had a temperature that falls as its mass grows5657. For a black hole of one Sun that temperature is about 6.2 × 10⁻⁸ K, some 62 billionths of a degree above absolute zero58.

What is Planck's constant?

The size of the packets: the energy of a packet of light divided by its frequency, 6.62607015 × 10⁻³⁴ joule seconds. Since 20 May 2019 it has been exact by definition, and the kilogram is defined from it45.

Sources

  1. NIST Atomic Spectroscopic Data: the ionisation energy of hydrogen, 13.598 eV
  2. Planck, M. (1901), On the Law of Distribution of Energy in the Normal Spectrum, Annalen der Physik 4, 553 (energy elements ε = hν, first presented 14 December 1900)
  3. HyperPhysics, Georgia State University: the Rayleigh-Jeans law and the ultraviolet catastrophe
  4. NIST CODATA: the Planck constant, 6.62607015 × 10⁻³⁴ J s (exact)
  5. NIST: the kilogram defined by an exact Planck constant from 20 May 2019
  6. NIST CODATA: Wien's displacement constant, 2.897771955 × 10⁻³ m K
  7. IAU 2015 Resolution B3: the Sun's nominal effective temperature, 5,772 K
  8. Levesque, E. M. and Massey, P. (2020), Betelgeuse Just Is Not That Cool, ApJ Letters 891, L37 (3,600 K)
  9. Adelman, S. J. (2004), The physical properties of normal A stars, IAU Symposium 224, 1 (Sirius A 9,940 K)
  10. Przybilla, N. et al. (2006), Quantitative spectroscopy of BA-type supergiants, A&A 445, 1099 (Rigel 12,000 K)
  11. Howarth, I. D. and van Leeuwen, F. (2019), The distance, rotation, and physical parameters of ζ Pup, MNRAS (40,000 K)
  12. Bohr, N. (1913), On the Constitution of Atoms and Molecules, Philosophical Magazine 26, 1
  13. NIST Atomic Spectroscopic Data: strong lines of hydrogen (Balmer lines in air, Lyman-alpha 121.567 nm)
  14. NIST CODATA: the Rydberg constant, 10,973,731.568157 per metre (13.6057 eV)
  15. Fraunhofer, J. (1817), Bestimmung des Brechungs- und Farbenzerstreuungs-Vermögens verschiedener Glasarten, Denkschriften der Akademie zu München 5, 193 (the dark lines, lettered A to H)
  16. Dutta Roy, P. (2025), The origin of the dark bands found in the Solar Spectra, arXiv:2510.21747 (Fraunhofer's 574 lines from B to H)
  17. Kirchhoff, G. and Bunsen, R. (1860), Chemische Analyse durch Spectralbeobachtungen, Annalen der Physik 110, 161
  18. Linda Hall Library: Gustav Kirchhoff, the D line and sodium in the Sun
  19. NIST Atomic Spectroscopic Data: the sodium D lines, 588.995 and 589.592 nm in air
  20. NIST Atomic Spectroscopic Data: the magnesium b lines, 516.73, 517.27 and 518.36 nm in air
  21. NIST Atomic Spectroscopic Data: iron at 527.04 nm in air (Fraunhofer's E)
  22. NIST Atomic Spectroscopic Data: ionised calcium K and H, 393.366 and 396.847 nm in air
  23. Babcock, H. D. and Herzberg, L. (1948), Fine Structure of the Red System of Atmospheric Oxygen Bands, ApJ 108, 167 (the A band is oxygen in our own air)
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  25. NIST Atomic Spectra Database: the helium D3 line, 587.56 nm in air
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  29. NIST CODATA: the Bohr radius, 5.29177 × 10⁻¹¹ m
  30. Davisson, C. and Germer, L. H. (1927), Diffraction of Electrons by a Crystal of Nickel, Physical Review 30, 705
  31. APS Physics, Focus: Landmarks, Electrons Act Like Waves (Davisson and Germer, 1927)
  32. Nobel Prize in Physics 1929: Louis de Broglie, for his discovery of the wave nature of electrons
  33. Nobel Prize in Physics 1937: Davisson and Thomson, for the diffraction of electrons by crystals
  34. Tonomura, A. et al. (1989), Demonstration of single-electron buildup of an interference pattern, American Journal of Physics 57, 117 (50 keV electrons)
  35. NASA: Sun facts (the core at about 15 million °C)
  36. Rosen, A., ASTR 201 reading: Nuclear Fusion and the Four Forces (core heat of 1.29 keV against a 1.44 MeV barrier)
  37. University of Oregon: Necessary Conditions for Nuclear Fusion (15 million K in the core, 17 billion K needed without tunnelling)
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  39. Atkinson, R. d'E. and Houtermans, F. G. (1929), Zur Frage der Aufbaumöglichkeit der Elemente in Sternen, Zeitschrift für Physik 54, 656
  40. Pauli, W. (1925), Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren, Zeitschrift für Physik 31, 765
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  42. NASA Earth fact sheet (mean radius 6,371 km)
  43. Nauenberg, M. (1972), Analytic Approximations to the Mass-Radius Relation and Energy of Zero-Temperature Stars, ApJ 175, 417 (the limiting mass, about 1.45 Suns for two nucleons per electron)
  44. Riley, T. E. et al. (2019), A NICER View of PSR J0030+0451, ApJ Letters 887, L21 (1.34 Suns, radius 12.7 km)
  45. Chandrasekhar, S. (1931), The Maximum Mass of Ideal White Dwarfs, ApJ 74, 81
  46. Nobel Prize in Physics 1983: Subrahmanyan Chandrasekhar, for his studies of the structure and evolution of the stars
  47. Nobel Prize in Physics 1918: Max Planck, for his discovery of energy quanta
  48. Einstein, A. (1905), On a Heuristic Point of View about the Creation and Conversion of Light, Annalen der Physik 17, 132
  49. Nobel Prize in Physics 1921: Albert Einstein, for his discovery of the law of the photoelectric effect
  50. Hellwig, H. et al. (1970), Measurement of the Unperturbed Hydrogen Hyperfine Transition Frequency, IEEE Transactions on Instrumentation and Measurement 19, 200 (1,420,405,751.768 Hz)
  51. NRAO, Essential Radio Astronomy: the 21 cm line (2.85 × 10⁻¹⁵ per second, about 11 million years)
  52. Leiden Observatory Annual Report 2000: Hendrik van de Hulst, who predicted the 21 cm line on 15 April 1944
  53. Ewen, H. I. and Purcell, E. M. (1951), Observation of a Line in the Galactic Radio Spectrum, Nature 168, 356
  54. Oort, J. H., Kerr, F. J. and Westerhout, G. (1958), The Galactic System as a Spiral Nebula, MNRAS 118, 379
  55. Levine, E. S., Blitz, L. and Heiles, C. (2006), The Spiral Structure of the Outer Milky Way in Hydrogen, Science 312, 1773
  56. Hawking, S. W. (1974), Black hole explosions?, Nature 248, 30
  57. Hawking, S. W. (1975), Particle Creation by Black Holes, Communications in Mathematical Physics 43, 199
  58. Paris Observatory, Etymological Dictionary of Astronomy: the Hawking temperature, about 6.2 × 10⁻⁸ K for one Sun

The scenes run on the formulas in their readouts. Sizes, wavelengths and times are scaled so they can be seen, and each readout gives the real values. The atoms are drawn from Schrödinger's equation for hydrogen, with their brightness set by eye.