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FROM QUANTUM STATES TO THE ELECTRIC GRID

Tiny atom.
Big energy.

Explore the physics behind nuclear power.

Find out where an electron might be, watch a nucleus split, and follow the released energy all the way to the electrical grid.

Open the field guide ↓

4 CHAPTERS · INTERACTIVE MODELS · EVERY MOTION HAS A MEANING

The nucleus is about 100,000 times smaller across than an atom. The nucleus marker and zoom are schematic, not drawn to scale. In nuclear diagrams, coral = proton; purple = neutron, whether bound or free.

01 Quantum orbitals ↗ 02 Nuclear fission ↗ 03 Power station ↗ 04 Tiny mass, big energy ↗

01 / TWO SCALES, TWO INTERACTIONS

Let’s go really small.

An atom has a tiny nucleus of protons and neutrons. Electrons are found around it. An orbital is a map of where an electron is more or less likely to be found. The dots below build that map from many possible measurements of one hydrogen electron.

Electrons ↔ nucleus

Negative electrons are attracted to the positive nucleus by the electric force. An orbital shows possible positions; it is not a planet-like path.

Inside the nucleus

Positive protons repel one another, but a short-range nuclear force helps hold protons and neutrons together. Neutrons add to this binding without adding electric repulsion. A nucleus with too many or too few neutrons may be unstable.

FIG. 1.1 / THE ORBITAL VIEWER

A cloud, not a path.

HYDROGEN · ONE ELECTRON

VIEW: ±4 a₀ INITIALIZING INTERACTIVE VIEW…

ψ positive ψ negative Nucleus (enlarged)

One dot = one possible measurement of the same electron. The cloud is not thousands of electrons or an orbiting path.

The two colors mark opposite signs of the mathematical wavefunction ψ, not positive and negative electric charges. The chance of finding the electron comes from |ψ|². The 1s cloud looks the same from every angle; choose 2p or 3d to see a shape change as the view rotates.

2p_z: two lobes and one node

Quantum numbers
Angular nodes
Energy in hydrogen

The number in 1s, 2p, or 3d names an energy level. The letter names a family of shapes; the small subscript tells its direction. eV is a tiny unit of energy.

Show nodal surfaces Camera angle 25°

Build the distribution from measurements. Each dot represents one position measurement on a newly prepared atom in the same state.

3,000 probability samples shown.

Distance from the nucleus

Key idea: The curve shows how likely a measurement is to land at each distance from the nucleus. A wider spherical shell contains more possible positions, so this differs from the chance at one exact point.

For readers who know wavefunctions: the radial probability density is P(r) = r²|R(r)|².

a₀ = 5.29 × 10⁻¹¹ m is a useful distance scale for hydrogen. A node is a place where the chance of finding the electron is zero. The 3D view flattens depth onto a screen, so a dot can appear over a node while actually being in front of or behind it. The nucleus marker is enlarged.

What s, p, and d mean
Subshell	Orbital angular momentum ℓ	Number of orbitals	Representative shapes
s	0	1	Spherically symmetric
p	1	3	Two lobes, with different orientations
d	2	5	Four-lobed shapes, or two lobes and a torus

In atoms with many electrons, an orbital can hold up to two electrons. This viewer shows one electron in hydrogen. Nuclear fission changes the nucleus; ordinary chemical reactions mainly rearrange electrons.

02 / NUCLEAR BINDING, FISSION & CONSERVATION

Follow one nucleus
through the split.

A neutron enters a uranium-235 nucleus. The new nucleus has extra energy, can stretch, and may split. Follow the four pictures to see one possible outcome.

²³⁵₉₂U + ¹₀n → ²³⁶₉₂U* → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n

The small raised numbers count protons plus neutrons; the low numbers count protons. Check: 235 + 1 = 141 + 92 + 3, and 92 = 56 + 36. Gamma rays are left out of this short equation. Other splits are possible.

Proton (+) Neutron (0 charge), bound or free Gamma radiation (γ)

FIG. 2.1

Capture

A ²³⁵U nucleus absorbs a neutron. A neutron has no electric charge, so there is no electric repulsion barrier.

FIG. 2.2

Excitation

The new nucleus, ²³⁶U*, has extra energy. The star means “excited.” It may now split.

FIG. 2.3

Deformation

The excited nucleus stretches. A narrow neck forms between two halves before they separate.

FIG. 2.4

Separation

The two positive pieces repel and fly apart. Neutrons and gamma rays also carry energy away.

Protons + neutrons: 235 + 1 = 141 + 92 + 3 = 236

Protons: 92 = 56 + 36

These balances do not imply equal total rest masses. Nuclear binding changes rest energy.

FIG. 2.5 / FISSION TIMELINE

Watch the split—and the recoil.

SCHEMATIC · TIME STRETCHED

Reaction progress 0%

Capture Excitation Deformation Separation

This animation shows the order of events, not measured paths or reaction times. Real fission also releases neutrons and radiation; their momentum must be included in a complete balance.

Why is energy released?

The new nuclei are generally bound more tightly than uranium. Add the rest masses of both pieces and the released neutrons: the total is a little lower than before. The difference becomes motion and radiation.

Q = (m_initial − Σm_final)c²

Where does the energy go?

A uranium-235 fission yields roughly 200 MeV of heat energy, including heat released later by radioactive fragments. Most immediate energy is in the motion of the two large pieces. As they slow in the fuel, that motion becomes heat.

The exact energy varies by split. Neutrinos carry away some energy that does not heat the reactor. Radioactive fragments keep producing heat after fission stops, so cooling is still needed after shutdown.

03 / FROM NUCLEAR ENERGY TO ELECTRICAL ENERGY

Three water circuits.
One energy journey.

This is a simplified pressurized-water reactor. Follow the colored paths: hot reactor water heats a separate steam loop, and a third water loop cools the used steam. The three water paths stay separate.

How the reactor keeps making heat: One split can release neutrons that trigger more splits. Control rods absorb some neutrons to help control the chain reaction.

FIG. 3.1 / SELECT A STAGE TO TRACE THE TRANSFER

Scroll sideways to see the full diagram →

Follow the energy: split nucleus → hot fuel → hot water → steam → spinning turbine → electricity.

Red = hot reactor water; gold/blue = steam and returning water; green = cooling water. Arrows show flow or energy transfer. Moving dashes show the selected step. The drawing is simplified and not to scale.

FIG. 3.2 / THE ENERGY ACCOUNT

Heat in ≠ electricity out.

Some heat turns the turbine; the rest must move to a cooler place. Change the slider to see how much of 3,000 MW becomes electricity in this example.

Illustrative efficiency η 33%

η = P_electric / P_thermal

Illustrative gross energy budget, not a real plant control. Plant pumps and other internal uses would reduce net electricity delivered.

3,000 MW thermal input

990 MW electricity

2,010 MW rejected heat

Nuclear rest energy → fragment kinetic energy → thermal energy → turbine work → electrical energy.

04 / THE SURPRISING SCALE OF NUCLEAR ENERGY

One split is tiny.
One gram adds up.

When uranium splits, the products have slightly less total rest mass. The difference becomes motion and radiation. Most of that motion ends up as heat in the fuel. How much can many tiny splits add up to?

FIG. 4.1 / FROM ONE ATOM TO ONE GRAM

Zoom in. Then zoom way out.

Switch scales to see why a tiny change in each nucleus can matter so much.

1 grampure U-235 · hypothetical

HEAT ENERGY~23,000kWh

If every U-235 atom in one gram split, the released heat would add up to about 23,000 kilowatt-hours.

AT AN ILLUSTRATIVE 33% ELECTRIC EFFICIENCY~7,500 kWh of electricity

Enough to run a 10-watt LED continuously for about 86 years.

This is an idealized scale comparison: pure U-235, every atom fissioning, about 200 MeV of reactor heat per split, and 33% gross conversion to electricity. A real fuel pellet and power plant have additional limits and losses. The drawing is not to scale.

Show the calculation and the full equation

One fission deposits roughly 200 MeV of heat. One gram of U-235 has about 2.56 × 10²¹ atoms. Multiplying gives about 8.2 × 10¹⁰ J, or 22,800 kWh of heat. At 33%, that is about 7,500 kWh of electricity. The mass equivalent of 200 MeV is about 0.215 atomic mass units per split.

For a moving particle, total energy and momentum satisfy E² = (mc²)² + (pc)². The familiar E = mc² is the at-rest case, when momentum p is zero.

01Count the particles.

Protons and neutrons are accounted for in the split.

02Follow the energy.

A small rest-mass difference becomes motion and radiation.

03Keep the full balance.

Total energy and momentum are conserved.

CONNECT THE SCALES.

Quantum states. Nuclear binding.
Energy and momentum, conserved.

The diagrams are models. The conservation laws keep the explanation honest.

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Read the physics behind the models

Original diagrams and interactive models. Background references:

Tiny atom.Big energy.