Nuclear Fission vs Fusion

The binding-energy curve

Plot binding energy per nucleon against mass number A, and you get a curve that rises steeply from A = 1, peaks near iron-56 at about 8.79 MeV/nucleon, and falls slowly to about 7.6 MeV/nucleon at uranium-238. Mid-mass nuclei are more tightly bound than either extreme. So:

• Splitting a heavy nucleus (U-235) into two mid-mass fragments increases the average binding energy per nucleon — the freed energy comes out as kinetic energy.
• Joining two light nuclei (D and T) into helium-4 also increases binding energy per nucleon — again, the freed energy is kinetic energy of the products.

Both processes are "downhill" on the curve, just approaching the peak from opposite sides. The energy per event is set by Δm·c²: the products are slightly less massive than the reactants, and the missing mass becomes energy.

  Binding energy per nucleon  (MeV)
  9 │                ⎯⎯⎯ Fe-56 (peak ≈ 8.79)
    │              ⎯⎯⎯⎯⎯
  8 │           ⎯⎯⎯       ⎯⎯⎯⎯⎯⎯
    │         ⎯⎯⎯                ⎯⎯⎯⎯⎯⎯ U-235 (~ 7.6)
  7 │       ⎯⎯
    │     ⎯⎯
  6 │   ⎯⎯
    │  ⎯
  5 │ ⎯
    │⎯ He-4 (~ 7.07)
  4 │
    │── D (1.11), T (2.83)
   ─┴───────────────────────────────────────────►   A
       1   4    50    100    150    200    250

       FUSION  ──►  ──►  ──►  ──►  ──► (climbing to peak)
       PEAK at Fe-56
       FISSION  ◄──  ◄──  ◄──  ◄──     (climbing to peak from right)

How fission works

A neutron strikes a U-235 nucleus and is absorbed, forming an excited U-236 compound nucleus. Within ~ 10⁻¹⁴ s, the elongated excited nucleus pinches off into two unequal fragments — typical mass split is around 95 / 137 — plus 2 or 3 fast neutrons:

      ²³⁵_{92}U  +  n  →  ²³⁶_{92}U*  →  ⁹²_{36}Kr  +  ¹⁴¹_{56}Ba  +  3 n   (one common channel)
                                  →  ⁸⁹_{36}Kr  +  ¹⁴⁴_{56}Ba  +  3 n
                                  →  ⁹³_{38}Sr  +  ¹⁴⁰_{54}Xe  +  3 n
                                  +  many other channels

About 200 MeV is released per fission, distributed roughly as:

• Kinetic energy of fragments: ~ 169 MeV (the bulk; deposited locally as heat)
• Prompt neutrons: ~ 5 MeV
• Prompt gammas: ~ 7 MeV
• Beta and gamma from short-lived fission products: ~ 19 MeV

The 2–3 neutrons are the basis of the chain reaction. If on average more than one neutron from each fission triggers another fission (k_eff > 1), the reaction grows; if exactly one (k_eff = 1), the reaction is critical and self-sustaining; if less (k_eff < 1), it dies out. Reactors operate at k_eff ≈ 1 with control rods adjusting reactivity in real time. Weapons rely on a brief supercritical phase (k_eff > 1) before the assembly disperses.

Worked example: ²³⁵U mass defect

For the reaction ²³⁵U + n → ⁹²Kr + ¹⁴¹Ba + 3n, atomic masses (in u, where 1 u = 931.494 MeV/c²):

      Reactants:  m(²³⁵U) + m(n)        = 235.04393 + 1.00867   = 236.05260 u
      Products:   m(⁹²Kr) + m(¹⁴¹Ba) + 3·m(n)
                                        = 91.92616 + 140.91440 + 3·1.00867
                                        = 235.86657 u
      Mass defect:                       Δm = 0.18603 u
      Energy:     Q = Δm · 931.494 MeV/u = 173 MeV (this channel)

Other fission channels release between 170 and 190 MeV directly; the additional ~ 20 MeV from beta/gamma decay of fission products brings the total to ~ 200 MeV per fission. The ~ 0.08 % of mass converted is more than 50 million times the energy per atom from chemical combustion.

Per kilogram of U-235:

      Atoms in 1 kg = 6.022 × 10²³ / 0.235 = 2.56 × 10²⁴
      Energy        = 2.56 × 10²⁴ × 200 × 1.602 × 10⁻¹³ J
                    ≈ 8.2 × 10¹³ J
                    ≈ 23 GWh
                    ≈ energy of 2,700 metric tons of coal

How fusion works

Two light nuclei must approach close enough (~ 1 fm) for the strong nuclear force to capture them, but they share positive charge and repel via Coulomb interaction. The Coulomb barrier for D + T fusion is about 0.4 MeV; thermal energies sufficient to give a meaningful tunneling probability correspond to plasma temperatures of about 10⁸ K (10 keV). At these temperatures, atoms are fully ionized into a plasma of bare nuclei and free electrons.

The most accessible fusion reaction is D-T:

      ²_{1}H  +  ³_{1}H  →  ⁴_{2}He  +  n   +  17.6 MeV

The 17.6 MeV is split: 14.1 MeV to the neutron (carries 80 % of the energy out of the plasma; absorbed in the surrounding "blanket" to heat coolant and breed tritium) and 3.5 MeV to the alpha particle (stays in the plasma, helps maintain temperature — the "alpha heating" critical for self-sustaining burn).

Other fusion reactions:

      D + D → ³He + n + 3.27 MeV (50 % branch)
      D + D → T + p + 4.03 MeV (50 % branch)
      D + ³He → ⁴He + p + 18.35 MeV     (aneutronic — no neutron output, but harder ignition)
      p + ¹¹B → 3·⁴He + 8.7 MeV         (aneutronic; very hard, but tritium-free)

D-T is the easiest because its cross-section peaks at about 70 keV plasma temperature with a particularly favorable resonance. D-D needs about 5× higher temperature, and aneutronic reactions need 10–100×.

Worked example: D-T mass defect

      Reactants:  m(²H) + m(³H)         = 2.01410 + 3.01605 = 5.03015 u
      Products:   m(⁴He) + m(n)         = 4.00260 + 1.00867 = 5.01127 u
      Mass defect:                       Δm = 0.01888 u
      Energy:     Q = Δm · 931.494 MeV  = 17.59 MeV

Per nucleon, that's 17.59 / 5 ≈ 3.5 MeV — about four times the 0.85 MeV/nucleon of fission. That ratio is why fusion is sometimes described as "more efficient" — but fission's edge is the easier trigger, larger absolute energy per event, and smaller per-watt fuel volume in practice.

Per kilogram of D-T mix (in 2:3 mass ratio):

      Atoms / kg = 6.022 × 10²³ / 0.005 = 1.20 × 10²⁶
      Energy     = 1.20 × 10²⁶ × 17.6 × 1.602 × 10⁻¹³ J
                ≈ 3.4 × 10¹⁴ J
                ≈ 94 GWh per kg

About 4× the per-kg energy of fission, with a fuel that's also far more abundant — deuterium from seawater, tritium bred from lithium.

Fission vs Fusion side by side

	Fission	Fusion
Reaction direction on binding curve	Heavy nucleus → mid-mass fragments (climbing left)	Light nuclei → helium (climbing right)
Canonical fuels	²³⁵U (0.72 % natural U), ²³⁹Pu (bred), ²³³U (Th-bred)	D (0.015 % of natural H), T (bred from ⁶Li), ³He (rare)
Trigger	Thermal neutron (no Coulomb barrier)	~ 100 million K plasma (overcome Coulomb)
Energy per event	~ 200 MeV	17.6 MeV (D-T)
Energy per nucleon	~ 0.85 MeV	~ 3.5 MeV
Energy per kg of fuel	~ 23 GWh / kg ²³⁵U	~ 94 GWh / kg D-T mix
By-products	Two heavy fission fragments + 2–3 neutrons + radioactive decay products	⁴He + 14.1 MeV neutron (D-T) — no fission products
Long-lived waste	Cs-137, Sr-90, I-129, Tc-99, transuranics — tens of thousands of years	Activated reactor structure (decades-century scale, no transuranics)
Self-sustaining mechanism	Neutron chain reaction, k_eff ≥ 1	Alpha heating (D-T), ignition condition n·τ_E·T > ~ 3 × 10²¹
Working examples	440 power reactors (~ 380 GWe global); naval propulsion; weapons	None at grid scale yet; NIF achieved scientific gain Q = 1.5 (Dec 2022); ITER targets Q = 10
Failure mode	Loss-of-coolant melt (Three Mile Island, Fukushima); supercritical excursion (Chernobyl)	Plasma disruption — quenches itself, no runaway

Real-world fission

• Hiroshima Little Boy (1945). Gun-type uranium weapon, ~ 64 kg of U-235 enriched to ~ 80 %. About 1.4 % of the fissile material actually fissioned. Yield ~ 15 kt TNT (6.3 × 10¹³ J). The first fissile bomb used in war.
• Nagasaki Fat Man (1945). Implosion plutonium weapon, ~ 6.4 kg of Pu-239. Compressed to supercriticality by an explosive lens. Yield ~ 21 kt TNT. Implosion was needed because reactor-bred Pu-240 spontaneously fissions and would predetonate a slow gun-type assembly.
• Light-water reactors. Fuel: U enriched to 3–5 % U-235 in UO₂ pellets. Coolant doubles as moderator (slows fast neutrons to thermal energies where U-235 cross-section peaks at ~ 580 barns). Output: typical 1 GW electrical from a 3 GW thermal reactor. Worldwide fleet ~ 380 GWe.
• Chernobyl (26 Apr 1986). RBMK-1000 graphite-moderated reactor; positive void coefficient meant that loss of cooling water increased reactivity. Operator error during a low-power test pushed the reactor supercritical; runaway power surge to ~ 30 GW (10× rated) destroyed the core. Cs-137 and Sr-90 contamination dominates today (40 years later, Cs-137 at ~ 40 % of 1986 levels).
• Fukushima Daiichi (11 Mar 2011). Tōhoku earthquake plus 14 m tsunami knocked out diesel-generator backup; loss of coolant in three BWR units led to fuel melt and hydrogen explosions. No prompt criticality (unlike Chernobyl); contamination dominated by I-131 (short-term) and Cs-137 (long-term).
• Spent fuel. A typical 1 GWe reactor produces ~ 30 t of spent fuel per year. About 96 % is unburned U; 1 % is plutonium; 3 % is fission products. Long-term geological storage (Onkalo in Finland, the only operating one) targets 100,000-year containment.

Real-world fusion

• The Sun. p-p chain (3 steps) at core temperature ~ 15 million K, density ~ 150 g/cm³. Gravitational confinement; energy from each He-4 produced is ~ 26.7 MeV. Solar luminosity ~ 3.86 × 10²⁶ W requires ~ 4 × 10³⁸ p-p reactions per second.
• Hydrogen bomb (Ivy Mike, 1952). Two-stage Teller-Ulam design. Fission primary (Pu-239) compresses and ignites a fusion secondary (lithium-6 deuteride; ⁶Li + n → T + ⁴He breeds tritium in situ). Yield: 10.4 megatons. Modern thermonuclear warheads use the same physics at smaller scale.
• ITER (under construction, France). Tokamak with major radius 6.2 m, plasma volume 840 m³. D-T fuel, plasma temperature ~ 150 million K, magnetic field ~ 5.3 T from superconducting Nb₃Sn coils. Target: 500 MW thermal output for 50 MW heating — Q = 10 — for 400 s. First plasma now scheduled for 2034.
• NIF (Lawrence Livermore). Inertial confinement: 192 lasers deliver 2 MJ in 20 ns onto a deuterium-tritium pellet, compressing it 1,000× to a few hundred g/cm³ for ~ 10⁻¹¹ s. December 2022 shot delivered 2.05 MJ in, 3.15 MJ out — first scientific net gain (Q_target = 1.5; Q_grid is far less because lasers consume ~ 300 MJ).
• JET (Joint European Torus, decommissioned 2023). Predecessor to ITER. 1997 record D-T pulse: 16 MW peak fusion power for 0.85 s; Q ≈ 0.67. Demonstrated tritium handling and D-T plasma physics that informed ITER design.
• Cold fusion (Pons-Fleischmann, 1989). Claim of room-temperature fusion in palladium electrodes; never reproduced under controlled conditions; widely regarded as artifact (palladium loading and electrochemistry, not fusion).

D-T cross-section sketch

  σ (barns)
  10 │
     │             ●●●  peak ~ 5 barns at ~ 70 keV
   1 │           ●●   ●●
     │         ●●        ●●
  0.1│       ●●            ●●●
     │    ●●                    ●●●
  0.01│  ●                          ●●●
     │ ●                                 ●●●●●
     ●                                          ●●●●●●●●
     ─┴───────────────────────────────────────────► E (keV)
       1     10     100    1000   10000

   Cross-section rises steeply from threshold, peaks around 70 keV
   (corresponding to ~ 100 million K Maxwellian plasma), then falls.
   D-D peaks at ~ 1 barn near 1 MeV — much harder to ignite.

Common misconceptions

• "Fusion has no waste." Fusion produces no fission products and no transuranics — but the 14.1 MeV neutrons activate reactor structural materials (vanadium, tungsten, steel). Waste lifetime is decades to a few centuries, far less than fission, but not zero.
• "You need a lot of U-235 for criticality." The bare-sphere critical mass of pure U-235 is ~ 52 kg. With a beryllium reflector (which bounces neutrons back into the assembly) it drops to ~ 25 kg. For Pu-239 it's ~ 11 kg bare, ~ 5–6 kg reflected. Modern weapons use these reflected configurations.
• "E = mc² is unique to fission/fusion." E = Δm·c² applies to every reaction — even chemical combustion has a tiny mass defect. Chemistry's mass defect is ~ 10⁻¹⁰ of the reactants (eV per atom out of GeV rest mass); nuclear reactions have ~ 10⁻³ mass defect, hence the ~ 10⁷ × energy density.
• "Fission requires only U-235." Pu-239 (bred from U-238 + n) and U-233 (bred from Th-232 + n) are also fissile. India's three-stage program targets thorium fuel cycle. Naval reactors and some research reactors use highly enriched U-235.
• "Fusion ignition was achieved in 2022 at NIF." Strictly, NIF achieved scientific net gain (output exceeds laser energy delivered to the target) but not engineering breakeven (the lasers themselves consume ~ 100× more from the wall plug). Both metrics matter for power reactors.
• "Tritium is radioactive so D-T fusion is dirty." Tritium has half-life 12.3 years, decays β⁻ (low-energy electron, blocked by skin). D-T reactors will produce tritium in situ from ⁶Li + n → ⁴He + T, so no shipping of significant tritium is required. Inventory at any time is small (a few kg in a power plant).
• "Iron-56 is the most stable nucleus." Slightly more bound is nickel-62 (8.794 MeV/nucleon vs Fe-56's 8.790). The peak is broad and the choice depends on subtle pairing. Stellar nucleosynthesis ends at iron-group elements because alpha-fusion past Si-28 produces them in stellar burning; further synthesis requires the more energetic conditions of supernovae and neutron-star mergers (r-process for elements heavier than iron).