What is the difference between fission and fusion in terms of energy per unit mass?

Fission of U-235: ~8.2 × 10¹³ J/kg (8.2 × 10¹⁰ J/g). D-T fusion: ~3.4 × 10¹⁴ J/kg - approximately 4 times more energy per kg than uranium fission. However, per fission event, U-235 releases ~200 MeV while D-T fusion releases only ~17.6 MeV per reaction. The higher per-mass energy of fusion comes from the much lower mass of the fuel (deuterium + tritium molar mass ~5 g/mol vs U-235 at 235 g/mol).

What is nuclear decay heat and why does it matter for reactor safety?

Decay heat is the heat produced by beta and gamma decay of fission products after the chain reaction stops. It accounts for about 7% of reactor power immediately after shutdown, dropping to ~1% after 1 hour and ~0.1% after 1 day. Decay heat is why reactor cooling must continue after shutdown - it was the cause of the Fukushima Daiichi disaster (2011), where loss of cooling after reactor shutdown led to core meltdown. The Wigner-Way formula estimates decay heat: P(t)/P₀ ≈ 0.066 × (t⁻⁰·² − (t + T)⁻⁰·²).

What is the critical mass of uranium-235 and plutonium-239?

Critical mass is the minimum amount of fissile material needed to sustain a chain reaction. For U-235 bare sphere: ~52 kg. With beryllium reflector: ~15 kg. For Pu-239 bare sphere: ~10 kg; with reflector: ~4 kg. Plutonium has a higher fission probability (cross-section) than U-235, requiring less mass. These values are open-literature estimates; weapons design uses implosion to compress the material above critical density, reducing required mass significantly.

What is the difference between nuclear fission and radioactive decay?

Radioactive decay is spontaneous - a nucleus transforms with no external trigger, emitting alpha, beta, or gamma radiation. It involves one nucleus at a time and cannot chain-react. Nuclear fission (especially of U-235, Pu-239) is triggered by neutron absorption - the compound nucleus oscillates and splits into two medium-mass fragments + 2–3 neutrons. These neutrons can trigger more fissions (chain reaction). Fission releases ~50–100 million times more energy per event than typical radioactive decay.

What is a chain reaction and what is the criticality condition?

A chain reaction occurs when each fission event produces at least one neutron that triggers another fission. The criticality condition is k = 1 (exactly critical): on average each fission produces exactly 1 subsequent fission. k > 1 is supercritical (weapons, prompt criticality accidents). k < 1 is subcritical (no self-sustaining chain reaction). The multiplication factor k depends on the fission cross-section, neutron capture probability, geometry, and neutron moderator/reflector. Reactor control rods absorb neutrons to maintain k = 1.

What is the energy equivalent of 1 kilogram of uranium-235 fully fissioned?

One kilogram of U-235 fully fissioned releases approximately 8.2 × 10¹³ joules = 82 terajoules. Equivalences: ~19,600 tonnes of TNT; ~22.8 GWh of electrical energy (at 100% conversion); ~2.7 million kg of coal equivalent; ~57 million cubic feet of natural gas equivalent. In practice, nuclear power plants convert fission heat to electricity at ~33% efficiency, so 1 kg U-235 yields ~7.5 GWh of electricity.

Nuclear Fission Energy Calculator

Q: What is the Q-value of a nuclear reaction and how is it calculated?

The Q-value is the energy released (positive Q) or absorbed (negative Q) in a nuclear reaction. It equals the mass defect converted to energy: Q = (sum of reactant masses − sum of product masses) × 931.494 MeV/u. A positive Q means the products have less mass than the reactants - the difference has become kinetic energy of the products. For U-235 fission: Q = (M_U235 + M_neutron) − (M_Ba141 + M_Kr92 + 3×M_neutron) ≈ 200 MeV.

Q: How much energy is released in uranium-235 fission?

A single U-235 fission event releases approximately 202 MeV (about 3.23 × 10⁻¹¹ J). This includes ~168 MeV kinetic energy of fission fragments, ~5 MeV prompt neutron kinetic energy, ~7 MeV prompt gamma rays, and ~12 MeV from subsequent beta/gamma decay of fission products. Per kilogram of U-235, assuming complete fission: approximately 8.2 × 10¹³ J - equivalent to ~19,600 tonnes of TNT.

Q: What are the typical fission products of uranium-235?

U-235 fission does not always produce the same fragments - there is a distribution of fragment masses peaking around A ≈ 95 and A ≈ 138 (asymmetric fission). Common fragment pairs include Ba-141 + Kr-92, Cs-137 + Rb-96, I-131 + Y-103. The most probable neutron yield is 2.43 neutrons per thermal fission (ν̄). The fission product yield is described by a double-humped distribution known as the fission yield curve.

Q: How does a nuclear reactor differ from a nuclear bomb?

Both use the U-235 or Pu-239 fission chain reaction. A reactor maintains k = 1 (controlled, steady power) by using fuel with low enrichment (~3–5% U-235 for commercial reactors), a moderator (water, graphite) to slow neutrons, and control rods (boron, hafnium) to absorb excess neutrons. Reactors operate on delayed neutrons (0.65% of fissions, emitted seconds after fission), making them controllable. A bomb requires highly enriched fuel (>90% U-235 or >90% Pu-239), achieves supercriticality (k >> 1) in microseconds via implosion or gun assembly, and relies on prompt neutrons - the entire chain reaction completes before the material blows apart.

Q: What is the energy equivalent of 1 kilogram of uranium-235 fully fissioned?

One kilogram of U-235 fully fissioned releases approximately 8.2 × 10¹³ joules = 82 terajoules. Equivalences: ~19,600 tonnes of TNT; ~22.8 GWh of electrical energy (at 100% conversion); ~2.7 million kg of coal equivalent; ~57 million cubic feet of natural gas equivalent. In practice, nuclear power plants convert fission heat to electricity at ~33% efficiency, so 1 kg U-235 yields ~7.5 GWh of electricity.

Calculate the Q-value energy released per nuclear fission event from atomic masses. Scale to joules per gram and kiloton-TNT equivalent.

Reaction: ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n | masses in atomic mass units (u, AME2020)

Reactant Masses (u)enter all reactants

Reactant 1 (e.g. U-235)

Reactant 2 (e.g. neutron)

Product Masses (u)enter all products, leave unused fields as 0

Product 1 (e.g. Ba-141)

Product 2 (e.g. Kr-92)

Product 3 (e.g. 3n combined)

Product 4 (0 if unused)

Fissile Fuel Molar Massg/mol - for per-gram/kg scaling

💥 What is Nuclear Fission Energy?

Nuclear fission is the process by which a heavy atomic nucleus (typically uranium-235 or plutonium-239) absorbs a neutron and splits into two lighter nuclei (fission fragments), releasing 2–3 neutrons and an enormous amount of energy. The energy comes from the mass defect between the reactants and products: the fragments weigh slightly less than the original nucleus plus neutron, and this mass difference - via Einstein's E = mc² - manifests as kinetic energy of the fragments, neutron energy, and gamma radiation.

Fission was discovered by Otto Hahn, Fritz Strassmann, Lise Meitner, and Otto Frisch in 1938–1939. Meitner and Frisch provided the theoretical explanation: the compound nucleus formed by neutron capture oscillates and deforms until the electrostatic repulsion between the two forming fragments overcomes the surface tension of the strong nuclear force, and the nucleus splits. They calculated an energy release of about 200 MeV - confirmed experimentally immediately. This discovery triggered the Manhattan Project and the first nuclear reactor (Chicago Pile-1, Enrico Fermi, December 2, 1942).

A single U-235 fission event releases approximately 202 MeV (3.2 × 10⁻¹¹ J). While small, the sheer number of atoms in macroscopic quantities makes this enormous in aggregate. One kilogram of U-235 contains 2.56 × 10²⁴ atoms. If all fission, total energy = 2.56 × 10²⁴ × 3.2 × 10⁻¹¹ J = 8.2 × 10¹³ J - equal to about 20,000 tonnes of TNT, or enough to power a 1 GW power station for 82 seconds continuously.

This calculator computes the Q-value from the mass difference between all reactants and all products, using the exact AME2020 atomic masses. It then scales to energy per gram and per kg of fissile material, and computes the kiloton-TNT equivalent. It applies to any fission reaction where the reactant and product masses are known - not just uranium - making it useful for reactor physics coursework, nuclear engineering studies, and JEE/NEET modern physics problems.

📐 Formula

Q-Value from Mass Defect:

Q = (∑M_reactants − ∑M_products) × 931.494 MeV/u

∑M_reactants = sum of atomic masses of all reactants (u)

∑M_products = sum of atomic masses of all products (u)

931.494 MeV/u = energy equivalent of 1 atomic mass unit (CODATA 2018)

Positive Q → exothermic reaction (energy released); negative Q → endothermic

Example: ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n

Reactants: 235.043930 + 1.008665 = 236.052595 u

Products: 140.914411 + 91.926156 + 3 × 1.008665 = 236.866562 u

Δm = 236.052595 − 232.866562 ≈ 0.18604 u → Q ≈ 173.3 MeV (prompt only)

Energy per gram of fuel:

E/g = Q(J) × N_A / M_molar

N_A = Avogadro's number = 6.02214076 × 10²³ mol⁻¹

M_molar = molar mass of fissile fuel (g/mol)

TNT equivalent: 1 kiloton TNT = 4.184 × 10¹² J

📖 How to Use This Calculator

Select a preset reaction (U-235 + n or Pu-239 + n) or choose Custom to enter your own masses.

Enter the reactant masses in atomic mass units (u). Use the free neutron mass = 1.008665 u.

Enter the product masses. For multiple neutrons, multiply: e.g. 3 neutrons = 3 × 1.008665 = 3.025995 u.

Enter the fuel molar mass (235 for U-235, 239 for Pu-239) for per-gram/kg scaling.

Click Calculate - results show Q-value in MeV and J, energy density, and TNT equivalent.

💡 Example Calculations

Example 1 - Uranium-235 fission (Ba-141 + Kr-92 channel)

²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n. Masses: U-235 = 235.043930 u, n = 1.008665 u, Ba-141 = 140.914411 u, Kr-92 = 91.926156 u

∑M_reactants = 235.043930 + 1.008665 = 236.052595 u

∑M_products = 140.914411 + 91.926156 + 3 × 1.008665 = 236.866562 u

Δm = 236.052595 − 236.866562 = −0.000033 u - wait, let's recalculate: ∑products = 140.914411 + 91.926156 + 3.025995 = 235.866562 u

Δm = 236.052595 − 235.866562 = 0.186033 u

Q = 0.186033 × 931.494 = 173.3 MeV (prompt; total ~202 MeV including delayed decay)

Q-value: 173.3 MeV per fission | Energy per kg U-235: ~7.1 × 10¹³ J

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Example 2 - Plutonium-239 fission (Ba-144 + Sr-94 channel)

²³⁹Pu + n → ¹⁴⁴Ba + ⁹⁴Sr + 2n. Masses: Pu-239 = 239.052163 u, Ba-144 = 143.922953 u, Sr-94 = 93.915361 u

∑M_reactants = 239.052163 + 1.008665 = 240.060828 u

∑M_products = 143.922953 + 93.915361 + 2 × 1.008665 = 239.855644 u

Δm = 240.060828 − 239.855644 = 0.205184 u

Q = 0.205184 × 931.494 = 191.2 MeV

Q-value: 191.2 MeV per fission | ~20% more than this U-235 channel

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Example 3 - Thorium-232 capture + Pa-233 decay (reactor breeding)

²³²Th + n → ²³³Th + γ. Q-value from mass capture. M(Th-232) = 232.038055 u, M(Th-233) = 233.041581 u

∑M_reactants = 232.038055 + 1.008665 = 233.046720 u

∑M_products = 233.041581 u (Th-233, gamma has negligible mass)

Δm = 233.046720 − 233.041581 = 0.005139 u

Q = 0.005139 × 931.494 = 4.79 MeV (gamma emission energy)

Capture Q-value: 4.79 MeV - this is the neutron capture that starts the thorium fuel cycle

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Frequently Asked Questions

What is the Q-value of a nuclear reaction and how is it calculated?+

The Q-value is the energy released (positive Q) or absorbed (negative Q) in a nuclear reaction: Q = (sum of reactant masses − sum of product masses) × 931.494 MeV/u. Positive Q means exothermic - products weigh less and the mass difference becomes kinetic energy and radiation. For U-235 + n → Ba-141 + Kr-92 + 3n, Q ≈ 173 MeV (prompt energy).

How much energy is released in uranium-235 fission?+

A single U-235 fission releases approximately 202 MeV total (3.23 × 10⁻¹¹ J): ~168 MeV kinetic energy of fragments, ~5 MeV prompt neutrons, ~7 MeV prompt gamma, ~12 MeV from delayed beta/gamma decay. Per kilogram, assuming complete fission: ~8.2 × 10¹³ J, equivalent to ~19,600 tonnes of TNT or ~22.8 GWh of electricity at 100% conversion.

What are the typical fission products of uranium-235?+

U-235 fission produces a distribution of fragment pairs. The most likely fission yields have a double-humped distribution peaking around A ≈ 95 (light fragment) and A ≈ 138 (heavy fragment). Common pairs: Ba-141 + Kr-92, Cs-137 + Rb-96, I-131 + Y-103, Sr-90 + Xe-144. Average neutron yield is 2.43 per thermal fission. Most fragments are neutron-rich and decay by beta emission.

What is the difference between fission and fusion energy per unit mass?+

U-235 fission: ~8.2 × 10¹³ J/kg. D-T fusion: ~3.4 × 10¹⁴ J/kg - about 4× more per kg of fuel. The higher mass-specific energy of fusion arises from the low molar mass of D+T (~5 g/mol vs 235 g/mol for U-235). Per event, U-235 fission (~202 MeV) releases far more energy than D-T fusion (~17.6 MeV) because the heavier nuclei have a larger mass defect.

What is nuclear decay heat and why is it a safety concern?+

After a reactor shuts down, fission products continue decaying, producing heat at about 7% of operating power immediately, declining to ~1% after 1 hour. This decay heat must be continuously removed or the fuel melts. It was the root cause of the Fukushima Daiichi meltdowns in 2011, where loss of cooling after tsunami shutdown led to fuel damage despite the reactor having scrammed (shut down).

What is critical mass and how does it work?+

Critical mass is the minimum quantity of fissile material needed to sustain a chain reaction (k = 1). For bare U-235 sphere: ~52 kg. For Pu-239: ~10 kg. With reflectors (beryllium, water), critical mass is reduced significantly (to ~15 kg for U-235 with Be). Below critical mass (k < 1), neutrons escape faster than they create fissions and the chain reaction dies. Weapons use implosion to rapidly compress material above critical density.

How does a nuclear reactor differ from a nuclear bomb?+

A reactor uses low-enriched fuel (3–5% U-235), a moderator to slow neutrons, and control rods to maintain k = 1 (steady, controlled power). It operates on delayed neutrons (0.65%), making it controllable on a seconds timescale. A bomb uses highly enriched fuel (>90%), achieves k >> 1 in microseconds via implosion, and relies on prompt neutrons - the entire chain reaction occurs before the material blows apart. A reactor cannot explode like a bomb.

What is the energy equivalent of 1 kilogram of U-235 fully fissioned?+

1 kg of U-235 fully fissioned releases ~8.2 × 10¹³ J. Equivalences: ~19,600 tonnes of TNT; ~22.8 GWh of electricity at 100% efficiency; ~2.7 million kg of coal; ~57 million cubic feet of natural gas. A commercial nuclear power plant (1 GW electric, 33% efficiency) burns ~3.1 kg of U-235 per day as fissile material (though the physical fuel loading is much higher due to partial burn-up).

🔗 Related Calculators

📌 Quick Tips

💡A single U-235 fission event releases ~200 MeV (ranging 160–220 MeV depending on fission fragment pair). Per kilogram of fuel, this is about 8.2 × 10¹³ J - equivalent to ~20,000 tonnes of TNT per kg.

💡The Q-value from atomic masses gives the prompt energy (kinetic energy of fragments + prompt neutrons + prompt gamma). An additional ~8–12 MeV per fission comes from beta/gamma decay of fission products over time - the source of nuclear reactor decay heat.

💡Pu-239 fission releases ~210 MeV per event, slightly more than U-235. Pu-239 has a higher fission cross-section than U-235 for thermal neutrons (742 barns vs 585 barns), making it a potent reactor fuel and weapon material.

💡The Nagasaki bomb (Fat Man, Pu-239) released energy equivalent to ~21 kilotons of TNT. The Hiroshima bomb (Little Boy, U-235) released ~15 kilotons. 1 kiloton = 4.184 × 10¹² joules.

💡The mass defect in fission is much smaller than in fusion per unit mass but fission releases more energy per event because it involves heavy nuclei (A ≈ 200–240). Per unit mass, D-T fusion releases ~4 times more energy than U-235 fission.