Chemistry 2e · Nuclear Chemistry
Transmutation and Nuclear Energy
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Transmutation Changing one element into another by altering the nucleus Full entry → is the conversion of one element into another. It happens naturally whenever a radioactive nucleus decays, and it can also be forced: scientists fire accelerated particles at target nuclei, and when a projectile sticks, the target becomes a new nuclide — sometimes an element that does not exist naturally on Earth. Induced transmutation is how every synthetic element from neptunium (element 93) to the newest superheavy elements was created.
The same nuclear forces that drive transmutation explain the enormous energies of nuclear Fission Splitting a heavy nucleus into two medium fragments plus neutrons Full entry → and Fusion Combining two light nuclei into a heavier nucleus Full entry →. Einstein's E = mc2 says mass and energy are interchangeable: when a nucleus forms or splits, a small loss of mass appears as a large release of energy because the conversion factor c2 is enormous. This topic connects the bookkeeping of nuclear equations to the physics of Binding energy Energy holding a nucleus together, Eb = Δm c2 Full entry →, and it explains both nuclear reactors and the Sun.
Why this matters
Nuclear energy supplies a substantial share of the world's electricity, and its fuel cycle — mining, enrichment, reactor operation, and waste storage — is built on transmutation chemistry. Medical isotopes are manufactured by bombardment reactions in cyclotrons and reactors. Binding energy explains why fission of heavy nuclei and fusion of light nuclei both release energy, while iron sits at the bottom of the energy well. On exams, transmutation problems test balanced nuclear equations with an added projectile, and energy problems test converting a tiny Mass defect Mass "missing" when nucleons bind Full entry → into a large energy release with E = mc2.
The college version
Core Concepts
Natural and induced transmutation
Natural transmutation is radioactive decay: uranium-238 becomes thorium-234, which continues decaying down the chain to lead-206. Induced transmutation needs outside help. In 1919, Ernest Rutherford fired alpha particles at nitrogen gas and produced oxygen-17 plus a proton — the first human-made transmutation. In 1934, Irène and Frédéric Joliot-Curie bombarded aluminum-27 with alpha particles to make phosphorus-30, the first artificially produced radioisotope:
2713Al + 42He → 3015P + 10n
Modern bombardment uses particle accelerators to give projectiles enough speed to overcome the electric repulsion of the target nucleus. Firing neutrons (which carry no charge) is easier, which is why reactors use neutron capture; but making elements heavier than uranium generally requires charged-ion beams from accelerators.
Balancing bombardment equations
A bombardment equation balances exactly like a decay equation: total mass numbers on the left must equal those on the right, and total atomic numbers must match. To find an unknown product, sum the left side and subtract the known right-side particles. The 1950 reaction that first made californium-245 from curium:
24296Cm + 42He → 24598Cf + 10n
Check mass numbers: 242 + 4 = 246 = 245 + 1. Check charges: 96 + 2 = 98 = 98 + 0. Both numbers must balance, so the unknowns solve uniquely.
Mass defect and binding energy
The mass of a stable nucleus is measurably less than the sum of the masses of its separate protons and neutrons. This missing mass is the mass defect, Δm, and it represents the energy released when the nucleons bind. Using E = mc2, the binding energy of a nucleus is
Eb = Δm c2
Because nuclear masses are tiny, energy is reported in mega-electronvolts (MeV), using the conversion 1 amu = 931.5 MeV/c2:
Eb = Δm × 931.5 MeVamu
Dividing total binding energy by the number of nucleons gives the Binding energy per nucleon Binding energy divided by nucleon count Full entry →. A plot of this quantity against mass number rises steeply to a broad peak near iron-56 (about 8.8 MeV per nucleon) and then falls slowly. Two consequences follow: heavy nuclei can release energy by splitting (fission), and light nuclei can release energy by merging (fusion), because both move toward the peak.
Nuclear fission
In fission, a heavy nucleus absorbs a neutron and splits into two medium-mass fragments plus extra neutrons. A typical uranium-235 fission:
23592U + 10n → 14156Ba + 9236Kr + 3 10n
Each fission releases roughly 200 MeV — tens of millions of times a typical chemical reaction — mostly as kinetic energy of the fragments and gamma rays. The extra neutrons can trigger further fissions, creating a Chain reaction Self-sustaining sequence where fission neutrons trigger more fissions Full entry →. In a reactor, the chain is deliberately controlled: a moderator slows neutrons to make them easier to capture, control rods absorb excess neutrons, and coolant removes the heat that boils water to drive turbines. Building or operating reactors belongs in supervised power-plant and laboratory settings, not in casual practice.
Nuclear fusion
In fusion, two light nuclei combine into a heavier one. The easiest fusion on Earth combines deuterium and tritium, isotopes of hydrogen:
21H + 31H → 42He + 10n
This reaction releases about 17.6 MeV per event. Because both nuclei are positively charged, they repel each other; fusion requires temperatures of tens of millions of kelvin to give nuclei enough speed to collide. That is why fusion powers the Sun (hydrogen fusing to helium) and why controlled fusion on Earth — in tokamaks and laser facilities — remains a major engineering challenge. Fusion produces little long-lived radioactive waste and cannot sustain a runaway chain reaction, but holding those extreme conditions is hard.
How It Works / Step-by-Step Process
- Write the bombardment equation with target and projectile on the left and known products on the right.
- Add the mass numbers on the left; subtract known right-side mass numbers to find the unknown nuclide's A.
- Repeat for charges to identify the unknown element; confirm both sides balance.
- For energy problems, find Δm by subtracting product masses from reactant masses (or nucleon sums minus the nucleus mass).
- Convert Δm in amu to energy with E = Δm × 931.5 MeV/amu, and divide by nucleon count for per-nucleon values.
Common Confusions
| Do not confuse | With | Difference |
|---|---|---|
| Transmutation | Chemical reaction | Transmutation changes the nucleus and the element; chemical reactions only rearrange electrons |
| Mass defect | Mass disappearing | Mass is conserved in the E = mc2 sense; the defect appears as binding energy |
| Fission | Fusion | Fission splits a heavy nucleus; fusion merges light nuclei; both move toward the iron peak |
| Binding energy | Chemical bond energy | Nuclear binding energies are millions of times larger (MeV vs. eV) |
| Projectile that "sticks" | Projectile that always bounces off | Only a small fraction of collisions fuse; most are deflected by electric repulsion |
| Nuclear reactor power | Chemical combustion power | Reactors extract nuclear energy via fission; combustion uses electron rearrangement |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Transmutation is like changing one kind of LEGO brick into another by snapping a new piece onto it — a whole new element is born. When a nucleus is built or broken, a little bit of its weight turns into a huge burst of energy, like a tiny magic coin turning into a pile of gold. Fission breaks a big brick into two medium bricks; fusion squishes two small bricks into one bigger one — both ways, energy comes out.
Worked example
Example 1: Binding energy of helium-4
Compute the binding energy and binding energy per nucleon for a helium-4 nucleus. Relevant atomic masses: proton (as in H-1 atom) 1.007825 amu, neutron 1.008665 amu, helium-4 atom 4.00260 amu. The nucleus holds 2 protons and 2 neutrons. First find the mass of the separated parts:
2(1.007825 amu) + 2(1.008665 amu) = 4.03298 amu
The mass defect is the difference:
Δm = 4.03298 amu - 4.00260 amu = 0.03038 amu
Now convert mass to energy using the formula before substituting:
Eb = Δm × 931.5 MeVamu = (0.03038 amu)(931.5 MeVamu) = 28.3 MeV
Per nucleon, divide by 4:
EbA = 28.3 MeV4 nucleons = 7.07 MeVnucleon
Helium-4 is unusually tightly bound — which is why alpha particles are emitted intact during decay.
Example 2: Energy from one gram of uranium-235
Each U-235 fission releases about 200 MeV. How much energy does the fission of 1.00 g of U-235 release? This is a dimensional-analysis problem. Convert step by step:
1.00 g U-235 × 1 mol235 g × 6.022 × 1023 nuclei1 mol × 200 MeV1 nucleus × 1.602 × 10-13 J1 MeV
Grams, moles, and nuclei cancel, leaving joules:
(1.00)(4.26 × 10-3)(6.022 × 1023)(200)(1.602 × 10-13) J = 8.2 × 1010 J
So 1 g of U-235 releases about 8 × 1010 J — comparable to burning roughly three tonnes of coal. The mass converted per fission is 200/931.5 ≈ 0.21 amu, less than one electron's mass per nucleus, yet the cumulative effect is enormous.
Example 3: Identifying an unknown product
Bombarding uranium-238 with carbon-12 nuclei produces californium-246 and neutrons. Left side: 238 + 12 = 250 mass units and 92 + 6 = 98 charge units. Let the number of neutrons be x; then 250 = 246 + x, so x = 4:
23892U + 126C → 24698Cf + 4 10n
The reaction balances with four neutrons, consistent with heavy-ion synthesis of californium-246.
Key takeaways
- Transmutation = one element becomes another, by decay (natural) or bombardment (induced).
- Balance bombardment equations by conserving mass number A and charge Z on both sides.
- Mass defect Δm = (separate nucleon masses) − (actual nucleus mass).
- Binding energy: Eb = Δm c2; in amu units multiply by 931.5 MeV/amu.
- Binding energy per nucleon peaks near iron-56 (~8.8 MeV/nucleon).
- Fission: U-235 + n → Ba-141 + Kr-92 + 3n, ~200 MeV per event; chain reactions are controlled by moderators and control rods.
- Fusion: D + T → He-4 + n, ~17.6 MeV; needs extreme temperatures to overcome repulsion.
- E = mc2: tiny masses convert to enormous energies because c2 is huge.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
Balance the reaction: 94Be + 42He → 126C + ?. What is the missing particle?
Show answer
Mass numbers: 9 + 4 = 13 on the left; 12 + ? = 13, so the particle has A = 1. Charges: 4 + 2 = 6 = 6 + ?, so Z = 0. The particle is a neutron, 10n. (This is the 1932 reaction in which James Chadwick discovered the neutron.)
Why is iron-56 at the peak of the binding-energy-per-nucleon curve, and what does that imply for fission and fusion?
Show answer
Iron-56 has the highest binding energy per nucleon (~8.8 MeV), so it is the most stable nucleus. Heavier nuclei release energy by fission (moving down toward iron); lighter nuclei release energy by fusion (moving up toward iron).
Which releases more energy per event, one U-235 fission (~200 MeV) or one D-T fusion (~17.6 MeV)? Why is fusion still attractive?
Show answer
Fission releases about ten times more energy per event, but fusion fuel (hydrogen isotopes) is abundant, produces little long-lived radioactive waste, and cannot sustain a runaway chain reaction — hence its appeal, despite the difficulty of achieving the required temperatures.
A nucleus has a mass defect of 0.00200 amu. What is its binding energy in MeV?
Show answer
Eb = Δm × 931.5 MeV/amu = (0.00200)(931.5) = 1.86 MeV.
Why must fission neutrons be slowed (moderated) in a reactor?
Show answer
Slow (thermal) neutrons are captured far more readily by U-235 than fast neutrons, so moderating keeps the chain reaction self-sustaining at controllable power levels.
How does induced transmutation differ from natural radioactive decay?
Show answer
Natural transmutation occurs spontaneously in unstable nuclei; induced transmutation requires a projectile and external energy, and it is the only way to make elements heavier than uranium and many medical isotopes.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Transmutation
- Changing one element into another by altering the nucleus
- Bombardment reaction
- A nuclear reaction in which an accelerated particle strikes a target nucleus
- Mass defect
- Mass "missing" when nucleons bind
- Binding energy
- Energy holding a nucleus together, Eb = Δm c2
- Binding energy per nucleon
- Binding energy divided by nucleon count
- Fission
- Splitting a heavy nucleus into two medium fragments plus neutrons
- Fusion
- Combining two light nuclei into a heavier nucleus
- Chain reaction
- Self-sustaining sequence where fission neutrons trigger more fissions
Sources & references
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