Chemistry: Atoms First 2e · Nuclear Chemistry
Transmutation and Nuclear Energy
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transmutation Changing one element into another by altering the nucleus is the conversion of one element into another. It happens naturally every time a radioactive nucleus decays, and it can also be forced: accelerated particles fired at target nuclei can fuse with them to form a new nuclide — sometimes an element that does not occur naturally on Earth. Every synthetic element from neptunium (element 93) onward was created this way, by bombardment reactions.
The same nuclear forces that make transmutation possible also explain the staggering energies of fission Splitting a heavy nucleus into two medium fragments plus neutrons and fusion Combining two light nuclei into a heavier nucleus. Einstein's E = mc2 says mass and energy are interchangeable: when nucleons bind, a small amount of mass is lost and appears as binding energy Energy holding a nucleus together, Eb = Δm c2; when a heavy nucleus splits or two light nuclei merge, that stored energy is released. This topic connects nuclear equations to binding energy and explains both reactors and the Sun.
Why this matters
Nuclear energy supplies a substantial share of the world's electricity, and its fuel cycle is built on transmutation chemistry. Medical isotopes such as technetium-99m are manufactured by bombardment reactions. Binding energy explains why both fission and fusion release energy: both move nuclei toward the binding-energy peak near iron. On exams, expect bombardment equations to balance and energy problems to use 931.5 MeV/amu.
The college version
Core Concepts
Natural and induced transmutation
Natural transmutation is simply radioactive decay: uranium-238 becomes thorium-234, which decays further down the chain to lead-206. Induced transmutation requires outside energy. In 1919, Ernest Rutherford fired alpha particles at nitrogen gas and produced oxygen-17 plus a proton — the first deliberately induced transmutation. In 1934, the Joliot-Curies bombarded aluminum-27 with alpha particles to make phosphorus-30, the first artificial radioisotope:
2713Al + 42He → 3015P + 10n
Modern bombardment uses particle accelerators to give projectiles enough kinetic energy to overcome electric repulsion. Neutrons, being uncharged, are captured much more easily — which is why reactors use neutron capture — but making elements heavier than uranium requires charged-ion beams.
Balancing bombardment equations
A bombardment equation balances exactly like a decay equation: total mass numbers on the left equal those on the right, and total atomic numbers 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-242:
24296Cm + 42He → 24598Cf + 10n
Mass numbers: 242 + 4 = 246 = 245 + 1. Charges: 96 + 2 = 98 = 98 + 0. Both sides balance, so the unknown is unique.
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. That missing mass is the mass defect Mass "missing" when nucleons bind into a nucleus Full entry →, Δm, representing the energy released when the nucleons bind. Using E = mc2, the binding energy is
Eb = Δm c2
Because nuclear masses are tiny, energy is reported in mega-electronvolts (MeV), using
1 amu = 931.5 MeVc2
so the binding energy follows directly from a mass defect in amu:
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. A plot against mass number rises steeply to a broad peak near iron-56 (about 8.8 MeV per nucleon), then falls slowly. Two consequences follow: heavy nuclei can release energy by splitting (fission), and light nuclei 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 U-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 in which fission neutrons trigger more fissions Full entry →. In a reactor the chain is deliberately controlled: a moderator slows neutrons so they are captured more readily, control rods absorb excess neutrons, and coolant carries away the heat that boils water to drive turbines.
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, fusion requires temperatures of tens of millions of kelvin to give nuclei enough speed to collide. That is why fusion powers the Sun and why controlled fusion on Earth remains a major engineering challenge. Fusion produces little long-lived 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 the target and projectile on the left and known products on the right.
- Sum the mass numbers on the left; subtract the known right-side mass numbers to find the unknown nuclide's A.
- Repeat for charges to identify the element; confirm both sides balance.
- For energy problems, find Δm by subtracting product masses from reactant masses.
- Convert Δm to energy with Eb = Δm × 931.5 MeV/amu, then divide by nucleon count for per-nucleon values.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| Transmutation | Chemical reaction | Transmutation changes the nucleus and element; chemical reactions rearrange electrons only |
| 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 rearranges electrons |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Transmutation is like baking: you put specific ingredients (nuclei) together with enough energy and you get a brand-new substance — sometimes one that doesn't exist in nature. When a nucleus is built or broken, a tiny bit of its weight turns into a huge burst of energy, like a coin that melts into a pile of gold. Fission breaks one giant cookie into two medium ones; fusion presses two tiny cookies into one bigger one — both ways, energy comes out.
Worked example
Example 1: Binding energy of lithium-7
Compute the binding energy and binding energy per nucleon for a lithium-7 nucleus (3 protons, 4 neutrons). Masses: proton (H-1 atom) 1.007825 amu, neutron 1.008665 amu, Li-7 atom 7.01600 amu. First find the mass of the separated parts:
3(1.007825 amu) + 4(1.008665 amu) = 3.023475 amu + 4.034660 amu = 7.05814 amu
The mass defect is the difference:
Δm = 7.05814 amu - 7.01600 amu = 0.04214 amu
Convert mass to energy using the formula before substituting:
Eb = Δm × 931.5 MeVamu = (0.04214 amu)(931.5 MeVamu) = 39.25 MeV
Per nucleon, divide by 7:
EbA = 39.25 MeV7 nucleons = 5.61 MeVnucleon
Lithium-7 is less tightly bound than helium-4 — which is why lithium is not a major fusion fuel on its own.
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? 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.
Example 3: Identifying an unknown product
Bombarding nitrogen-14 with alpha particles produces oxygen-17 and one other particle. Left side: 14 + 4 = 18 mass units and 7 + 2 = 9 charge units. Let the unknown have mass number A and atomic number Z:
18 = 17 + A ⇒ A = 1
9 = 8 + Z ⇒ Z = 1
The particle with A = 1 and Z = 1 is a proton, 11H:
147N + 42He → 178O + 11H
This is the famous 1919 Rutherford reaction — the first human-made transmutation.
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, computed in MeV with 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 electric 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 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 reaching the required temperatures.
A nucleus has a mass defect of 0.00300 amu. What is its binding energy in MeV?
Show answer
Eb = Δm × 931.5 MeV/amu = (0.00300)(931.5) = 2.79 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.
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 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 into a nucleus
- 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 in which fission neutrons trigger more fissions
Sources & references
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