eduKate Learning Manual · Nuclear Physics × Accelerators × Energy Science · JC → Edge · Accelerate → Tunnel → Transmute → Measure → Balance Mass–Energy
Wait, What? A Proton With Less Than 1 MeV of Kinetic Energy Can Trigger a Reaction That Releases About 17 MeV
John Cockcroft and Ernest Walton built one of the first successful particle accelerators and in 1932 directed accelerated protons into lithium. The lithium nuclei disintegrated into alpha particles.
The outgoing kinetic energy was much larger than the proton’s incoming kinetic energy. That does not violate conservation. The rest mass of the final nuclei is lower than the rest mass of the initial proton-plus-lithium system. The mass difference appears as released energy.
The experiment therefore linked three scientific worlds: engineered high voltage, quantum penetration of the Coulomb barrier, and nuclear mass–energy accounting.
high voltage accelerates proton → proton approaches lithium nucleus → quantum tunnelling allows some reactions below the naive classical barrier → lithium-plus-proton system rearranges into two alpha particles → lower product rest mass becomes kinetic energy → measured reaction validates nuclear transmutation and mass–energy accounting.
The Big Question
How can an electrical accelerator trigger a nuclear reaction whose released energy is far greater than the projectile energy?
Quick Answer
The key reaction can be written:
⁷Li + p → α + α
The reaction Q-value is approximately:
Q = (minitial − mfinal)c² ≈ 17.3 MeV
That Q-value is added to the incoming kinetic energy and shared mainly by the two alpha particles, subject to momentum conservation. The accelerator supplies enough proton energy to make the reaction probable; the large released energy comes from nuclear binding-energy differences.
What You Will Learn
- how a Cockcroft–Walton voltage multiplier creates high accelerating potential
- how proton energy relates to voltage
- why positively charged nuclei repel one another
- why quantum tunnelling matters below the classical Coulomb barrier
- how lithium-7 plus proton produces two alpha particles
- how reaction Q-value comes from rest-mass difference
- why energy release is not “free energy”
- how alpha-particle energies provide a reaction check
- why the experiment was artificial nuclear transmutation
- how accelerators became general tools for probing nuclear structure
Part 1 — Accelerating a Proton With Voltage
A particle of charge q accelerated through potential difference V gains kinetic energy approximately:
K = qV
For a proton, q = +e. A proton accelerated through 400 kV therefore gains about:
K ≈ 400 keV
The engineering problem was to generate a stable very high voltage without requiring one impossibly large conventional supply.
Part 2 — The Cockcroft–Walton Voltage Multiplier
Cockcroft and Walton used a network of capacitors and rectifiers to convert alternating voltage into a much larger direct potential.
The accelerator then sent protons down an evacuated tube toward a target.
The device established an enduring accelerator principle:
electrical potential difference → controlled charged-particle kinetic energy → collision with microscopic target.
Part 3 — Why the Coulomb Barrier Looks Impossible Classically
Both a proton and a lithium nucleus are positively charged, so they repel electrostatically.
A naive classical picture says the proton must possess enough kinetic energy to climb the Coulomb potential barrier all the way to nuclear-force distances.
That required energy can be much larger than the proton energies Cockcroft and Walton could conveniently generate.
Quantum mechanics changes the prediction. A particle has a non-zero probability of penetrating a classically forbidden barrier.
Part 4 — Gamow Tunnelling Changed the Engineering Target
George Gamow’s quantum theory of alpha decay and barrier penetration showed that nuclear reactions could occur below the simple classical barrier energy.
Cockcroft recognised the experimental implication: the accelerator did not need to reach the full classical Coulomb-barrier height before reactions became observable.
This is a beautiful theory-to-engineering bridge:
quantum probability revises required energy → feasible accelerator becomes worth building → experiment tests the predicted penetration.
Part 5 — Lithium Disintegrates Into Two Alpha Particles
The landmark reaction is commonly represented as:
⁷Li + ¹H → ⁴He + ⁴He
or:
⁷Li(p,α)α
Charge is conserved:
- lithium Z = 3 plus proton Z = 1 → total charge +4e;
- two alpha particles each have Z = 2 → total charge +4e.
Nucleon count is also conserved: seven plus one gives eight nucleons, equal to two helium-4 nuclei.
Part 6 — The Mass Defect Releases Energy
Use atomic masses approximately:
- ⁷Li atom: 7.016004 u;
- ¹H atom: 1.007825 u;
- ⁴He atom: 4.002603 u.
Initial mass:
mi ≈ 8.023829 u
Final mass:
mf ≈ 8.005206 u
Mass difference:
Δm ≈ 0.018623 u
Using 1 u c² ≈ 931.5 MeV:
Q ≈ 0.018623 × 931.5 ≈ 17.35 MeV
The products’ lower total rest mass is the source of the reaction’s released kinetic energy.
Part 7 — Why the Two Alpha Particles Have Large Kinetic Energy
Momentum is conserved. In the centre-of-mass frame, the two equal-mass alpha particles emerge approximately back-to-back with equal momentum.
If the incident proton energy is modest compared with the 17.3-MeV Q-value, each alpha carries roughly half of the released energy, with laboratory-frame corrections from the initial projectile momentum.
The unexpectedly energetic alpha tracks were therefore not merely “radiation appeared.” Their energies were a quantitative receiver for the nuclear mass difference.
The Historical Carrier — 1932
Cockcroft and Walton performed their pioneering accelerator work at the Cavendish Laboratory. Nobel historical records describe their 1932 bombardment of lithium with accelerated protons, producing two alpha particles.
They received the 1951 Nobel Prize in Physics for pioneering work on the transmutation of atomic nuclei by artificially accelerated particles.
The experiment did not invent nuclear transmutation — Rutherford had already observed artificial nuclear transformations using naturally emitted alpha particles. Cockcroft–Walton changed the control architecture by producing the projectile energy electrically.
Part 8 — Was This a Direct Proof of E = mc²?
The reaction provided an important early quantitative demonstration that nuclear mass differences correspond to released energy in agreement with mass–energy equivalence.
But “Cockcroft and Walton proved E = mc² in one experiment” is too compressed. Einstein’s relation preceded the experiment, nuclear mass measurements had uncertainties, and the result joined a wider body of evidence linking mass defects and nuclear energies.
The precise claim is:
measured nuclear reaction energies were quantitatively consistent with the energy predicted from the reactant–product mass difference.
Part 9 — Energy Accounting: Where Does the Accelerator Fit?
The accelerator supplies the incident proton’s kinetic energy and helps the projectile reach a reaction configuration.
Once the nuclear rearrangement occurs:
Kproducts = Kincoming + Q
for the simple isolated reaction energy ledger.
The 17.3-MeV Q-value comes from the difference in nuclear binding/rest mass, not from the high-voltage supply.
This prevents the false inference that a sub-MeV electrical input somehow produced many MeV from nothing.
RFE Stress Test — Nuclear Reaction or Detector Artefact?
- beam-off control: do alpha counts disappear when accelerated protons stop?
- target test: does changing/removing lithium remove the characteristic reaction?
- range/energy test: are outgoing particles consistent with alpha energies expected from the Q-value?
- charge/nucleon accounting: does the proposed reaction conserve quantum numbers?
- voltage dependence: does reaction yield change with projectile energy as barrier penetration predicts?
- background test: could natural radioactivity create the same directional, beam-correlated alpha signal?
The transmutation claim becomes strong because the signal follows beam, target, energy and reaction kinematics together.
Observation vs Inference
Observation: accelerated protons striking lithium produce energetic alpha particles correlated with the beam.
Nuclear inference: lithium-plus-proton nuclei undergo artificial transmutation into helium nuclei.
Energy inference: product kinetic energy agrees with the positive Q-value associated with lower final rest mass.
Common Misconceptions and How to Repair Them
- “The accelerator supplied all 17 MeV.” Repair: most released energy comes from nuclear mass/binding difference.
- “The proton classically climbed the full Coulomb barrier.” Repair: quantum tunnelling makes sub-barrier reactions possible.
- “Splitting lithium means nuclear fission in the reactor sense.” Repair: this is a light-nucleus reaction producing two alpha particles, not heavy-nucleus fission chain reaction.
- “Cockcroft–Walton was the first artificial transmutation ever.” Repair: Rutherford had earlier transmuted nuclei using natural alpha particles; this work used artificially accelerated projectiles.
- “Mass disappears.” Repair: lower rest mass appears as other energy forms; total mass–energy is conserved.
Checkpoint Questions
- How much kinetic energy does a proton gain through voltage V?
- Why do proton and lithium nucleus repel?
- What makes reaction possible below the naive classical barrier?
- Write the lithium-7 proton reaction.
- What is a reaction Q-value?
- Why can product kinetic energy exceed projectile kinetic energy?
- What experimental observation confirms artificial transmutation?
Apply It — Double the Accelerating Voltage
Doubling V doubles the proton’s electrical kinetic-energy gain qV. It does not double the nuclear Q-value, which is set by reactant and product masses. It can, however, greatly increase reaction probability because barrier-penetration probability is extremely energy-sensitive.
Unfamiliar Transfer — Accelerators as Controlled Microscopes
Once projectile energy can be engineered, accelerator experiments can choose which nuclear scales and reactions to probe.
- higher energy can overcome or tunnel through stronger barriers;
- beam species selects charge, mass and interaction channel;
- detector angle and energy reconstruct reaction products;
- resonances reveal nuclear energy levels.
The reusable architecture is:
engineer projectile → collide with target → measure products → enforce conservation → reconstruct microscopic interaction.
Answer Key
1. K = qV. 2. Both are positively charged. 3. Quantum tunnelling. 4. ⁷Li + p → α + α. 5. Rest-mass difference converted to available reaction energy. 6. A positive Q-value adds released binding/rest-mass energy. 7. Beam-correlated energetic alpha products with correct kinematics and target dependence.
Can You Explain WHY?
Explain why a 400-keV proton can participate in a reaction releasing about 17 MeV without violating conservation. A strong answer should connect accelerator qV → Coulomb barrier → tunnelling → nuclear rearrangement → mass defect → Q = Δmc² → alpha kinetic energy.
Singapore JC Science Bridge
JC Physics supplies electric potential, charged particles, nuclei and mass–energy. Cockcroft–Walton connects them into a full experimental chain: electrical engineering controls projectile energy, quantum mechanics controls reaction probability, and relativistic mass–energy closes the nuclear ledger.
Deep Science Windows
- Gamow factor: tunnelling probability through a Coulomb barrier changes exponentially with particle energy.
- Nuclear binding energy: Q-values map differences in how tightly nucleons are bound.
- Accelerator voltage multipliers: Cockcroft–Walton circuits remain useful for high-voltage generation.
- Reaction thresholds: endothermic reactions require projectile energy above a kinematic threshold.
- Beam-target experiments: modern nuclear and particle physics extend the same controlled-collision architecture to far higher energies.
Evidence and Safety Boundaries
This article explains historical accelerator and nuclear-reaction physics, not construction or operation of high-voltage or ionising-radiation equipment. The Q-value depends on precise nuclear masses and reaction channel. The experiment supported mass–energy equivalence through reaction energetics but was part of a broader evidence base rather than a single standalone proof of relativity.
Manual Summary — KNOW → CONNECT → EXPLAIN → APPLY → CHECK
- KNOW: qV sets projectile energy and Q = Δmc² sets reaction energy release.
- CONNECT: quantum tunnelling allows reaction below the naive classical barrier.
- EXPLAIN: lithium plus proton rearranges into two more tightly bound alpha particles.
- APPLY: calculate Q-values and distinguish them from beam energy.
- CHECK: beam, target, product energy, conservation laws and background.
Teaching Guide for Parents, Tutors and Teachers
Why this opening works: output kinetic energy exceeding projectile kinetic energy looks impossible until students distinguish accelerator input from nuclear Q-value.
- Central reasoning model: qV → barrier penetration → nuclear reaction → mass defect → kinetic products.
- Teaching sequence: accelerating voltage → Coulomb repulsion → tunnelling → reaction equation → mass calculation → Q-value → alpha evidence.
- Diagnostic question: “Where does the extra 17 MeV come from if the proton had less than 1 MeV?”
- If stuck: calculate reactant and product masses before discussing the accelerator.
- Ready for more: introduce Gamow penetration, reaction cross sections and accelerator resonances.
Quiet Teaching Standard: never teach this as “scientists smashed atoms.” Require conservation of charge, nucleon number, momentum and mass–energy to identify the actual reaction.