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Rutherford had already changed nuclei by hitting them with alpha particles from radioactive sources. Cockcroft and Walton wanted particles they could make and control themselves, and they built the machine to do it, using voltages modest enough to fit in a large room. Their result also let them check E = mc² against a measured energy. This post covers who they were, how they did it, the energy calculation with real masses, and what students can learn from them.
Who were Cockcroft and Walton?
John Cockcroft's Nobel biography records that he was born in Todmorden, England, on 27 May 1897. He studied mathematics at Manchester, served in the First World War, studied electrical engineering, and did an apprenticeship at Metropolitan Vickers before taking the Mathematical Tripos at Cambridge in 1924. He began work on accelerating protons in 1928. He died on 18 September 1967.
Ernest Walton's Nobel biography records that he was born in Dungarvan, County Waterford, Ireland, on 6 October 1903. He graduated from Trinity College Dublin in 1926 with first-class honours in mathematics and experimental science, then came to the Cavendish Laboratory in 1927 to work under Rutherford. He returned to Trinity College Dublin in 1934 and died on 25 June 1995.
They shared the 1951 Nobel Prize in Physics "for their pioneer work on the transmutation of atomic nuclei by artificially accelerated atomic particles".
Why did they think modest voltages would work?
In his Nobel lecture, Cockcroft explains that in 1928 George Gamow, Ronald Gurney and Edward Condon had shown that alpha particles escape nuclei by quantum tunnelling, without enough energy to climb over the barrier. Gamow visited the Cavendish, and Cockcroft asked the reverse question: how much energy would a proton need to get in? His memorandum to Rutherford showed a fairly high chance that a proton of only 300 kilovolts could penetrate a boron nucleus, and lithium looked even more favourable.
How did they reach the voltage?
Walton's Nobel lecture describes their first set-up, which gave several microamperes of protons at about 280 kilovolts. When they moved to a larger room, they built a voltage multiplier, adapted from a circuit by Schenkel. Capacitors charged through rectifiers stacked the transformer's voltage: the first version gave four times the transformer voltage, and the design could be extended to any even multiple. With it they reached currents of up to about 10 microamperes at up to about 700 kilovolts.
What did they see?
Cockcroft describes the moment. They placed a zinc sulphide screen opposite a thin mica window. "Almost at once, at an energy of 125 kilovolts, Dr. Walton saw the bright scintillations characteristic of α-particles." A first absorption test gave a range of about 8.4 cm. Two observers watching two screens and tapping keys showed the alpha particles came in pairs. Finer measurements gave 8.6 million volts each, a total release of 17.2 million volts. They reported it in Nature on 30 April 1932.
Worked example: where does 17 MeV come from?
Use atomic masses from NIST for lithium-7, hydrogen-1 and helium-4, and the CODATA energy equivalent of 1 u, 931.494 MeV.
Mass before: 7.016003 u + 1.007825 u = 8.023828 u.
Mass after: 2 × 4.002603 u = 8.005206 u.
Mass lost: 8.023828 − 8.005206 = 0.018622 u.
Energy: 0.018622 × 931.494 ≈ 17.35 MeV.
Add the proton's energy: 17.35 + 0.125 ≈ 17.47 MeV shared by two alphas, about 8.7 MeV each.
Their measured 8.6 MeV per alpha and 17.2 MeV in total sit close to this, so mass really did turn into kinetic energy in the amount E = mc² predicts.
Mistakes to avoid:
Mixing atomic and nuclear masses. Atomic masses work here because the electrons balance: 3 + 1 on the left, 2 + 2 on the right.
Rounding too early. The mass difference is in the second decimal place, so keep at least six decimals.
Getting the sign backwards. Energy is released when the products are lighter than the reactants.
Our guide to nuclear binding energy problems has more practice on mass defects. For a different route to high energies from the same years, read about Ernest Lawrence and the cyclotron. If you want to check a Q-value calculation one step at a time, the Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer.
What can a student take from how they worked?
Let theory set the target. Gamow's tunnelling idea told them they did not need millions of volts.
Build what you need. The multiplier was their own engineering answer to a physics problem.
Use simple checks. Two people tapping keys was enough to show the alphas came in pairs.
Close the loop with numbers. They compared the energy released with the mass lost.
Try it: protons on boron-11 give three alpha particles. Write the reaction and check that charge and mass number balance.
