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Some discoveries need a huge machine. Anderson's needed a cloud chamber, a strong magnet and a slab of lead about as thick as a pencil. With them he found the first antimatter particle ever seen. This post covers who he was, how he read his photographs, the physics of his famous track with numbers, and what you can learn from his caution.
Who was Carl Anderson?
His Nobel biography records that Carl David Anderson was born in New York City on 3 September 1905 to Swedish parents. He took his B.Sc. in physics and engineering at the California Institute of Technology in 1927 and his Ph.D. there in 1930, studying photoelectrons ejected from gases by X-rays. He stayed on at Caltech as a research fellow and then a faculty member, becoming a professor in 1939. He died on 11 January 1991.
He shared the 1936 Nobel Prize in Physics with Victor Hess, "for his discovery of the positron". The Nobel facts page notes that Paul Dirac's quantum theory had predicted that charged particles should have antiparticles of opposite charge.
How did Anderson study cosmic rays?
His Nobel lecture explains that in spring 1930 he and Robert Millikan planned a cloud chamber for cosmic rays. It measured 17 × 17 × 3 cm and sat inside an electromagnet that could reach 24,000 gauss. A charged particle moving through a magnetic field curves, and the tighter the curve, the lower its momentum.
The first results came in summer 1931. Positive particles turned up about as often as negative ones. The negative ones were clearly electrons. The positive ones were at first taken to be protons, the only known particle with a unit positive charge. But protons with such tight curves should have left much denser tracks, and they did not.
How did a lead plate settle it?
A positive particle moving down and a negative particle moving up curve the same way in a magnetic field. So Anderson needed to know which way each particle was going. He put a lead plate across the middle of the chamber. A particle loses energy in the lead, so its curve is tighter after the plate than before it. That tells you the direction.
One photograph showed a positive particle crossing a 6 mm lead plate in a field of 15,000 gauss. Assuming electron mass, its energy was 63 million electron-volts before the plate and 23 million after. A proton with the curvature seen after the plate would have had only 200,000 electron-volts and a range of about 5 mm, but the track ran for more than 50 mm. In Anderson's words: "The only possible conclusion seemed to be that this track, indeed, was the track of a positively charged electron."
He announced it in Science in September 1932, followed by The Positive Electron in Physical Review (1933). Its abstract reports that of 1300 cosmic-ray photographs, 15 tracks were of positive particles that could not be as heavy as a proton, and that their mass had to be less than twenty electron masses. In spring 1933 Blackett and Occhialini confirmed positrons with a counter-triggered chamber.
Worked example: the radius of the 23 MeV track
For a charge q moving perpendicular to a field B, the radius is r = p/(qB). At 23 MeV an electron-mass particle is highly relativistic, since its rest energy is only 0.511 MeV. Its momentum is very close to E/c.
Momentum: p ≈ 23 MeV/c. In SI terms, pc = 23 × 10⁶ eV, so p = (23 × 10⁶ × e)/(3.0 × 10⁸) kg m/s.
Field: 15,000 gauss = 1.5 T.
Radius: r = p/(eB) = (23 × 10⁶)/(3.0 × 10⁸ × 1.5) ≈ 0.051 m, about 5 cm. The charge e cancels neatly.
Before the plate: with 63 MeV, r ≈ (63 × 10⁶)/(4.5 × 10⁸) ≈ 0.14 m.
The radius shrinks from about 14 cm to about 5 cm across the plate, which is how the photograph shows the particle was moving from the 63 MeV side to the 23 MeV side.
Mistakes to avoid:
Using ½mv² at these energies. Setting 23 MeV = ½mv² for an electron gives v ≈ 9.5c, which is impossible. Use p ≈ E/c when the energy is far above the rest energy.
Forgetting the sign. The force is qv × B. Reverse q and the curve reverses.
Mixing units. Convert gauss to tesla (1 T = 10,000 gauss) before calculating.
For the non-relativistic version of this formula, which is what JEE usually tests, see our guide to the magnetic force and the right-hand rule. The theory behind the discovery is in our post on Paul Dirac and antimatter. If you want to check a curved-track problem 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 he worked?
Try the ordinary explanation first. He spent real effort on the idea that the tracks were electrons moving upward.
Design a test that decides. One lead plate turned an argument into a measurement.
Check with a second clue. Curvature and track density both pointed the same way.
Report numbers, not just a claim. Fifteen tracks out of 1300 photographs is a result others could check.
Try it: what radius would a 23 MeV positron have in a 2.0 T field?
