Bainbridge's test of mass-energy equivalence

Kenneth Bainbridge was an early pioneer of mass spectroscopy. The Wikipedia article about him says:

He used this instrument to verify Albert Einstein's mass-energy equivalence, E = mc2

with a footnote to this paywalled paper from 1933. (Thanks, Physical Review, for making sure that I can't read a paper from almost a century ago.) The paper does not seem to be available from SciHub. WP also gives a quote from a 1933 book by Aston, which says:

By establishing accurate comparisons of the masses of the light particles concerned in nuclear disintegrations, particularly that of 7Li, discovered by Cockcroft and Walton, he achieved a noteworthy triumph in the experimental proof of the fundamental theory of Einstein of the equivalence of mass and energy.

A 1997 obituary in Physics Today says:

[...] he continued to use his mass spectrographs to measure isotopic masses and to compare nuclear mass differences with the energies measured in transitions as a check on Einstein's mass-energy equivalence.

Can anyone explain what measurement he actually did? 7Li is a stable element. One quote refers to "transitions," the other to "nuclear disintegrations." Would this be a beta decay from 7Be (half-life of 50 days) to 7Li? Or maybe disintegration of 7Li by neutrons or something?

• See here. – user58697 Apr 20 at 1:48
• @user58697 is pointing you in the right direction. Cockcroft and Walton were the first to measure a human-controllable nuclear reaction, accelerating protons onto 7Li. This makes an 8Be compound nucleus that would much rather be 2 alpha particles. Their measured Q value is within 1% of the currently accepted value (not bad for a first measurement). – Jon Custer Apr 22 at 15:21

2 Answers

I actually managed to get it from SH

Here is a summary of what I was able to figure out from various sources, including the copy of Bainbridge's paper that a.c. bruno uploaded.

At the Cavendish laboratory, Cockroft and Walton built a kind of electrostatic generator called a Cockroft-Walton generator, which was capable of creating DC voltages of up to 280 kV. They used this to accelerate beams of protons.

They read a paper by Gamow predicting quantum-mechanical tunneling, and realized that their proton beams ought to be able to fuse with lithium and beryllium, even though the energies were below the Coulomb barrier. Natural lithium is 92% 7Li.

In 1932, they observed a reaction which they interpreted as $$\text{p}+{}^7\text{Li}\rightarrow2\alpha+17.0\ \text{MeV}$$, for the following reasons. They had seen neutrons from their reactions, and had also hoped to see gammas but didn't. But in this experiment, they knew these were alphas because they stopped in air. Because the beam is much lighter than the target, the lab frame approximately coincides with the center of mass frame, in which the two alphas have equal energy due to conservation of energy and momentum. The range of the alphas in air was 8.4 cm, which determined their energies to be 8.6 MeV each, so the energy released in the reaction was roughly double this amount (but not quite the same due to the beam's kinetic energy and maybe also the fact that the c.m. frame doesn't quite coincide with the lab frame?).

This was a big deal because they had discovered induced nuclear disintegration, or "splitting the atom." (Apparently it was not as much of a conceptual exploit to use a proton to knock off a neutron.) They got the Nobel Prize in 1951 for this work.

As a bonus, Bainbridge was able to use this as a test of mass-energy equivalence. The energy of 17.0 MeV was equivalent to 0.0182 amu. Aston and Bainbridge had measured the atomic masses involved using sector mass spectrometers, so they could compute that the change in mass was 0.0181(6) amu. This verified $$E=mc^2$$.

• The machine used for the 1932 paper was an 800kV machine (their earlier 600kV machine did not give much signal). They had not seen neutrons - that was Chadwick (also in 1932 - a good year for nuclear physics). – Jon Custer Apr 24 at 13:04