In December 1938, on the eve of World War II, a letter arrived in Sweden that changed the trajectory of human history. Chemist Otto Hahn in Berlin had bombarded uranium with thermal neutrons expecting to create heavy transuranic elements, but instead found barium—an element nearly half the atomic weight of uranium. Exiled Austrian physicist Lise Meitner and her nephew Otto Frisch walked through the snowy woods of Kungälv and realized what had happened: the atomic nucleus had split, unleashing the cataclysmic energy predicted by Einstein’s $E = mc^2$.
Probing the Nucleus: The Discovery of the Neutron
For two decades following Rutherford’s model, the nucleus remained an enigma. In 1932, James Chadwick at the Cavendish Laboratory identified the missing constituent of the nucleus: the neutron, an electrically neutral nucleon with mass $m_n approx 1.6749 times 10^{-27} text{ kg}$.
Because neutrons carry zero electric charge, they experience no Coulomb electrostatic repulsion from positively charged nuclei. In Rome, Enrico Fermi realized that slow (thermal) neutrons were the ultimate bullets to penetrate heavy atomic nuclei, systematically bombarding every element in the periodic table.
The Berlin Laboratory and the Barium Riddle
In Berlin-Dahlem, the brilliant partnership between chemist Otto Hahn and physicist Lise Meitner investigated the bombardment of uranium ($Z = 92$). In July 1938, Meitner, an Austrian Jew, was forced to flee Nazi Germany on an illegal train to Holland, eventually finding refuge in Stockholm at the Nobel Institute.
Hahn and his assistant Fritz Strassmann continued the experiments. When examining the products of neutron-bombarded uranium, their rigorous chemical fractional crystallizations repeatedly identified isotopes of barium ($Z = 56$). Hahn wrote desperately to Meitner in Sweden: “Could it be that uranium-235 bursts into barium and krypton? We would be so happy if you could find some sort of physical explanation for this.”
The Liquid Drop Model and the Cleaving of Uranium
Sitting on a fallen tree trunk in Kungälv, Meitner and Frisch applied George Gamow and Niels Bohr’s liquid drop model of the nucleus. A heavy atomic nucleus is held together by the short-range strong nuclear force acting like surface tension, fighting against the immense electrostatic repulsive Coulomb force between its 92 protons.
When a slow neutron strikes a Uranium-235 nucleus, it forms an excited compound nucleus ($^{236}text{U}^*$) that elongates into an oscillating dumbbell shape:
$$^{235}_{92}text{U} + ^1_0text{n} to ^{236}_{92}text{U}^* to ^{141}_{56}text{Ba} + ^{92}_{36}text{Kr} + 3 ^1_0text{n} + Q$$
Once the waist of the dumbbell narrows, the mutual electrostatic Coulomb repulsion between the two fragments ($Z_1 = 56, Z_2 = 36$) overpowers the nuclear surface tension, snapping the nucleus apart at roughly one-tenth the speed of light.
The Energy Calculation: E = mc² in Action
Meitner immediately calculated the energy release. The Coulomb repulsion between two nascent nuclei at separation $r approx 1.4 times 10^{-14} text{ m}$ is:
$$E_{text{Coulomb}} = frac{1}{4pi varepsilon_0} frac{Z_1 Z_2 e^2}{r} approx 200 text{ MeV} approx 3.2 times 10^{-11} text{ Joules}$$
Where did this vast energy originate? Meitner checked the nuclear masses: the combined mass of the fission products was lighter than the initial uranium nucleus by roughly one-fifth of a proton mass ($Delta m approx 0.215 text{ u}$):
$$Q = Delta m c^2 approx 0.215 times 931.5 text{ MeV} approx 200 text{ MeV}$$
The numbers matched with breathtaking exactitude. Frisch borrowed the term fission from cellular biology. When Leo Szilard realized that each fission event emitted secondary neutrons, the prospect of a self-sustaining nuclear chain reaction became a terrifying technological reality, ushering in the atomic age.
