Nuclear fission

In 1938 Otto Hahn and Fritz Strassmann discovered that bombarding ${}^{235}$U with neutrons produced nuclei of barium and krypton: the uranium nucleus had split in two. Lise Meitner and Otto Frisch — exiled in Sweden because of the Nazi persecution of their Jewish origins — interpreted the result and, in 1939, coined the term fission, by analogy with cell division in biology.

A typical reaction is: $n + {}^{235}\text{U} \to {}^{141}\text{Ba} + {}^{92}\text{Kr} + 3\,n + 200\;\text{MeV}$

The resulting fragments, being closer to the maximum of the binding curve, have a higher $B/A$ than uranium: the difference in binding energy, about $200\;\text{MeV}$ per fission, comes out as the kinetic energy of the fragments and neutrons.

The decisive feature is that each fission produces on average $2{,}5$ neutrons. Each of them can trigger the fission of a new ${}^{235}$U nucleus: if the mass of fuel is large enough (the critical mass), a neutron generates on average more than one subsequent neutron and the reaction becomes self-sustaining in a chain reaction. The very same phenomenon, depending on how it is controlled, becomes two very different things:

• in a nuclear reactor the reaction is held in a steady state by means of absorbing rods (cadmium) that capture the excess neutrons, and moderators (water, graphite) that slow them down;
• in a nuclear weapon the reaction is instead accelerated, causing an exponential growth in the number of fissions within a few microseconds.

Example — How many grams of uranium for a city?

A single fission event releases $\sim 200\;\text{MeV} \approx 3{,}2\cdot 10^{-11}\;\text{J}$. One gram of ${}^{235}$U contains $\frac{N_A}{235\;\text{g/mol}}\cdot 1\;\text{g} \approx 2{,}6\cdot 10^{21}\;\text{atoms}$ hence a total fission energy of $\ev{E \approx 2{,}6\cdot 10^{21}\cdot 3{,}2\cdot 10^{-11} \approx 8\cdot 10^{10}\;\text{J}}$ the equivalent of about $20$ tonnes of TNT. This is fundamental physics in its crudest form: less than a gram of uranium to destroy a barracks.

Historical context — from discovery to the bomb

Fewer than seven years passed from Hahn and Strassmann’s discovery (December 1938) to the first nuclear explosion (Trinity Test, 16 July 1945). In that short span Albert Einstein wrote to Roosevelt suggesting a weapon be built before Germany did; the Manhattan Project was born (Robert Oppenheimer, $130\,000$ people, about $2$ billion dollars of the time); and it led to Hiroshima and Nagasaki (6 and 9 August 1945). Otto Hahn, interned in England with other German scientists, learned of the bomb from the radio and fell into deep depression (Rhodes 1986).

Collegamenti

Argomenti: Fisica nucleare Concetti: Fissione nucleare · Energia di legame nucleare

Esercizi collegati: Perché la fissione conviene · Curva di Aston e direzione dell’energia · Stabilità relativa di quattro nuclei