The destructive power of an atomic bomb originates from a rapid physical process that releases immense energy from a minuscule amount of matter. The core of this power lies in nuclear fission, where heavy atomic nuclei are intentionally destabilized to split apart. To fully appreciate the scale of this reaction, one must quantify the number of atoms involved in the milliseconds of the explosion. The calculation requires converting the weapon’s explosive energy yield into the number of individual fission events required to produce it. This final number reveals the extraordinary efficiency with which nature’s fundamental forces are harnessed to create a large-scale detonation.
Understanding Nuclear Fission
Nuclear fission is the process where a large, unstable atomic nucleus is split into two or more smaller nuclei, typically accompanied by the release of a significant amount of energy. The reaction is initiated when a heavy nucleus, such as Uranium-235, absorbs a single neutron. This absorption causes the nucleus to become highly unstable and immediately split apart.
This splitting produces two medium-mass fission fragments, which fly apart at high speed, along with several new neutrons. These newly liberated neutrons are the driving force behind a self-sustaining chain reaction. If the surrounding material is dense enough, these neutrons will strike other fissile nuclei, causing them to split and release even more neutrons, exponentially increasing the reaction rate.
In an atomic weapon, this chain reaction is deliberately engineered to be uncontrolled and extremely fast, releasing energy in a fraction of a second. Each individual fission event releases approximately 200 million electron volts (MeV) of energy, which is vastly more than the energy released by any chemical reaction. The immense power of the bomb is therefore a direct result of multiplying this massive single-atom energy release across trillions upon trillions of nuclei.
Critical Mass and Fission Efficiency
A successful atomic detonation depends on achieving a state known as supercriticality, which relates directly to the concept of critical mass. Critical mass is the minimum quantity of fissile material necessary to sustain a chain reaction where the average number of neutrons produced is greater than the number lost to escape or absorption. Below this mass, the assembly is subcritical, and any chain reaction quickly dies out.
The fissile materials most commonly used in nuclear weapons are the isotopes Uranium-235 and Plutonium-239. The required mass to reach criticality is highly dependent on factors like the density, shape, and purity of the material. For example, a solid sphere of pure Plutonium-239 requires a bare critical mass of about 10 kilograms, while the use of a neutron-reflecting tamper can significantly reduce this minimum mass.
In a deployed weapon, high explosives are used to rapidly compress the subcritical material, increasing its density and instantly forcing it into a supercritical state. Despite this engineering, the efficiency of the reaction is surprisingly low. For the first-generation weapons, like the Plutonium-239 bomb detonated over Nagasaki, only about 20% of the pit material actually underwent fission. The Uranium-235 bomb dropped on Hiroshima was even less efficient, fissioning less than 1% of its total uranium mass.
Deriving the Number of Split Atoms
The question of how many atoms split can be answered by connecting the weapon’s measurable energy yield to the known energy of a single fission event. A standard unit for measuring the energy of a nuclear explosion is the kiloton (kT), which represents the energy released by one thousand tons of TNT. A common reference point for a pure fission weapon is a yield of 20 kilotons, similar to the bomb dropped on Nagasaki.
One kiloton of TNT is equivalent to \(4.184 \times 10^{12}\) Joules of energy, meaning a 20-kiloton explosion releases a total energy of approximately \(8.37 \times 10^{13}\) Joules. To find the number of atoms split, this total energy must be divided by the energy released per single fission event. The energy released from one atom splitting is approximately 200 MeV, which translates to about \(3.2 \times 10^{-11}\) Joules.
Dividing the total energy yield by the energy per fission event provides the final count of split atoms. For a 20-kiloton detonation, the number of atoms that must split to release that energy is calculated to be approximately \(2.6 \times 10^{24}\) atoms. This represents \(2.6\) septillion individual atomic nuclei undergoing fission in a fraction of a microsecond.
To put this number into perspective, \(2.6 \times 10^{24}\) atoms corresponds to a mass of just over one kilogram of fissile material, such as Plutonium-239. This calculation shows that the massive destructive power of an atomic bomb is generated by the complete fission of only about one kilogram of material, even when the weapon initially contains a much larger mass of fissile fuel.
The Mass-Energy Relationship
The enormous energy released by the fission of trillions of atoms is a direct manifestation of the principle of mass-energy equivalence, described by Albert Einstein’s equation, \(E=mc^2\). This equation explains that energy (\(E\)) and mass (\(m\)) are interchangeable. A small amount of mass can be converted into a tremendous amount of energy because the conversion factor (\(c^2\), the speed of light squared) is so large.
In the fission process, the combined mass of the fission products and the released neutrons is slightly less than the initial mass of the single, heavy nucleus. This tiny difference in mass, known as the mass defect, is the mass that is converted into the kinetic energy of the fragments and the resulting blast. The vast majority of the atom’s mass remains in the form of the lighter fission fragments.
For the 20-kiloton explosion that split \(2.6 \times 10^{24}\) atoms, the total mass that was annihilated and converted into pure energy was less than one gram. The entire force of the atomic blast comes from the complete disappearance of this tiny mass. The calculation of \(2.6 \times 10^{24}\) split atoms represents the count of nuclei that participated in the reaction, while the mass converted to energy is only a tiny fraction of the total mass of those participating atoms.