# Uncontrolled chain reaction and the atom bomb

In an uncontrolled chain reaction, there is no control on energy released in a fission. And this reaction is completed within about a microsecond. Atom bomb works on this principle. In the construction of atom bomb, two or more mass pieces of enriched uranium-235 or plutonium-239 are taken. The mass of each piece is less than its critical mass. In this state rate of production of neutrons after fission is less than the rate of loss of neutrons i.e. multiplication factor of each piece is less than one, as a result, fission reaction does not take place in these pieces.

But if these pieces are brought together suddenly by chemical explosives, then the total mass of pieces becomes greater than the critical mass i.e. k>1 and the chain reaction starts in an uncontrolled way releasing the tremendous amount of energy. In atom bomb, enriched uranium-235 pieces of subcritical mass are placed at a fixed distance separately and enclosed in a very tight metal cover as shown as fig.

## Theory

A neutron source is placed at the center of the pieces. And chemical explosives are fitted with uranium pieces in such a way that when they explode, the pieces will join together tightly to form a single piece. In this situation, the size and mass of the fissile material become greater than the critical mass. And the bombardment of neutrons starts an uncontrollable chain reaction. The metal cover of the bomb is taken so strong that unless chain reaction reaches to a maximum, it does not explode.

The tremendous amount of energy released by the uncontrolled chain reaction depends upon the speed of chemical explosive. With which it makes to join the fissile pieces, the strength of the cover and the time taken in completing the chain reaction.

### The energy released by an atom bomb

For calculating the energy released by an atom bomb, let us take an example of an atom bomb having one kg of fissile material. Number of uranium atoms in one kg

=6.02×10²⁶/235=2.56×10²⁴

Since fission of one uranium nucleus releases energy 200 Me V. Therefore the amount of energy released incomplete fission of one kg uranium

=200×1.6×10⁻¹³×2.56×10²⁴=8.27×10¹³ J

Since the number of uranium atoms one kg is  2.56×10²⁴, therefore to fission all the nuclei 2.56×10²⁴ neutrons are required. The multiplication factor in the first atom bomb built in 1945 was K=1.1. The time taken in between the production of successive two generations is about 10 nanosecond i.e. 10⁻⁸ s, therefore the number of neutrons produced by one neutron (Nο=1),

N=exp[(1.1−1)t/(10×10⁻⁹)]

∴   Time taken in the production of N=2.56×10²⁴ neutrons

t=10 loge(2.56×10²⁴)

t=1.06×10⁻⁶ s

Thus the complete fission of one kg fissile uranium in atom bomb releases 8.2×10¹³ J energy in 1.06 microsecond. As a result, it increases the temperature up to 10⁷ degrees. And pressures up to the 10⁵ atmospheric pressure of the environment. Which is equivalent to the temperature and pressure produced by the 20000 TNT explosive. The united states dropped atom bombs of the Japanese cities of Hiroshima and Nagasaki in August 1945 at the end of Second World War.

The bombing which killed about at least 129,000 people remains the only use of nuclear weapons for warfare in history. The first time India carried an underground bomb type explosion of nuclear fuel plutonium -239 at Pokhran in Rajasthan on 18 May 1974. Implosion method was used in joining the subcritical pieces of plutonium-239. This explosion was equivalent to 10-13 kiloton TNT. Indian again carried 5 atomic explosions on 13 May 1998.

#### Conclusion

In this particular article Uncontrolled Chain Reaction and The Atom Bomb, we have discussed uncontrolled chain reaction in detail. We have also discussed working of the atomic bomb in the easiest way possible.