A Sword of Damocles: Nuclear Weapons

James Richard Fromm

The fundamental relationship linking mass and energy is the Einstein equation E = mc2 where the energy obtainable by conversion of mass is given by the product of the mass and the square of the speed of light, c. Since c is a universal constant equal to about 3.0 x 10+8 m/s, the energy contained in 1 kg of mass is then 1.0 x (3 x 10+8)2 kg m2s-2 = 9 x 10+16 J. We would usually write this as 9 x 10+10 kJ/g for comparison with chemical reaction energies.

In the actual fission of uranium-235 in a nuclear reactor or nuclear weapon, not all of the mass of the uranium-235 is converted into energy. In fact, of the mass of fissioning uranium-235, only about 0.1% is converted into energy; the rest of it makes up the mass of the fission fragments. Thus fissioning uranium-235 produces only 9 x 10+13 x 0.001 = 9 x 10+7 kJ per gram. This is still a very large value relative to the energies involved in chemical reactions. The explosion of one gram of the military explosive trinitrotoluene (TNT) will produce 2.760 kJ. Thus the energy of one gram of fissioning uranium-235 is about equal to that of 30 tonnes of exploding TNT. Clearly, the energy involved in nuclear devices is very much larger than the energy involved in the chemical reactions of chemical explosive devices. The first use of nuclear energy was a military use, the atomic bombs dropped by the United States on the Japanese cities of Hiroshima and Nagasaki in 1945.

Nuclear explosive devices, or nuclear weapons, were first tested and used by the United States, in 1945. Since then nuclear weapons have been manufactured and tested by the Russia (since 1949), the United Kingdom (since 1952), France (since 1960), China (since 1964), and India (since 1974). Some other nations may have built nuclear weapons but have not openly declared or tested them. Many nations, including Canada, have formally renounced construction of nuclear weapons by signing the Nuclear Nonproliferation Treaty of 1968. In 1974, the United States and Russia agreed to ban all tests of nuclear weapons save those which can be carried out underground with explosive yields equivalent to less than 150 kilotons. Other treaties restricting nuclear weapons have more recently come into force, and further negotiations continue.

In Western literature it is traditional to consider the power of nuclear weapons in terms of the unit of tons of TNT required to produce the same energy. The nuclear weapons used on Hiroshima or Nagasaki in 1945 were comparatively small atomic bombs rated at about 20 kilotons, or 20,000 tons of TNT equivalent. For these weapons, the effects were as follows:

Effects of 20 kT Nuclear Weapons at Hiroshima/Nagasaki

		Effect (Result)               Radius    Casualties
		                              (miles)      (%)
		blast (complete destruction)  0.5          70+
		blast (severe damage)         1.0
		flash (ignition)              1.0          25
		radiation (severe radiation)  0.5         5-15

The effect of scaling up the size of the nuclear weapon, in terms of its energy output is of course related to the radius of damage done. The increase is not linear, but the radius increases approximately as the cube root of the energy output. These are relatable to those of a 20 kT bomb using the observations of the Hiroshima and Nagasaki explosions; the radius of severe blast damage is (W/20)1/3 miles where W is the energy output of the bomb in kT of TNT. Thus the Eniwetok hydrogen fusion bomb test of 1952, which had an energy output of about 5000 kilotons or five megatons, had a radius of severe blast damage of 2501/3 or 6.3 miles. The radius of severe flash, which will produce burns or ignition, falls off with distance somewhat more slowly than does the effect of the blast. It falls off roughly as the square root, rather than the cube root, of the energy output of the bomb. This would leave the Eniwetok test bomb with a flash radius of about sixteen miles. Modern hydrogen fusion bombs are known to range up to at least 20 megatons if not 50 megatons. In addition, nuclear missiles can now be made with several independently-moving warheads which can spread the destruction over a wider area.

Copyright 1997 James R. Fromm