As we discussed, each^235U atom that undergoes fission releases approximately 20

Question

As we discussed, each^235U atom that undergoes fission releases approximately 200 MeV of energy. The energy of a nuclear weapon is expressed in terms of an equivalent amount of TNT (2,4,6-trinitrotoluene), for example a 20 mega-ton warchead. TNT contains 4.7 megajoules per kilogram and a ton of TNT is a unit of enery equal to 4.184 gigajoules. The Little Boy atomic bomb dropped on Hiroshima on August 6,1945, exploded with an energy of about 15 kilotons oif TNT. The W88 is a modern United States thermonuclear warhead, with an estimated yield of 475 kiloton, and is small enough that the Trident 11 submarine-launched ballistic missile can be aimed with up to 8 w88 warheads. 1) What was the mass (in kg) of the 235U used in Little Boy? 2) How much would a Trident II missile weigh, if it also used^235U?

Explanation / Answer

a) Little boy had energy equal to 15kilotons of TNT

= 15*103 ton TNT = 15*103*4.184*109 J = 6.276*1013 J

1 atom of 235U produces energy of 200MeV energy = 200*106 * 1.602*10-19 = 3.204*10-11 J

So number of equivalent 235U atoms needed = 6.276*1013/3.204*10-11 = 1.9588*1024

or 1.9588*1024/6.022*1023 = 3.252742 moles = 764.4g = 0.7644 kg

b) W88 with 475 kiloton yield has energy of 31.67 Little Boy which will be equivalent to 24.206 kg of 235U

So Trident II missle should weigh 8*24.206 = 193.648 kg

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