A uranium `U^(235)` nucleus liberates an energy of 200 MeV in the process of fission. 1.5 kg of uranium take part in the reaction during the explosion of a uranium bomb. What is the mass of an equivalent TNT bomb, if the heating capacity of TNT is 4.1 MJ/kg?

Answer

`3xx10^(7)kg=30000` tonnes.

Explanation

The number of the nuclei that took part in the reaction is `N=mN_(A)//A`, where m is the mass of uranium reacted, `N_(A)` is the Avogadro number, and A the mass number. Multiplying the number of the nuclei by `Deltaepsi=200MeV`, we obtain the energy of the explosion :
`W=(1.5xx6.02xx10^(26)xx200xx1.6xx10^(-13))/235J=1.2xx10^(14)J`
Dividing by the calorific value of TNT, q, we obtain the TNT equivalent: `m_(TNT)=W//q`.