Thursday, 25 October 2018

nuclear physics - Energy Released in a Fission Reaction


I've been told the following is incorrect, but I can't really see how.


Consider the fission event described by the equation $$ \rm ^{235}U+n\rightarrow{}^{93}Rb+{}^{140}Cs+3n $$ The energy released is given by \begin{align} Q&=\Delta mc^2 \\&=(m_\mathrm U+m_\mathrm n-m_\mathrm{Rb}-m_\mathrm{Cs}-3m_\mathrm n)c^2 \\&=(m_\mathrm U-m_\mathrm {Rb}-m_\mathrm {Cs}-2m_\mathrm n)c^2 \end{align} and writing the nuclear masses in terms of the masses of their constituent nucleons less than nuclear binding energy we find $$ Q=B_\mathrm{Rb}+B_\mathrm{Cs}-B_\mathrm{U} $$ You could then estimate these binding energies using the SEMF giving a value of roughly $$Q=145\rm\,MeV$$ (in reality it should be something like $200\rm\,MeV$). However I'm just concerned about whether or not the general method is correct or not. Thanks in advance.




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