How is it possible to calculate the energy liberated by a given fission process? For example, in the fission of a $^{235}$U induced by capturing a neutron?
1 Answer
When 235U captures a neutron, it forms the compound state 236U*, the excitation energy is given by
E_ex = [m(236U*)-m(236U)]c^2
To find the energy of the compound state, the mass energies of 235U and n can be used - assuming that the neutron will be thermalised for this reaction to occur and thus it's kinetic energy is negligible.
m(236U*) = m(235U)+m(n) = (235.043924u + 1.008665u) = 236.052589u
Thus:
E_ex = (236.052589u - 236.045563u)931.502MeV/u = 6.5MeV
This causes a fission event to occur, which can produce over twenty different products, one example is:
235U+n-->236U*-->93Rb+141CS+2n
The energy liberated is defined by the Q value: the initial mass energy minus the final mass energy
Q = (m_initial - m_final)c^2
Using the masses of 93Rb (92.92172u) and 141Cs (140.91949u)
Q = (236.052589u-(92.92172u+140.91949u+(2*1.008665u)))*931.502MeV/u = 180.76 MeV
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$\begingroup$ But then 236U* will gamma decay to 236U which will then actually fission and liberate energy... $\endgroup$ Nov 3, 2010 at 0:42