# How is it possible to calculate the energy liberated by a given fission process?

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?

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

• But then 236U* will gamma decay to 236U which will then actually fission and liberate energy... – Cedric H. Nov 3 '10 at 0:42
• Ahh yes. Updated the answer to reflect this. – Geodesic Nov 3 '10 at 0:55
• nicely done ! – Cedric H. Nov 3 '10 at 1:00