snorkack said:
The yield of n emitters in thermal neutron fission of U-235 is given as 0,64% out of 200 %. If so, in an assembly with prompt k of 0,9900, 1 spontaneous fission would on average induce 100 prompt fissions, but 280 fissions total... meaning that 180 fissions out of 280 (64%) would be due to delayed neutrons. Whereas if k is 0, then the neutron yield from delayed neutrons would be about 0,34%
This is not correct after "The yield of n emitters in thermal neutron fission of U-235". One does not compare 0.64% to 200%, or 2.
The fraction of delayed neutrons is usually designated by β, which is approximately 0.0064 or 0.0065 for
235U for thermal neutrons. The β is dependent on the fissile nuclide, e.g., for
233U β = 0.00261 and for 239Pu β = 0.0021. However, some fissions occur in
238U due to fast neutrons, and in reality β > 0.007, the greater the better for reactor control.
The fraction, β, represents a fraction of the total neutrons produced from fissions occurring at the same point in time. The lag of seconds up to 56 ~seconds allows one to make small changes in reactivity (removing a control element or control rod, typical in a BWR) or diluting/reducing boron in the coolant gradually (in a PWR).
The statement "in an assembly with prompt k of 0,9900, 1 spontaneous fission would on average induce 100 prompt fissions, but 280 fissions total... meaning that 180 fissions out of 280 (64%) would be due to delayed neutrons" is just wrong. I have never heard prompt k, or prompt k
eff, and certainly not for an individual assembly in a reactor core (we do refer to prompt critical, which is a reactor condition to be avoided). The value of k (or k
eff) applies to the entire system. One will not find 64% of fissions due to delayed neutrons, and it is not clear where one gets 100 fissions, but 280 total.
One neutron causes on fission, which releases 2 or 3 (on average about 2.2 to 2.3) neutrons. Some will be absorbed by structural materials, e.g., cladding, grids, guide tubes, in-core instrumentation or by the coolant (certainly the boron in the coolant in a PWR, but also the H in the H
2O), or by a control rod in BWR, or by a burnable absorber in the fuel or in a special element. The fuel components,
235U and
238U may absorb neutrons without fissioning, and simply emit a gamma ray instead, and then fission products, particularly Xe-135, absorb thermal neutrons. And finally, a small fractions of neutrons simply exit the core (i.e., leak out) and do not return.
Furthermore,
235U is consumed, or depleted during reactor operation, and some if it is replaced by
239Pu,
240Pu,
241Pu,
242Pu and heavier transuranic elements. Both
238U and
240Pu are important with respect to the Doppler broadening of absorption resonances, which mitigate thermal reactor transients.
I'm not sure from where the last statement, "Whereas if k is 0, then the neutron yield from delayed neutrons would be about 0,34%. I've never heard of k = 0, except for a defueled, or mostly empty, or a fully depleted core.
The OP was asking about binding energy and how it related to energy produced from fission. That question has been answered.