The note about total mass of bound particles is the key. The sum of the masses of the fission products is less than the masses of the exited 236U nucleus.
Wow this result is impressive. May I ask you to try to explain the reason behind the drop in the total mass, please?
Total mass drops if, and because, the total binding energy increases.
Nuclei are held together by the strong force -- which is strong, as the name says, but has a very short range. So in bigger nuclei it has relatively more difficulty overcoming the Coulomb repulsion. Hence the downward slope for larger ##Z## in your picture in post #3. And energy = mass.
Where the masses of the products of a reaction are less than the reactants, the difference in mass is manifest in the kinetic energy of the products, and is exothermic, i.e., produces excess energy. The nuclei of fission products are more tightly bound than the original U-235 (or Pu-239,-241). Fertile (or fissionable) atoms like U-238 or Pu-240, require fast neutrons to induce fission, otherwise, they tend to emit gamma radiation instead of fissioning.
That's an example of spallation reaction. One would not expect to see a fission reaction with that result.
Which is kind of a matter of definition. Endothermic reactions, like
I don't believe that losing energy (or endothermic reaction) is a qualifier for a reaction being classified as 'spallation', but perhaps it could be. Spallation reactions do release some energy, but it's more the case they transform energy. Usually, in a spallation reaction, one or more of the products is similar in size to the incident (projectile) particle that hits a nucleus, e.g., (n,p), (p,n), (n,d), (n,α), or even (p, #n), where the # depends in the energy of the incident p and the target.
Source: https://inis.iaea.org/collection/NCLCollectionStore/_Public/23/015/23015552.pdf
In which case, if fission is really symmetric, you would get two nuclei of Pd-118. Which promptly decay to Sn.
However, the fission of uranium usually releases at least two neutrons, or sometimes 1, or 3, or 4, but on average slightly more than 2. So one might expect 2 atoms of 117Pd, which would promptly decay to 117Ag > 117Cd > 117In > 117Sn. Meanwhile, these nuclides may absorb a neutron. Furthermore, one might find 116Pd, 118Pd rather than two 117Pd. However, Pd is much less probable than other fission products.
This is incorrect. Where did one get such information?
Cluster decay:
SF of 235U, 239Pu, 240Pu, 241Pu, . . . is NOT vital for a nuclear reactor, even in the cold zero power, because there are insufficient neutrons produced, as calculated above, and SF contributes an insignificant, minuscule amount of neutrons to the neutron production.
We usually only refer to subcritical (keff < 1), critical (keff = 1) or supercritical (keff > 1)). The idea of using a neutron source in a reactor is to approach criticality with some idea of how close one is to criticality, without unknowingly exceeding criticality. The number of neutrons (on average) emitted by SF is given in the table in the Wikipedia article one cited. For 252Cf the average is 3.73, which is roughly twice that of 235U. Note also the half-lives of those nuclides.
But in a core with all fresh fuel that has never undergone chain reaction the only source of neutrons (if no additional n source is present) is SF is it not?
This depends on the criticality state of the assembly.
Yes, which is why neutron sources are placed in fresh fuel in order to monitor approach to criticality during startup.
Fission products from SF would be very low, since during processing of ore to concentrated oxide and oxide to UF6, undesirable elements are removed. There are restrictions on elements in nuclear fuel ceramics, which are measured for each batch of fuel.
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.
To keep conversion simply, let's say we have 1000 neutrons at some time T and population P within a reactor that is at the very start aka low power end of a power up procedure. For a fresh fuel assuming the beta 0.0064 would that mean that of those 1000 fission neutrons 6 will be the delayed ones?
You are right. I confused two possible ways to measure delayed neutron production: delayed neutrons per fission event (which produces 2 fragments and a variable number of prompt neutrons) or delayed neutrons per neutron. The quoted value of approximately 0.0064 or 0.0065 for 235U for thermal neutrons is applicable per neutron.
If your keff is 0,9964 counting delayed neutrons or 0,9900 on account of prompt neutrons alone then on average one fission event should produce an avalanche producing 100 fissions through prompt neutrons. But one shake is what, 10 ns? The avalanche is on average over in a microsecond.
0,34% was mistake from assuming 0,64% to be per fission and converting to per neutron, whereas it was per neutron to begin with. My point was to compare the state of k=0 (no subcritical multiplication at all) to the situation where k is near but below 1, so the neutron flux is dominated by subcritical multiplication.
The wording was "why do fission reactions release energy".
I agree that delayed neutrons can start fission just like SF neutrons but how can a core "not be subject" to a neutron flux when in "supercritical" state?
Look at the derivation above. For the critical mass of 50 kg HEU, the SF rate is just 8 events per second by high estimate - and there is a far lower estimate offered.
In high subcritical state, yes. What you see is the outcome of avalanches, which is determined by the conditions for the final stages of avalanches, not the originating event (intentionally added neutron source, SF, delayed neutron from fission product, photoneutron due to fission product gammas, α-n reaction, cosmic ray...). And what you could see is the frequency of avalanches.
Yes, roughly a delayed neutron fraction 0.0064 means that of 1000 neutron at a given instant, approximately 6 would be delayed. I'm not sure what one means by "at the very start aka low power end of a power up procedure." A fresh core starts at cold zero power (CZP) then gradually comes to hot zero power by running pumps to get flow and establish temperature at hot zero power (HZP). From there, approach to criticality begins, and since there are no delayed neutrons and very few neutrons from SF, neutron sources are used to produce enough neutrons to count. From criticality, control rods are moved (withdrawn) gradually (and in the case of a PWR, boron concentration in the coolant reduced), just enough to get a small increase in power (fissions). This occurs in steps to hot full power (HZP). There are periods of holds, or constant power, where the reactor instrumentation is checked to verify accuracy and consistency of readings in temperature and power (neutron flux) distribution.
The convention is to normalize the neutron population to 1. Remember, we consider about 1E20 neutrons per second, of which 6.4 E17 would be delayed, if all fissions originated in 235U. In reality, since fissions occur in 238U, the delayed neutron fraction is greater. I've seen different numbers, so I will contact a colleague and try to get a typical number for his power reactors.
The delayed neutron population may vary slightly. As the neutron flux increases, the fission rate increases (as does the thermal energy), or as the neutron flux decrease, the fission rate decreases, which is how one operates a reactor. Usually power reactors operate with a constant power, within an allowable band. The delayed neutron fraction is more or less constant with constant power, but may change based on neutron energy spectral changes and change in core composition.
One is describing a reactivity insertion accident (RIA) scenario in which some amount of reactivity is introduced into the system. Reactivity (that is, positive reactivity) can be introduced by various means, e.g., inadvertent dilution of boron in the coolant (in a PWR), or by inadvertent removal of a control rod in either PWR or BWR. In PWRs, one is concerned about control rod ejection under different conditions, and in BWR, one is concerned about control rod drop. When reactor is shutdown, all control rods are usually in the core, or some could be removed, but one would never remove enough control rods to the point where the core would be critical.