Nuclear Physics Explanation for Each Taste

What is the formula when two exponential-decay processes take place simultaneously?

Nuclear fission mechanism: neutron capture
Consider this nuclear fission reaction:
${}^{235}\mathrm{U}+{}^1\mathrm{n}\to <!--\; \to \; -->{}^{236}\mathrm{U}\text{ (excited)}\to <!--\; \to \; -->{}^{92}\mathrm{K}\mathrm{r}+{}^{141}\mathrm{B}\mathrm{a}+3{}^1\mathrm{n}$
I have not understand why a thermal neutron (${}^1$n should be captured by the nuclei of ${}^{235}$U.
What are the conditions under which this neutron is captured?
My reasoning is the following: the energy that the neutron must have to be captured by the ${}^{235}$U should be equal to the $S_{\mathrm{n}}$ (separation energy for a neutron) of ${}^{236}$U which I found is 6.34 MeV, higher than the energy of the thermal neutron. So my reasoning must be wrong but I cannot understand where I make mistakes...
I looked on the Povh Rith Particles and Nuclei but it does not explain the reaction well. Could anyone give me a reference or explain here the fission reaction ?

Control of Nuclear Fission
What is it precisely which prevents current technology in nuclear fission from controlling the size of fission products; in other words, why is it not feasible, presuming that such an approach would permit the translation of binding energies to heat in nuclear fission reactions, to create lighter more manageable fission products, thus rendering that fission technology relatively safe? Further, if this constraint is due to the electrical neutrality of the neutron, what prevents the induction of a manageable charge or manipulation of the neutron magnetic dipole moment?

You are given 230 grams of a substance with a half-life of 0.75 years. How much will remain after 3 years?

Science project on the Sun. I have found that in order for nuclear fusion to work, it needs both helium 3 and 4.
1. Why can't nuclear fusion be done with just helium 4?
2. How can we create nuclear fusion on Earth?
3. Can we even do so?

Why is radioactive half-life important?

If a Tadalafil 10 mg/tab has a typical half life of 17.5 hours, how long will it take until the blood concentration of this dosage falls to 25% of its initial strength?

Apart from thermo-nuclear reactions in the Sun, (and in hydrogen bombs and other methods developed by scientists) does nuclear fusion occur naturally in the planets? If not, why?
Also, do the Sun and the Outer planets - Jupiter through Neptune - have rocky cores similar to the Earth (consisting of iron, nickel, silicon etc) in addition to the gases? I have read that there is not much of hydrogen or helium in the inner planets because of their low escape velocities and the solar winds from the Sun. Hence only the heavier elements remained.

What is meant by the half-life of a radioactive isotope?

Why is radioactive decay measured in half-life instead of the full time?

Birth of a star. Now in order for a star (or proto-star) to be born, there must be nuclear fusion that happens between hydrogen atoms. My question is what happens to the electrons? Sal never mentions them, only isotopes of hydrogen, and basically only focuses on the nucleus of the atom. Do the electrons even matter?

What is the half-life of Americium-242?

What are first order half life units?

Nuclear Feedback Loop (Fusion and Fission)
What are the main factors that prevent a feedback loop being created by using a hybrid method of fission and fusion. Fusion building up to fissionable materials, and fission breaking down till fusion is possible. Ex: numbers of neutrons, cross section for interaction, the gap between elements, amount of energy needed, probability of correct species being generated.
Further, would it be possible to at least get a few occurrences of the fission/fusion cycle.

At the temperature range of ordinary fire or maybe even ordinary boiling water, is the Coulomb potential between light atomic nuclei occasionally overcome to give way to fusion?
Basically, how are the nuclear fusion cross sections calculated and are they a function of temperature?

The half-life of calcium-47 about 5 days. Starting with 64 g of this isotope, what would be the amount remaining after 20 days?

What is the half life decay rate formula?

Calculate kinetic energy of neutrons in nuclear fission
How can I calculate the mean kinetic energy of an emitted neutron in a nuclear fission. Take for example the fission of U-235 to Ba-141 and Kr-92.
A calculation which just shows that the mean energy will be in the range of "fast" neutrons (> 1MeV) would be enough for me.

Energy released in nuclear fission
In induced fission of U-235, neutrons are bombarded at the U-235, producing U-236. This U-236 then undergoes fission:
U-235 + n --> U-236 --> Ba-141 + Kr-92 + 3n
As far as I understand, the energy released in fission is gained as kinetic energy of the products, and also released as gamma photons/beta particles and neutrinos when the products decay. My confusion lies in calculating the energy released, as I do not think the method in the textbook is correct.
The absorbed neutron loses nuclear potential energy. This causes the binding energy of U-236>U-235, meaning the rest mass of U-236 is less than the rest mass of U-235 + n. This increase in binding energy is then used to deform the nucleus into a double-lobed drop allowing the two fragments to separate due to electrostatic repulsion.
The two fragments formed have a greater binding energy per nucleon than U-236, and hence the binding energy of the fragments is greater than U-236. (In turn causing the mass of the products to decrease). However this increase in binding energy is gained as kinetic energy of the products/released as gamma photons etc.
Mo1 = Mass(U235+n)
Mo2= MassU236
Mo3 = Massfissionproducts
B1=binding energy of U235
B2=binding energy of U236
B3 = binding energy of fission products
The energy released in fission is due to the increase in binding energy B3-B2. The increase in binding energy B2-B1 is used to deform the nucleus - it is not 'released'. Therefore the energy released in the fission process = (Mo2-Mo3)c^2.
However my textbook states that the energy released in the fission process =(Mo1-Mo3)c^2. I don't understand this as they are including the energy to deform the nucleus, (Mo1-Mo2)c^2, when this is not actually released.
Any help is greatly appreciated!

What is meant by the half life of a radioactive nuclide?