# Peter Lux

## Uranium Enrichment Formula

This is another one of those background information posts deriving the mass balances for uranium enrichment. Let us consider the following enrichment  scenario: We have mass F of unenriched uranium entering on the left. It has Nf of U-235 (0.72% for natural uranium). After enrichment mass P of product enriched to Np of U-235 and […]

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## Secular and Transient Equilibrium Formula

I will give the full derivation since although it is quite long and looks complicated it uses nothing more than A-level mathematics. Despite this the solution of the differential equations is usually given as a standard solution rather than derived. Consider a parent isotope (P) decaying into a daughter product (D). The rate of decay […]

## Secular Equilibrium

The reason for this post is to help people understand ‘secular equilibrium’. The reason for people interest is mainly due to this report which is based on data here. I have a bit to say about this data but will not go into it now. If you want a more mathematical explanation the see here […]

## Thorium and Proliferation

I will probably write about the Thorium cycle a bit more at some later point. There seems to be a growing number of people who say that we can use Thorium as a nuclear fuel. One of the reasons they state is that you cannot make a bomb from Uranium-233 and therefore the thorium cycle […]

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## Nuclear Fusion

Let us look at the graph for the energy of various nuclei. Remember tht this graph is upside down and so Iron (Fe) has the lowest energy. We have seen when talking about alpha decay that some elements with atomic number higher than that of iron can decrease their mass by emitting an alpha particle […]

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It would be useful at this point to talk a bit more about Uranium and its isotopes. Uranium naturally occurs as two isotopes details of which are shown below. Atomic Mass Halflife Occurance 238 4.5×109years 99.3% 235 7×108 years 0.7% Of the two isotopes only Uranium-235 is fissile. However some of the Uranium-238 is converted […]

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## The Rate of Decay

The rate at which these unstable isotopes undergo decay varies greatly between the different isotopes. The process is random for each atom. However there is a fixed probability that an atom will disintegrate over a fixed time scale. It is rather like throwing a dice – on an individual throw then you cannot be certain […]

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When an atom undergoes alpha or beta decay it can leave the nucleus in a high energy state. The atom goes to a lower energy state by emitting light. This light is very high energy (high frequency – short wavelength) and is called gamma (γ) radiation. The nucleus stays the same i.e. its atomic mass […]

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## Decay Chains

When an atom undergoes radioactive decay the isotope produced is not necessarily stable itself. If it is not then that can undergo radioactive decay. This can carry on in what are called decay chains. In the diagram above the atomic mass is along the bottom (204-240) and the atomic number up the side. Starting with […]

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## Moderation

We have discussed fission and neutron capture. Now we are going to talk about how we can increase the likelihood that fission or neutron capture happening. What happens depends on the energy (speed) of the neutrons. The neutron induced fission process is much more likely to happen if the neutrons have a lower energy than […]

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