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A very odd counting geometry

Dear Reader,

After someone made the claim that cesium-137 inside humans is hard to measure I have been considering the geometry of the problem of counting the cesium-137 inside a person.

Now a long running joke in science is that real life objects have friction and a series of other features which make them harder to understand, but the special “physics” pulley (which does not exist in real life) has no friction. It is a perfect pulley. These “physics” objects are used to allow us to make progress in our reasoning, by making the system slightly more simple we can reduce the mathematical work load and then be able to consider a more simple system. After we deal with the simple system we might then add some more features to make it closer to real life.

When considering the absorption of gamma photons inside an object I choose to make the system more simple.

1. I choose to ignore the buildup effect

2. I imagined a 2D version of real life where a special radioisotope exists which only emits photons in the plane of the sheet of paper which I draw diagrams on was used.

This has allowed me to make some progress, but some things are a little different to the real world.

I imagined a perfect circle of material in which the radioisotope is placed, this circle is then placed inside another circle (coaxial arrangement) and the gap between the two circles is assumed to be filled with a perfect photon detector which is able to capture and detect every photon which crosses the circumference of the circle.

This geometry does lead to a change from real life.

In real life the intensity of a photon source (ignoring scattering effects) obeys the inverse square law. This means that the intensity is quartered each time you double the distance. This is because the surface area of a sphere is proportional to the square of the radius. A 2D object (circle) has a circumference which is proportional to the radius, as a result we can not use the inverse square law in our 2-D model.

I am still working on the model, I hope to be able to share the results with you soon and then move onto a 3D model.

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