Dear Reader,

After the horrible triple meltdown which was provoked by the giant tidal wave we have had a lot of people saying a lot of things on the internet.

One thing which seemed odd was the idea that the radioactivity inside a person was hard to detect, while there are some radionuclides which are hard to detect inside a person (such as Po-210) the vast majority of the radioactivity deposited onto the soil in Japan by the damaged reactors was beta/gamma emitters such as I-131 and Cs-137.

Now I am going to do a worst case calculation for the absorption of gamma rays by a torso for a key fission product. I am going to ignore the build up effects which make it slightly more easy for photons to escape from a torso and treat the problem in a simple way which will underestimate the fraction of photons which will escape from the body and thus can be detected.

Now I am not in the office right now so I can not get my hands on the “reference man”, while the name might sound like it only deals with men. This title is a bit of a misnomer, for example the copy of reference man which I have access to does give data on the typical size of parts of a woman. So the book should be the “reference person”. So I looked up on the web and found out that the average american woman has a bra size of 36C. Lets assume for a moment that all humans are identical to the average american woman.

If we assume that a torso is a cylinder with a circumference of 36 inchs, then as C = 2πr, then our torso cylinder has a radius of 5.7 inchs.

If we take the linear attenuation coefficient for cesium-137 to be 0.0862 cm^{-1} for water (and we assume that a human body is pure water), we can do the maths.

T = e^{-kx}

So as 5.7 inches is 14.5 cm we can get the answer.

T = exp (-1 x 0.0862 cm^{-1} x 14.5 cm) = exp -1.25 = 0.29

This means even for this very silly looking torso that if the cesium was concentrated in the form of a point source in the centre of the cylinder that 29 % of the gamma photons would escape from the torso. This value is very much the worst case value which you will soon see is far worse than the real value. This 29 % percent is not too bad, if we had 1000 counts per minute with a point source then the same point source inside the “torso” will give us 290 counts per minute. This is a bit lower but it should not be impossible to detect it.

1. In a real person the torso is not a cylinder, most people have torsos which are wider (side to side distance) than they are thick (front to back) hence is we have a 4 pi geometry for the counting (a sphere) then while for some directions the counting will be less efficient overall because the real human torso is closer to a phone book than a football in shape it should increase the efficiency.

Rather than just use an educated guess, I choose to consider the geometry. Right now I have not got around to programing the problem into excel so I am doing it with graph paper.

2. In a real human the cesium is likely to be evenly spread through the torso, thus the efficiency will increase. The photons from the cesium which is closer to the skin will be more able to escape from a person.

I drew a circle on my graph paper with a 3 cm radius, now at point A which is 1 cm from the centre I measured a series of distances from the point to the circumference of the circle.

2 cm (0^{o})

2.2 cm (45^{o})

2.85 cm (90^{o})

3.50 cm (135^{o})

4.0 cm (180^{o})

3.50 cm (225^{o})

2.85 cm (270^{o})

2.2 cm (315^{o})

While for the 2D version of a 4 pi geometry I predict that the effect of moving the cesium one cm from the centre of the 3 m radius circle will be very small (1 %), but for more normal geometries and sizes of torso it will have a greater effect in our favour.

When I recalculated for a 14.5 cm radius circle where the source was offset by 4.8 cm then the effect is now 9 % in our favour if we use the 2D version of a 4pi geometry.

I also made a calculation for a new point closer to the surface, this new point is 9.7 cm from the centre of the circle. Now the effect of moving the source towards the edge of the circle now makes the counting 40 % more efficient. I will improve my mathematical model and then report my findings to you good people.

I would like to point out that for smaller humans (such as children) that the smaller size of their torso will make the efficiency for the counting higher, this is because the self absorption effect will be smaller.

Filed under: cesium, Fukushima, Uncategorized |

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