Radiation adjacent to a cell as compared to 1 meter away
BRAWM, please comment on the following: Since radiation is inversely proportionate to the square of the distance from it's source; is the difference in the radiation from say, Cesium 137, one micrometer from a cell 1 trillion times greater than the radiation of Cesium 137 one meter from that cell? (radiation at 1 meter * 1,000,000 squared). If my math is correct the radiation received right next to a cell (internal exposure) is one trillion times greater than radiation from the same source when it is one meter from the cell. (or conversely, the radiation one meter from it's source is one trillionth it's level 1 micrometer from it's source). Is this correct? Please comment.
I hope I can shed some light
I hope I can shed some light on the inverse square law:
The purpose of this law is to answer the question: if I have something radioactive (it applies to other things, but of course here we care about radioactivity) and it's emitting some radiation in all directions, how much radiation ends up hitting an object some distance away? That object could be a detector, a wall, or a human being. To figure this out, we need to know how big the object "looks" to the radioactive source -- a concept called solid angle. The closer it is, the bigger it looks, and thus the more radiation will hit it. It doesn't take into account energy, particle type, or how much damage is done to a cell; it's only counting how many times the object is hit.
The solid angle for large distances away is proportional to the inverse square (hence the law). However, it's not so clear when the radioactive source is right next to the object in question. Consider the case you gave in the original post, where you are 1 meter away. The source is emitting radiation in all directions, so a lot of it doesn't travel towards you. We could use the inverse square law to estimate how much hits you -- roughly 1/(4 pi), or 8%.
Next, consider the case where the source is right next to you, on the surface of your skin. Do we take the distance to be zero? No, that would be silly, because then the inverse square law gives a result of infinity. We're too close to use it. We can say, though, that half the time the source emits radiation away from us, and the other half it goes toward us -- so now 50% of it hits your body.
Finally, consider when the source is inside you. No matter which way it emits the radiation, it will always hit your cells. 100% of the radiation hits your body.
If you tried to estimate danger only based on proximity, you'd find that internal sources are only twice as dangerous as external (100% vs 50%). We know that's not right; there are many more factors to consider, like what type of particle is emitted, where it accumulates, etc. These are the things considered when we calculate the dose.
Tim [BRAWM Team Member]
Well, other than that
External sources of Alpha and Beta emissions at a distance of 1 meter, pose virtually no health hazard whatsoever. We shall assign this circumstance a value of 0.
Internal sources of Alpha and Beta emissions pose great health hazards. We shall assign a value of 1.
And now the math ...
1/0 = undefined
Or in the language of calculus:
1/X
Lim X -> 1 = Infinity
Errata
Correction:
revise that to Lim X -> 0
More info
I've also made some comments that add to what Tim is saying:
http://www.nuc.berkeley.edu/node/4696#comment-12444
Mark [BRAWM Team Member]
Yes
Yes:
One trillionth is a good number.
1/1,000,000,000,000
Inverse Square Law
It is perhaps more accurate to describe a radionuclide within the nucleus of a human cell. The radionuclide is thus surrounded by the genes and DNA, which can be considered as a reference distance of 1 micron.
Alpha/Beta/Gamma/Neutron collision, with genetic material, located within the human cell nucleus is virtually assured.
At a distance of one meter, Alpha and Beta collision with internal cells is 'not a player'. The subtended spherical angles are tiny for a single point emission of Gamma/Neutron from a radial distance of 1 meter.
For example, one (1) degree in the horizontal plane and one (1) degree in the vertical plane would correspond to 1/(360 X 360).
Other factors such as scatter, velocity, shielding and the like, have some play in the inverse square law. So for example, a directed, coherent laser light would presumably not be subject to the inverse square law, while white light is.