# What is the distribution of energy between the alpha, beta and gamma particles emitted in nuclear fallout per one RAD?

I have been trying to find a relation to be able to convert from RAD to REM. What I found is that I need to know the "quality factor" as some sources call it, which is the effect of different ionizing radiation particles measured to the effect of gamma or x-rays on the human body. This quality factor is known for different particles as 1 for gamma and beta and 20 for alpha particles. Since I know very little about fission products decay and the sources for each particle in nuclear fallout, I can't seem to find an average for the overall effect of these particles unless I get to know the energy distribution between them, and since the alpha particles are easily stopped by a few inches of air it doesn't contribute directly to the hazards of fallout so the quality factor must be less than one, but by how much ? What I exactly need to know is how much of the 100 ergs of energy absorbed by 1 gram of matter (1 RAD) is actually from alpha particles. Any help would be appreciated.

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This is going to depend on how much time has passed since the radioactive material was released. The various products all have different half-lives. – Ben Crowell Oct 13 '14 at 1:52

You seem to have hit upon the challenge. Converting between the two is situation dependent. It depends on the source of the radiation and the amount of protection. One source might deliver energy as 50% alpha and 50% beta another might be 100% gamma. Put a sheet of paper in the way and the first source will shift and deliver a higher percentage of energy by beta (because fewer alpha particles will reach you).

To get all of this very correctly, you'll need to know what decay is going on (type, energy and rate). How much of it will reach the target, how much energy the particles may loose on the way (mostly an concern for neutrons and protons I think). Also, how much will actually get absorbed by the target for each kind (some stuff will zip right through you).

You can try to soften up on this up a bit with assumptions. There isn't really a generic answer to this question.

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This is absolutely right: the conversion from energy deposition (rad) to biological damage effectiveness (rem) requires a nontrivial amount of modeling. – rob Jul 30 '14 at 14:24

To illustrate the difficulty of answering your question, here are the components of a local fallout model, as given in Stanford's Fallout models and radiological countermeasure evaluations (PDF link):

1. Weapon models
2. Condensation models
3. Particle cloud models
4. Distribution models
5. Contamination models
6. Dose models
7. Resource models
8. Transport system models

Every one of these models contributes complexity and uncertainty to the final answer. If you want to investigate dose contributions without considering all the degrees of freedom of the physical system, you need to make gross assumptions about the radioactivity around your target.

You might start by finding data on airborne beta-gamma emitting radioactivity concentration at a given point in the plume at a given time after detonation, model the dose in the target, and then compare that to a simple ingestion model with an assumed airborne alpha-emitter concentration.

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