What is the significance of whole body dosage in radiation exposure?

[Dazz4C]

Hi Everyone,

I was just preparing for an exam I have next week regarding the use of Po-210 on Aleksandr Litvinenko. As I came across doing some calculations, something got me puzzled...the 'whole body dose' of energy is extremely low and to me shows no real significance. I'll show you what I mean.

In my exam, I am required to calculate a plausible amount of Po-210 that may have been used to kill Litvinenko.

Now to do this, the amount of dosage was equal to:
$$\frac{1 mol of Po-210 in grams*whole body dose}{Energy released by decayed atoms}$$

Now, I've already gone and found the other two variables (1Mol of Po-210 in grams, and Energy released) but will not write the calculation down as some other students might google this and come across it :P.

Anyway; here's the calculation for the whole body dose.

100% Death is guarenteed at 4.5 to 6 Siverts. For this example, I'll use 6 Sv (Siverts). Calculation of Siverts can be expressed by:

Siverts = Absorbed Dose (Grays) * Quality Factor

Now, we let the Siverts = 6; and let the Quality Factor = 20 because we are dealing with Alpha particle radiation. So therefore:

6 = AD * 20
AD = 6/20 = 0.3 Gy

Gray can also be written as J/Kg. Therefore, 0.3 Gy = 0.3 J/Kg. Therefore, for each Kilogram of bodyweight 0.3J of energy released by Polonium is absorbed.

Now, as I can't really find many sources on Litvinenko's weight; we'll assume a body weight of say, 85Kg (Fit male; he was ex-KGB)

So for the whole body dosage:

85Kg * 0.3J/Kg = 25.5 Joules

This is what I mean...25.5 Joules is not a lot. Humans consume and use more energy than that. Absorbing 25.5 Joules seems rediculous, unless I went wrong somewhere.

So..TL;DR - Can someone explain to me the significance of the Whole Body Dose (other than simply stating that it's used in calculation, because I've figured out how much Po-210 was used)

P.S. Sorry for not using LaTeX...school filter stops the Latex Reference from loading.

 

[Norman]

With 6 Sv (whole body dose, acute exposure), you see circulating blood cell death, moderate GI damage [1]. So, you stop being able to absorb nutrients well (GI damage) AND you are having trouble oxygenating your cells and fighting off disease (blood cell death).

A question you need to answer in order for you to understand what is going on here on the broader level is why is a Gy (J/kg) the relevant quantity (up to a scale factor) for radiation damage and not just Energy (Joules)? Eric Hall's book - Radiobiology for the Radiologist has a very nice discussion in which a comparison is made between the temperature change from drinking hot coffee and the mechanical energy needed to lift a person compared to the total body irradiation of 4 Gy. The relevant quantity is for damage done is (in a very loose sense) the actual area over which the energy is deposited. Radiation damage is deposited unevenly along the track the particle takes. So basically, the whole body dose is a poor description. It is really a systemic dose across the whole body, but deposited locally along the track each specific particle takes. I hope this helps.


Sources:
[1] DOE Office of Science, Ionizing Dose Ranges

 

[Dazz4C]

But even then, a deposit of 25.5 Joules is not alot...now you've got me thinking. Perhaps, as you said the particle deposits energy systematically along its path of travel(?) it might be 0.3J of energy radiated onto cells?

This whole thing is confusing :(.

 

[Norman]

But even then, a deposit of 25.5 Joules is not alot...now you've got me thinking. Perhaps, as you said the particle deposits energy systematically along its path of travel(?) it might be 0.3J of energy radiated onto cells?

This whole thing is confusing :(.

What class is this for? What level of physics have you had? What book are you using for this class? These things would help me to tailor my explanation for you.

It is exactly the fact that the energy is deposited locally along the tract. In addition, there is another issue: Po is an alpha emitter and an alpha has a very small range - it is easily stopped. It is often quoted that a piece of paper stops alphas. So a large enough amount of Po was given to him, which he ingested. The alphas could only act locally where their parent (the Po) is. The Po entered the stomach. I don't know much about the metabolism of Po, but it likely traveled through the body to some degree (this depends on the chemistry of Po, which I know nothing about).

The bottom line in this specific case is that enough dose was delivered some important internal organs and systems. It was not a whole body effect.

I just found this article: http://www.independent.co.uk/news/uk/crime/nuclear-fallout-alexander-litvinenko-died-in-agony-who-killed-him-and-why-425896.html It states that his liver and bone marrow were destroyed and triggered a massive heart attack. So the Po was taken up into the blood stream and deposited in the bone marrow and liver. Seems reasonable.

 

[NobodySpecial]

But even then, a deposit of 25.5 Joules is not alot

No but neither is the energy needed to break a strand of DNA (for example)
Look up the bond energy for some vital chemical in your body, imagine if the 25J was divided evenly to give each just this energy and work out haw many blood/brain/liver cells you could kill

 

[Barwick]

Well, to give you an idea, it's all related to the area the energy is being directed at. I mean, it only takes a fraction of a Joule to cut a main artery, and a person dies.

In his case, he ingested radiation that killed a significant portion of his GI tract, which alone will kill someone. If any of the radioactive material was absorbed into his blood, that would also cause damage.

To give you an idea, a 22 pistol only has 159 J of energy when it leaves the barrel, and starts going down from there. But it'll kill you without any trouble. In one second I can create 159 J of energy. Heck, I can do that for a very very long time, creating 159 J of energy every second for a while...

 

[Dazz4C]

I see. Thanks guys :).