eli5 How come if highly radioactive radium was on watches that the wearers didn’t succumb to radiation poisoning at the wrist?
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The danger of radiation scales down with distance *squared*. If you double the distance, then you get only 1/4 the dose. (The opposite is true: if you get twice as close to the source, you get 4x the dose of radiation.)
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The danger from radiation scales up with time. If you spend twice as long with the source, you get double the dose.
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Let’s make some very rough estimations to get a ball-park idea of how to compare these two exposures to radiation.:
If you were working in this factories, you were told to use your lips to put the paitnbrush to a point and help you get the finesse to paint the watch-hand without wasting materials. Just to make the calculation easy, let’s *assume* that the amount of radium ingested and later extreted through the body each day was maybe the same amount as on the average watch, and let’s assume it takes 24 hours for you to excrete it all.
If you wear a watch, you get get a small amount of radium maybe on average about 50cm (or nearly 2 feet) from your centre of mass, for half the day while you wear the watch.
If you ingest the radium, well, it probably absorbed into your body, but let’s only assume that it passes through your digestive system. Your digestive system is through a lot of your body, but let’s assume that on average it was like 10cm (~4 inches) away from your cnetre of mass on average as it travelled through your body.
Also, if you injest the radium, then you have it in your for 24 hours, not just half the day.
So, even assuming you simply urinate/poo-out the radium, and none of it gets absorbed into your body, we’ve approximated that you have 2x duration, and are 5x closer to the source. We square the closeness factor, so 25x there. Stack 2x with 25x to get 50x as much radiation.
So, as a *very* rough estimate, being a radium girl was probably as bad as wearing 50 radium watches.
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It gets worse, because you don’t simply poo out all the radium. A google search suggests maybe 20% of it gets absorbed into your bloodstream. Some of that will later pass through your urine, but some of it will stay in your bones, and directly radiate those bones. Let’s say that makes it twice as bad on average (I think this is underestimating it!)
Then it is 100x as bad as wearing a radium watch, and might get worse and worse the longer you work there.
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Now, this was **not** a valid calculation I’ve just done here. It was a very rough estimate, based on some flawed assumptions. (e.g. trying to estimate your ‘distance’ from atoms literally inside your bones is kind of strange.)
However, an accurate calcualtion would consider factors similar to what we considered here, and though they’d have more sophisticated methods, you can see how there are important factors that set the radium girls apart from the customers who bought their watches.
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