The American units for human equivalent dose are “rem,” which stands for “Roentgen equivalent in man.”

Dose rate: the “temperature” of radiation

Think about setting the oven. If you set it to 350, that’s hotter than setting it to 250, but if you put something in for 1 second, the difference doesn’t matter much. But baking something at 350 for an hour does more than baking it at 250 for the same hour. It’s not the temperature, it’s the total amount of heat that cooks the roast.

We usually confuse the amount of heat in something, and the temperature. In ordinary life, the difference doesn't matter -- materials are enough alike we don't care. But not always, even so -- a cake in a metal pan at 350 will brown more where it's in contact with the metal than it will in a glass pan.

We could work through a similar series of steps, and go from the amount of energy available, to the amount absorbed, to how fast it’s transferred, and get a number that would actually be a lot more useful than just temperature, as far as letting us know whether we want to touch something or not. This number would be the “heat rate” and we’d know that something with a high heat rate is something we don’t want to touch. And with that, we’re finally coming around to our “how’s the weather?” measurement of radiation; the dose rate, or how much radiation energy we absorb per unit time.

The usual measure for dose rate is Sieverts per hour or rem per hour: that’s what really tells us how much effect the radiation will have.

Total Dose

The usual assumption is that the dose of radiation is cumulative in the same way. If you’ve absorbed 1 Gy of gamma ray energy, that’s a 1 Sv dose. Just as with baking, where a really slow heat over time will dry things out but not bake them, this assumption isn’t completely true; the body does repair radiation damage over time. But it’s easier to make this assumption, for safety’s sake and because without knowing more details of what was exposed, when, and by what, it’s hard to guess how much repair there will be. So we simply assume that the health effects of radiation are proportional to the total dose accumulated over our lifetimes, or over some long period like a year.

Now, at last, we have all the pieces we need to understand what’s happening at Fukushima. Start with the dose rate. This is the “how’s the weather” number. As of the morning of March 20 in Japan (the evening of March 19 in the U.S.) the dose rate was around 1 mSv/hr (0.1 rem/hr) at the main gate. Some locations, where some amount of radioactive material released appears to have landed and concentrated, it’s as high as 14 mSv/hr (1.4 rem/hr). A few places inside the plant were measured as high as 400 mSv/hr, or 40 rem/hr.

Now, by comparison, the normal background dose rate — the amount of radiation we absorb from the world around us — is 2.5-3.5 mSv/year — considerably higher here in Colorado, and higher still in parts of Australia, Brazil, China and India. In fact in Ramsar, in Rajasthan, the natural background dose rate is 260 mSv/yr — 100 times the “normal background” as we’ve defined it.

And 2.5 mSv/yr is about 0.0003 mSv/hr, so clearly at even 1 mSv/hr it’s considerably “warmer” than background.

But it’s still not that hot; by comparison, a normal chest X-ray is about 0.1 mSv, a mammogram up to 3 mSv, a CT scan can be as much as 13-15 mSv.

Here’s a place the news readers step on themselves: that’s total dose, not dose rate. It’s the difference between setting the oven to 350, and baking at 350 for an hour. The right way to think about it is to think about how long it would take to have the radiation affect your health. So at 1 mSv/hr, it would take 15 hours to accumulate the dose from one CT scan, and several weeks to accumulate enough dose to make much difference to health.

Making comparisons: the “banana equivalent dose”

There is an interesting way of comparing different amounts of radiation, and we've now built up all the pieces to understand it. Nuclear physicists and safety engineers sometimes use a unit called the “banana equivalent dose.” This is basically how it’s calculated.

First you take a banana.

Like pretty well everything in nature, bananas are slightly radioactive. Because bananas concentrate potassium, they are more radioactive than a lot of other foods — natural potassium includes some part that is the radioactive isotope potassium-40. That means eating a banana, and thereby ingesting the potassium, adds a measurable radiation dose from the radioactive potassium-40.

Now, before you change to kumquats or something, it’s not much, and bananas aren’t the only source. Potatoes are another food that concentrates potassium. But it does mean we can usefully compare the total dose we get from a banana with other small amounts of radiation. The somewhat-joking term for this is the “banana equivalent dose,” or BED.

In the earliest reference I can find to the idea of a banana-equivalent dose, a note attributed to Gary Mansfield of Lawrence Livermore National Laboratory works out the BED this way. By the way, I’m going to convert all the radiation amounts to Becquerel; Curies are a really inconveniently large number of this.

- According to the CRC Handbook on Radiation Management and Protection (pg 620), a “reference banana” is listed at about 130 Bq per kilogram.

- A “standard banana” weight about 150 grams

- So we get right about 20 Bq per banana.

When you eat that banana, the radioactive potassium enters the body; if you have enough potassium, the kidneys will flush it out within about a day, so for a short time you have that little bit more potassium in your body; you get some radiation dose from it. (You’re also getting a radiation dose from the radioactive portion of all the other potassium you have in your body, of course, but we’re just talking about this one piddling little banana.)

To really figure the dose-rate from being exposed to 20 Bq of Potassium-40, we’d need to calculate it based on distance, the specific energy of the emitted radiation, and so forth. You will, I’m sure, be pleased that I’m not going to explain that. Instead, I’ll refer to the excellent RadProCalculator on line, which tells us that one banana’s worth of radioactive potassium gives a dose rate of about 0.0037 µSv/hr. If the banana’s potassium stays in the body for about 24 hours, the total dose is 0.09 µSv. µSv times 10 gives µrem, so that's 0.9 µrem — call it 1 µrem, what the hell.

So,

- the banana equivalent dose rate is about 0.04 µrem/hr

- the banana equivalent dose is about 1 µrem

- eating one banana a day for a year is about 365 µrem/year

Now is the time when we compare

Now, let’s compare this. We’ll assume that the normal background dose rate is around 300 mrem/yr. The most recent reports from Fukushima have dose rates at the plant of about 20 µrem/hr, so one hour at the gate is about 20 BED. (Again, be careful — a lot of the legacy media is reporting 20 millirem/hr; the IAEA has 2 µSv, or 20 µrem, 1/1000 as much.) Looked at another way, one banana dose for a year is 365 µrem/300 mrem — or just over 0.001, one tenth of one percent, of the normal background dose.

The 20 µrem/hr, over the course of a year (8760 hours) is about 1762 mrem — or about 6 times normal background dose. Which is about one-tenth a single abdominal CT scan.

The inestimable XKCD, interspersed with the usual comics, does some amazing scientific visualizations. There is a new one that clearly visualizes how much radiation (dose) we’re talking about.

Lots of interesting trivia in that chart; the big thing to remember is that it took three big changes in scale to get from the sorts of dose around Fukushima to anything like Chernobyl.