The Banana Dose RATE PROFILE

Figure 1. The Banana Dose Rate Profile

In a recent discussion, I stupidly brought up the banana dose. It's not dose. It's dose rate profile. Go to the blackboard and write that 50 times, Jack. Then I compounded my error by mischaracterizing what the banana dose rate profile looks like. Figure 1 shows a far better guess at the banana dose rate profile.

In concocting this profile, I had to make a string of pessimistic assumptions to push the profile's cumulative dose up to the conventional 0.1 microsievert. I had to assume a big banana. I had to assume 100% uptake.¹ A better average number would probably be 90%; but it depends on the eater's current potassium level. I had to assume 100% of the photon energy is absorbed in the body. Actually as much as 50% will escape, which is why sleeping with a banana eater is so dangerous. I had to assume a biological half-life of 30 days.² Actual tracer measurements indicates the absorbed potassium hangs around in the body between 10 and 28 days, with a mean of 16 days.\cite{rahola-1975}

Far more fundamentally, people have pointed out that the body is very good at regulating potassium levels. If a banana elevates the potassium level above normal, the body will speed up potassium elimination; and, since all the potassium in the body has the same K-40 concentration, the original level K-40 will be quickly reestablished. We will ignore those killjoys.

The profile we came up with starts out at about 0.002 microsieverts per day and is down to one tenth of that in about 100 days. The LNT cancer mortality is 4 parts in a billion. Pretty small, but if all 8 billion denizens of the Earth eat a banana a week, bananas are killing 1600 people a year. Perhaps we should consider banning them. Remember bananas are often the first solid food that a mother feeds to her baby.

I don't know what the SNT banana profile mortality is. The problem is the denominator in the logistic formula is so close to one that my floating point processor, which is only good out to 16 decimal digits, has to call it 1.00. After that it's zeros all the way. Mothers, if a 64 bit processor has to call a number zero, then you too can treat that number as zero. It's safe to feed bananas and all their good nutrients to your babies.

This silliness does make a couple of points. In order to determine "the dose", we need to first measure or somehow reconstruct the dose rate profile. After we have done that, we compute "the dose" by calculating the area under that profile, and ignore everything else. We throw away all the important information including the spikes. This reminds me of the old recipe for cooking a stew pot. Prepare a wonderful stew, beef, veggies, bouquet garni, simmer slowly in a good Bordeaux for 8 hours, and then throw away the stew and eat the pot.

The other takeaway is that, since SNT's slope goes to zero as the daily dose goes to zero, there is no practical difference between SNT and a zero threshold at the low end. In fact, my computer is adamant that there is no difference.

1. Uptake is the fraction of the consumed isotope that is absorbed into our blood stream. The rest is excreted in a day or two. Potassium has very high uptake. Some elements such as plutonium have essentially zero uptake.

2. Biological half life is the average time the absorbed portion of the isotope remains in the body, before it is eliminated in the normal course of events.