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Quantitative Reasoning & Problem Solving
54 © 2014 Pacific Crest
Model 2: Dangerous Bananas
A digested banana produces 0.1μSv of radiation (ionizing radiation is measured in sieverts: “Sv”)
and this has led to concern for radiation poisoning because the Potassium-40 (40K) in bananas
(the element that is radioactive) has a half life 1.25 billion years. It has also been confirmed that a
truckload of bananas once triggered a false alarm while passing through a radiation monitor that was
used to detect the smuggling of nuclear material. How concerned should we be? Here’s a bit more
information to help you make sense of the numbers:
1mSv (millisievert) = 0.001 Sv
1μSv (microsievert) = 0.000001 Sv
1 Sv gives the biologically equivalent effect of 1 joule of radiation in 1 kilogram of tissue
1 Sv gives a 5.5% chance of eventually developing cancer as a result of the exposure
5 – 10 μSv = 1 set of dental x-rays
0.02 mSv = A typical chest X-ray
2 – 3 mSv = natural radiation most people are exposed to per year
15 mSv = how much radiation the organ being studied typically receives during a CT scan
(adults only; the measure is closer to 30 mSv for a newborn infant)
Model 3: Homeopathy
The “homeopathy” entry in Wikipedia offers the following with respect to homeopathic dilution:
Three logarithmic potency scales are in regular use in homeopathy. Hahnemann created the
“centesimal” or “C scale”, diluting a substance by a factor of 100 at each stage. A 2C dilution
requires a substance to be diluted to one part in 100, and then some of that diluted solution
diluted by a further factor of 100. This works out to one part of the original substance in 10,000
parts of the solution. A 6C dilution repeats this process six times, ending up with the original
substance diluted by a factor of 100 −6 = 10−12 (one part in one trillion or 1/1,000,000,000,000).
Higher dilutions follow the same pattern. In homeopathy, a solution that is more dilute is
described as having a higher potency, and more dilute substances are considered by homeopaths
to be stronger and deeper-acting remedies. The end product is often so diluted as to be
indistinguishable from the dilutant (pure water, sugar or alcohol).
Is this the kind of “cure” we need for our poisonous bananas? The numbers just don’t make sense if we
consider how many molecules of the original substance are found in a substance diluted to 6C...quite
possibly, none.
Critical Thinking Questions Developing your understanding
1. What are at least five different estimation techniques that you use?