Physical Insights

An independent scientist’s observations on society, technology, energy, science and the environment. “Modern science has been a voyage into the unknown, with a lesson in humility waiting at every stop. Many passengers would rather have stayed home.” – Carl Sagan

On units, doses, and physical realities.

with one comment

If we’re going to talk about things like radioactivity and nuclear energy in a sensible, quantitative and scientifically sound way, we need to first establish some of the units and quantities involved, in an understandable way.

Firstly, we have the units of radioactivity, the Becquerel (Bq) and the Curie (Ci).

The Becquerel is a fundamental SI unit, simply 1 nuclear decay per second. As a fundamental SI unit, it is often used in professional and scientific literature.

But in the physical environment, 1 Bq is a very, very small thing, because 1 atom, or 1 nucleus, is a very, very small thing indeed.

Therefore, in practice, we usually consider multipliers on the units, such as kBq, MBq and so forth, as I’m sure we’re all familar with, from considering familar every day units such as the kilogram.

(I will take this opportunity to, once, apologize to readers of this blog in societies not yet illuminated by the wonders of the Metric System.)

The Curie (Ci) was originally defined as the radioactivity of 1 gram of Radium-226.

This corresponds to 37 GBq, or 37,000,000,000 Becquerel – 37 billion decaying Radium nuclei per second.

So, we see that in real-world contexts, 1 Bq really is very small.

Whilst the Curie is not fundamentally an SI based unit, it is very commonly encountered, and we see that it makes sense to use it in practical situations, instead of talking about billions or millions of Bq, although using the SI prefixes is acceptable, and SI-compatible, too.

1 Ci is actually a lot of radioactivity. Things such as medical diagnostics, medical treatment using radioisotopes, industrial gauges and radioisotopes used in scientific experiments typically involve on the order of 1-10 milliCuries.

Let’s consider a real-world example, in order to put, in context, just how small 1 Bq is, in the context of natural, background sources of radioactivity.

One average banana, or an avocado, contains about 500mg of natural Potassium, and all Potassium in nature contains 0.0117% Potassium-40, a radioactive beta emitter with a half-life of 1.277 billion years.

When discussing amounts of radioactive nuclide, it is often convenient to introduce a quantity called the specific activity, which is simply the amount of radioactivity per amount of mass of a given radionuclide.

The half-life of a radioactive nuclide is probably a concept all readers will be aware of.

The half-life of K-40 is 1.277 billion years, which means that over that amount of time, half the radioactive nuclei originally present in a sample will have decayed.

If we start with say 1g of K-40, there are (6.02*10^23 / 40) atoms present in the sample, where 40 is the atomic mass and 6.02*10^23 is Avogadro’s constant.

Thus, we can write down what the specific activity is, as 6.02*10^23 / (40 * 2 * 1.277*10^9 * 365.25 * 24 * 60 * 60) = 186.7 kBq /g, or 5.05 microcuries /g.

Therefore, a banana contains about 500*10^-3 * 0.0117*10^-2 * 186.7*10^3 = 10.92 Bq

That might not sound like much, and it isn’t, but it’s there, in every single banana, and all other fruits and vegetables, rocks and so forth.

And that’s only one radionuclide, Potassium-40. There are numerous other radionuclides which occur everywhere in nature and in your body, such as Carbon-14.

An average adult human contains, on average, 4000 Bq of K-40 and about 1200 Bq of C-14, amongst others. And that’s completely natural and normal.

One can calculate that solid Potassium Chloride contains about 16.35 Bq/kg in the form of K-40. From this, we can calculate that the 90 kBq released into the ocean following the effects of the widely publicised local earthquake on the Kashiwazaki-Kariwa nuclear generating station is the equivalent of 5.5 kg of KCl being released, or about a carton and a half of a salt substitute for food, such as “No-Salt”.

The Canadian Nuclear Society has a detailed fact sheet available, with further information on the K-40 activity of various foods.

Now that we’ve established how radioactivity is measured, it’s important also to consider doses of radiation to the body, and how they’re measured.

The sievert (Sv) is the SI derived unit of dose equivalent. It reflects the biological effects of ionising radiation as opposed to the physical aspects, which are characterised by the absorbed dose, measured in grays.

One gray (Gy) is the absorption of one joule of radiation energy by one kilogram of matter.

The average radiation dose from an abdominal X-ray is 1.4 mGy, that from an abdominal CT scan is 8.0 mGy, that from a pelvic CT scan is 25 mGy, and that from a selective spiral CT scan of the abdomen and the pelvis is 30 mGy.

The biological effects vary by the type and energy of the radiation and the organism and tissues involved, and it’s here where units such as the Sievert are employed, so as to quantify the biological effects of ionising radiation exposure.

The equivalent dose to a tissue is found by multiplying the absorbed dose, in Gy, by a “quality factor” Q, dependent upon the type of radiation, and a factor N, dependent on other factors, such as the part of the body irradiated – for example, tissues such as the sex organs are more sensitive to radiation damage – and the time and volume over which the dose was spread.

For example, gamma photon or beta particle radiation has Q=1, but for alpha particle radiation from an alpha emitter ingested or inhaled into the body, Q = 20, a significant increase.

The natural background radiation dose varies considerably in different geographical locations, but typically is around 2.4 mSv annually. For cases involving high dose single-dose whole-body irradiation, 2-5 Sv causes nausea, hair loss, hemorrhage and acute radiation poisoning which can be fatal. More than 3 Sv will lead to death in 50% of cases within 30 days. Over 6 Sv or so, fatality is almost certain.


Written by Luke Weston

July 25, 2007 at 2:59 pm

One Response

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  1. Hi Thanks for demonstrating the math.

    I am surprised at the coal pant figures

    Annual dose from living within 50 miles of a coal fired power plant: 0.03 millirem, or 5.45 Banana Units. You say this is per year. So the same as eating around 5 or 6 bananas a year? Am I missing something? I thought coal plants were much more harmful.


    March 11, 2011 at 5:37 am

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