Admit it, you didn’t think James Bond could teach you much about physics. But in the film Goldfinger (1964), the eponymous villain hatches a plan to irradiate the US gold reserve at Fort Knox, rendering it worthless, and increasing the value of his own gold hoard, meanwhile providing us with a chance to discuss radioactivity.
While discussing the plan in a civilised fashion (I have a memory of it being over a mint julep, but that might not be right…), Bond and Goldfinger give us the following dialogue.
Bond: His government’s given you a bomb!
Goldfinger: I prefer to call it an atomic device. It’s small, but particularly dirty.
Bond: Cobalt and iodine?
Goldfinger: Precisely.
Bond: Well, if you explode it in Fort Knox, the, uh, entire gold supply of the United States will be radioactive for… fifty-seven years!
Now, it’s lucky that no villain just shoots James bond and has done with it… But they never do. And since it seems that Bond will be around for a bit longer, somebody ought to take him aside and teach him how radioactivity works. So James, I hope you’re reading!
When an atom of a radioactive isotope ‘decays’ it emits energy from its nucleus is the form of ‘ionising radiation’. This ionising radiation is the source of the hazard with radioactive materials. Radioactivity is a ‘random’ or ‘stochastic’ process, in the sense that, although we know what each atom is going to do, we cannot, even in principle, predict when it is going to do it. All we can give is the probability that a nucleus will decay per unit time. Each nucleus of a given isotope has the same probability per unit time, which is then characteristic of that isotope, and is called the isotope’s ‘decay constant’. For example, if isotope X has a decay constant of 0.1 s-1, then there would be a probability of 1 in 10 that a given nucleus will decay in the next second.
Now consider a block of a radioisotope, rather than a single atom. Even a microscopic amount will contain countless trillions of nuclei present so that the fraction decaying per second will in practice be identical to the probability for a single nucleus [this is a key point – read it again if you aren’t sure. It’s like saying that if you threw a trillion dice, pretty much exactly one sixth of them would land on each of the six available numbers]. In the example above, one tenth of the nuclei of X will decay per second. One tenth of what remains will also decay in the next second, but that will be fewer, because it is one tenth of a smaller number.
So the ‘number of nuclei decaying per second’ in a sample (a quantity called the activity, ) depends only on the decay constant, and how many nuclei there are present. It falls with time, like the graph of activity against time shown below, in an ‘exponential relationship’, such that equal time intervals result in equal fractional changes.
The quantity ‘half life’ describes the time taken for the activity to fall to half its initial value. Another half-life will reduce the activity to half of that, and so on, as you can see in the graph. The half life of an isotope is another way of expressing the information given by the decay constant. The smaller the decay constant (the smaller the probability of decay), then the longer the half-life.
Now, this is where we start looking quizzically at Mr Bond. At no point on this graph does a rapid change happen; the activity does not disappear or drop off a graphical cliff at any point. So what could James have meant by ‘will be radioactive for 57 years’? Because radioactivity doesn’t just end, it gradually fades away, which makes “being radioactive for 57 years” a bit nonsensical. It also makes Goldfinger’s reply quite hilarious:
Goldfinger: Fifty eight, to be exact.
Bond: I apologize, Goldfinger. It’s an inspired deal. They get what they want – economic chaos in the West – and the value of your gold increases many times.
Now, a quick glance at the graph will show you that, whatever is happening after 57 years, nothing dramatic will happen in the next year. I mean, it’s not that kind of graph. Go on – imagine any point on the time axis to be 57 years, and then move further along by another one fifty-seventh of that. Yep, not much has changed. So when do we ever say that something is no longer radioactive? After all, the graph never falls to zero.
The time you have to wait before something is ‘no longer radioactive’ can only be a practical choice of a time to fall below a certain safety limit. So let’s give James his due – maybe he is an expert in radiation protection, and has calculated the time to fall below safety guidelines? There is a rule of thumb from the Radiological Health Handbook that ‘the activity of any radionuclide is reduced to less than 1 % after seven half lives’. And there seems to be a less official rule of thumb (not from the same source) that most sources are safe after ten half lives, when about 0.1 % of the initial activity remains.
Maybe that’s what James was referring to. Especially if the bomb is designed to spread cobalt-60, which would be a ‘sensible’ cobalt isotope to use, and which has a half-life of 5.27 years. 57 years would then bring us almost eleven half-lives along the graph, which would fit with the second rule of thumb.
But that second rule of thumb is about ‘most sources’. I’m not sure a bomb qualifies! Yes, the activity will have reduced to less than 0.1 %. But 0.1 % of what? 0.1 % of a more-than-catastrophic amount might still be catastrophic, whereas 50 % of a nearly-safe-much-lower level might well be within safety guidelines.
Bond described the bomb as being “cobalt and iodine.” Although the idea of a cobalt bomb is well known [see ‘historical footnote’], I can’t find any reference to iodine isotopes being deliberately used in the design of such weapons. Iodine-131 was one of the most problematic releases in the Chernobyl accident, due to iodine being readily taken up by the thyroid gland, and being responsible for the subsequent increase in childhood thyroid cancers in the Ukraine and Belarus. However, it has a half life of 8 days, so can’t be contributing much to Goldfinger’s long-term Fort Knox plan (try halving any number you like every 8 days for 57 years – you won’t have much left at the end!) .
Now, in the same year that Bond was saving us from Goldfinger, in Dr Strangelove a Russian ‘doomsday device’ was being discovered.
Ambassador: Cobalt thorium G has a radioactive half life of ninety three years. If you take, say, fifty H-bombs in the hundred megaton range and jacket them with cobalt thorium G, when they are exploded they will produce a doomsday shroud. A lethal cloud of radioactivity which will encircle the earth for ninety three years!
You should already see the fallacy in the idea of radioactivity “encircling the Earth for 93 years”. However, we can’t even give the ambassador the credit we gave Bond that he might be performing radiation protection calculations. Instead, the ambassador has equated the ‘radioactive time period’ with the half life. But we know that in 93 years all that will have happened is that activity levels will have fallen to half the original values – which could be still quite a lot…
Historical footnote
A ‘cobalt bomb’ is a real idea. It is designed to produce large amounts of radioactive fallout, thus rendering large areas uninhabitable for a long time, rather than to destroy infrastructure in the initial blast. The idea was ‘invented’ by physicist Leó Szilárd (who in the 1930s had proposed the chain reaction mechanism of fission that would lead to atomic weapons and nuclear power) in 1950. His purpose was to scare the world into realising that a doomsday device could soon be built, and should not be built. The films we have discussed were made in the early 1960s, with the world in the grip of the Cold War; it had taken only a decade at most for the idea of a doomsday device to gain purchase in popular culture.
In a strange twist, in 1960, Szilard underwent a cobalt-60 radiotherapy treatment for bladder cancer. He had designed the regimen himself. When the treatment didn’t work, he insisted that the dose be dangerously increased, on the basis that he would die anyway without it. The doctors were reluctant but went ahead; it worked and his cancer never returned.
And finally…
The most famous scene in Goldfinger is probably the laser-between-the-legs scene, with the accompanying dialogue “Do you expect me to talk?”, “No, Mr Bond, I expect you to die!” For a science link, you should see this hilarious xkcd comic strip, which in turn links nicely to our upcoming post “Centripetal or Centrifugal”.
Finally, finally, please don’t take this post to be criticism of two films I really like. Do we really need these films to be scientifically accurate? If they were, I wouldn’t get to write stuff like this… In any case, 1964 must have been a confusing time to be a high school physics student with an interest in film!