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The unit of measurement known as a Curie(after Pierre and Marie Curie) measures the rate of decay of Ra-226 in one second. It was originally measured at 3.7x10^10 decays per second. It has been more accurately measured to 3.6x10^10 decays per second.

I want to use the Curie and create a new unit of time measurement. I think if I measure how long it takes the radium to decay 1x10^10 I could create a new "second".

Is this even feasible? Is it reasonable to use this?

My thought process was to try and find a stable system to create a new unit of time measurement from it. It may be more ideal to use the more accurate measurement but I want to see if this is dumb or not.

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  • $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Worldbuilding Meta, or in Worldbuilding Chat. Comments continuing discussion may be removed. $\endgroup$
    – HDE 226868
    Aug 20, 2023 at 18:46
  • $\begingroup$ Sorry @Martamo, apparently the rule is now to close questions as story-based when it "is asking about in world decisions of a character" (ref : 1, 2). Unfortunately, whether it's reasonable is inherent to where your character choose it to be "reasonable", so I have to close even if I strongly disagree. If it gets closed and yet you aren't satisfied with the current answers, notify (@) me and I'll try to help you in chat $\endgroup$ Dec 25, 2023 at 21:15
  • $\begingroup$ @Tortliena to be fair, I don't think one closed question and another upvoted comment really constitute a rule, although I must agree that the trend does not seem healthy for the future of this SE $\endgroup$
    – M S
    Dec 28, 2023 at 15:13

3 Answers 3

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It depends on the span of time you wish to measure. To measure a short/human scale time, you may struggle due to the inaccuracies inherent in decay.

But if you want to measure 'oh, it happened 10 billion years ago' and aren't sure who will be around to read the clock, then radioactive decay may be a solution.

Uranium-238 has a half life of 4.5 billion years. There is no mechanical or electrical clock that can function that long, but a container can be made that contains 1kg of uranium-238. 4.5 billion years later it will contain half a kilogram of uranium 238 and some thorium, protectinium, uranium 234 and a bunch of other elements in uranium's decay chain. Even if you don't know the initial mass, the ratios of elements tells you how old it is.

Fun fact, the voyager space probe carried some uranium 238 (as pure as we could make it) for exactly this reason - so a potential alien civilization could figure out how long it had been travelling for.

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  • $\begingroup$ I do want to measure on a more human scale. I may have to find a new thing to base this measurement off of. $\endgroup$
    – Martamo
    Aug 18, 2023 at 23:00
  • $\begingroup$ @Martamo As an example of this, carbon dating works on a relatively human timescale, if you're thinking of a timescale of a human lifespan. It's not that accurate though - you need some pretty serious kit to get 1% accuracy. You also have a major problem with external interference, because your measurement system will be screwed over by external radiation sources. $\endgroup$
    – Graham
    Aug 19, 2023 at 8:20
  • $\begingroup$ @Graham I would like the inhabitants to use it like we would use a clock, so carbon dating may not be the right answer. $\endgroup$
    – Martamo
    Aug 19, 2023 at 14:57
  • $\begingroup$ Is there some kind of source on the Voyager probes carrying uranium-238? There's some plutonium-238 on board as part of the radio-thermal power supply, and by working back the decay on that someone finding the probe could calculate the age of the device. Keeping track of the age of the device is a fortunate side-effect of using radioactive decay for power but hardly the original intent. Pu-238 was used for power for many reasons, I doubt timekeeping factored in that decision. $\endgroup$
    – MacGuffin
    Dec 25, 2023 at 23:52
  • $\begingroup$ Yup. Quoting JPL's page on the golden record: "Electroplated onto the record's cover is an ultra-pure source of uranium-238.... The steady decay of the uranium source into its daughter isotopes makes it a kind of radioactive clock. Half of the uranium-238 will decay in 4.51 billion years" voyager.jpl.nasa.gov/golden-record/golden-record-cover $\endgroup$
    – sdfgeoff
    Dec 26, 2023 at 3:34
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Radioactive decay is nonlinear and the decay products will change the alpha detection rate.

This will not work as an absolute measure because it’s not possible to measure just the radium decay, and over time the decay rate slows down. The rate of nuclear decay depends only on the isotope and the quantity of material present. The number you gave us for the Curie, is the count we would see if you had exactly one gram of Radium-226. The calculation for how much radium-226 you have at any given time is as follows:

$$N = N_o\times\frac{t}{2}$$

Assuming you know that you started with n moles of radium (that will be $N_o$ in the formula); we already know that the half life is 1,600 years, so as time (t) goes on you can see you have less radium. Less radium means slower decay rate. Each isotope has a decay constant (λ) that can simply be multiplied by the amount of the element to find the decay rate at a given time:

$$λ = ln(2) / T_½$$

λ for 226Ra is ln(2)/1,600 years = $\frac{1.3737112e-11}{sec}$

With that constant in $s^{-1}$ (years were converted to seconds), you can predict how many counts per second you'll have from your radium. If you have exactly 1 mole of 226Ra, then you will have 8.2330422e+27 counts per second.

Why is that so much higher than your number? Because Radium is pretty heavy. To make one gram of radium-226, you only need 0.004424778761061947 moles of it, or exactly 2.6646641e+21 atoms. Let's try that out in the radioactive count formula:

$$ 2.6646641\times10^{21} \text{atoms} \times \frac{1.3737112\times10^{-11}}{sec} = 36604490741.7 \text{ counts per second.} $$

And that you will recognize is the Curie you referenced.

So there is no precise rate of alpha emissions from a sample of radium-226, the amount of radium you start with determines the rate of decay for the sample. But worse, it is also leaving behind daughter products, which are also producing alpha particles at very different rates. You will be detecting alpha particles from radium, and radon, polonium, and lead all the way down until it becomes stable as 206lead. As time goes on the radium, turning into other elements, will cause the detector to read alpha particles for those other elements, and your rate of detection is going to change. Overall this is a very small amount, and you can make a fairly precise clock using radium 226. But using it as a definition of a unit of time won’t work. When you lock up your block of radium and come back years later to measure it, you can’t reproduce those original numbers exactly. Because, it's no longer pure radium.

So what is it? Radium-226 (1600 year half life) yields an alpha particle and Radon-222. The half-life of radon-222 then is approximately 3.8 days. This means that after 3.8 days, half of the initial amount of radon-222 has emitted another alpha particle and transformed into polonium-218 (Po-218). Your alpha detector will see this and count it as a radon decay. Polonium-218 (Po-218) also undergoes alpha decay, emitting an alpha particle and transforming into lead-214 (Pb-214), and further screwing up your counts. Lead-214 (Pb-214) then undergoes beta decay, emitting a beta particle (an electron) and transforming into bismuth-214 (Bi-214). Beta particles won't register on your alpha detector Bismuth-214 (Bi-214) undergoes beta decay as well, transforming into polonium-214 (Po-214). Polonium-214 (Po-214) undergoes alpha decay with a half-life of approximately 164.3 microseconds, becoming lead-210 (Pb-210). Lead-210 (Pb-210) undergoes beta decay, transforming into polonium-210 (Po-210). Polonium-210 (Po-210) undergoes alpha decay, becoming lead-206 (Pb-206), which is a stable element. So, the decay chain of radium-226 ultimately leads to the stable element lead-206.

Radium-226 decay chain

(Decay chain of 226Ra)

If you were counting, that’s five alpha particles until Radium-226 becomes Lead-206, and only one of them were from the radium. It is incredibly complicated, but as the amount of radium goes down, you will see alpha particles coming out faster because the radon and polonium will be decaying.

This means that over time your initial block of radium will become a soup of several elements and the rates of decay for all of them are very different. Mostly you will have lead and radium at any given time since they linger longer. But as your radium turns into other stuff the rate at which alpha particles will be detected in any given second over time will constantly change.

Now to further confuse the problem, this isn't all guaranteed. I said that beta decay won't mess up your count, but that's not entirely true. 210Polonium has two other modes of decay: beta capture and spontaneous fission. When 210Po captures a beta (electron), it turns back into 210Pb. Now, 210Pb can also emit an electron in beta decay to become 210Bi, which in turn can create another alpha particle to return to Lead 208.

While you can keep very accurate time with a sample of Radium-226 for short intervals, it’s not something that would make a practical standard unit of measure.

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  • $\begingroup$ What if I measured how long the radium took to decay 1x10^10? I did this and got 0.27027027027. But because you are saying that it changes over time, the decay rate would be different at 0.270.. and at 1 second. $\endgroup$
    – Martamo
    Aug 19, 2023 at 12:12
  • $\begingroup$ Again the counts per second will be different depending entirely on the number of radium atoms you have in your sample. That math is simple: multiply the number of atoms you have by $ 1.3737112\times10^{-11}$ and that is how many decays per second will happen. Each decay turns a radium into radon, so your sample gets smaller with time. For your 0.2727… counts per second, we know you started with 0.2727…/λ atoms. One hour later, you have fewer radium atoms. So it’s not a standard. $\endgroup$
    – Vogon Poet
    Aug 19, 2023 at 13:57
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    $\begingroup$ Ok. The amount I am talking about is the same amount used for a Curie, one gram. But because it becomes less than a gram as it decays it decays “faster”. I see I made an error when researching this topic. $\endgroup$
    – Martamo
    Aug 19, 2023 at 14:56
  • $\begingroup$ Yes. It is useful for measuring time as @sdfgeoff showed, it’s simply not useful as a standard. There does not exist any source that can reliably produce “1 Curie” of radiation consistently every time. $\endgroup$
    – Vogon Poet
    Aug 19, 2023 at 16:12
  • $\begingroup$ So what is the problem in your world that you wanted to solve with a radium time standard? there’s probably another way to solve it. How important to your story is radium or radioactive decay in general? $\endgroup$
    – Vogon Poet
    Aug 19, 2023 at 17:18
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Yes, you can me. But it is impractical. The decay of Radium-226, and any other radioactive element, is exponential. It slows down as more of it decays. So you can’t do simple math to figure out how many milliseconds would have passed if 1x10^10 decays occurred.

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  • $\begingroup$ Actually, yes you can. You just need a material that decays faster to solve the innacuracies. The fact that decay slows down exponentially is the least of your problems, as long as you know logarithms. $\endgroup$ Dec 28, 2023 at 0:33
  • $\begingroup$ @TheSquare-CubeLaw But which element would that be? There are a lot of fast decaying elements. I originally wanted to find how long it would take Ra-226 to experience 1x10^10 decays. In one second it experiences 3.6x10^10 decays. $\endgroup$
    – Martamo
    Dec 28, 2023 at 0:43
  • $\begingroup$ How about measuring radiation levels rather than decay? A kilogram of bananas will emit a particle every now and then. If you have a lot of detectors under a ton of bananas you can find averages and measure time through that. $\endgroup$ Dec 28, 2023 at 2:57
  • $\begingroup$ @TheSquare-CubeLaw I’ll think over it. At the moment I have moved on to a different part of the project(hexapods turned quadrupedal with hands.) Thank you for your help. I’ll probably use something a bit more active than the potassium in bananas. $\endgroup$
    – Martamo
    Dec 28, 2023 at 5:35

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