1. Feb 26, 2015

### Calpalned

(Correct me if I am wrong as I am a novice in the area of chemistry) - If an element has a half-life of 10 years, half of its mass would turn into a daughter element. After another ten years, another half of it would decay, so that after 30 years only 12.5% of the mass of the original element remains. Therefore, the rate of decay slows down.

If we have a 15 kg sample of that element, we know that 7.5 grams will mutate after a decade. However, what if we managed to make a pure planet sized (diameter = 8000 km) sample of that element? How can half of that huge mass decay in the same amount of time (only ten years)? Because there is so little time to mutate so much mass, wouldn't the transformation be visible? Additionally, if the planet is fragmented, would the rate of decay change?

2. Feb 26, 2015

### e.bar.goum

You seem to be suggesting that the half-life is somehow dependent on the amount of material that you have. This isn't so - it doesn't matter if you have one atom, or a planet-worth - the half-life is still the same. So yes, the planet would change mass, and decay in 10 years.

But - recall that the mass change in a decay isn't really very large. We can work it out. Let's take our 8000 km planet, and let's make it out of 137Cs (The decay is pretty much monoenergetic, so it's easy to work with, the half life is longer though, no matter). 137Cs beta- decays into 137Ba releasing a 662keV gamma. So, the change in mass per decay is about 1*10-30kg. Then, with our 8000 km planet, the mass of 137Cs we have is about 4.*1024 kg about 1.8 *10^49 atoms - half of them decaying will end up giving a change in mass of 10^19 kg. A lot, but only 0.00025% of the mass of the planet!

You would expect the planet to be rather hot though!

3. Feb 26, 2015

### Simon Bridge

The number of disintgrations per unit time for a sample decreases over time, yes.
The probability that a particular atom decays does not.

It does not matter how big the sample is because it boils down to an individual atom having a certain probability of decaying.
Imagine you toss a coin, every time it shows heads, you remove it and toss the remainder.
The half-life of a sample of a large number N of coins does not depend on the value of N.

The basic radioactivity equations you get taught at the start do tend to assume smallish samples ... less than 1kg say. The equations sort of assume that all the radiation is removed from the sameple without anything else happening. However, it is possible for the radiation to trigger other reactions - or, even, the same reaction ... the latter case can result in a chain reaction, speeding the reaction rate considerably.

4. Feb 26, 2015

### Calpalned

Thank you Simon and e.bar.guom. While I did take AP Chemistry in high school and can solve math-like questions involving radioactivity, I was never taught how radioactivity actually worked, and so I always thought that it was dependent on mass. That incorrect belief had made radioactivity an enigma for me.

5. Feb 26, 2015

### Simon Bridge

Some atoms have a probability of changing into another atom ... that's pretty much it. We have models that help us predict the probabilities... it's all quantum.
You are discovering that your education is incomplete - it will never be complete. You are getting close to the kinds of questions nobody knows the answers to.

6. Feb 27, 2015

### DrDu

I think we have very good models of the atomic nucleus that allow a calculation of the decay rates. So I wouldn't say that nobody knows how radioactivity works.

7. Feb 27, 2015

### Hologram0110

I've only taken one particle physics class and one radio-chem class but I was under the impression the models are not particularly good for large nuclei. You have to solve the Schrodinger wave equation for a large number of particles simultaneously (all neutrons and protons) and its very hard to get an accurate approximation of the electric and nuclear potential fields (since the fields depends on location of the wave function of the particles and the wave function depends on the potential fields). For very small nuclei like deuterium or helium I would expect it to be pretty good (explaining things like excited states, transition energies, meta-stable states and decay mechanisms) but for larger nuclei I thought the approximations become more crude. Maybe its possibly with some sort of MC or iterative approach, but I've never studied numerical solutions to QM. I know that useful solutions to QM become more difficult for electrons around large atoms and they have fewer particles.

8. Feb 27, 2015

### Simon Bridge

... so how does it work?

9. Feb 27, 2015

### Staff: Mentor

Kinda like this:
And there are a host of sources online that can expand on that.

10. Feb 28, 2015

### Staff: Mentor

Indeed we have a good understanding of radioactivity, and we certainly know the how - how to create radioactive elements, and how it works, such that we can model it.

http://oregonstate.edu/instruct/ch374/ch418518/ - course
Beta decay - http://oregonstate.edu/instruct/ch374/ch418518/Chapter 8 Beta Decay-rev.pdf (See section 8.5 on the decay constant).
Alpha decay - http://oregonstate.edu/instruct/ch374/ch418518/Chapter 7 Alpha Decay-rev.pdf

http://nuclear.fis.ucm.es/PDFN/documentos/H Mach seminar for students.pdf

http://pibeta.phys.virginia.edu/docs/publications/ketevi_diss/node12.html

http://aesop.phys.utk.edu/qft/2012/Hayes/Fermi_Theory.pdf [Broken] (1968)

So we know quite a lot about radioactivity and decay of radionuclides, and we do a pretty decent job of predicting outcomes of experiments, e.g., particle accelerator interactions, behavior of nuclear reactors of many kinds.

Last edited by a moderator: May 7, 2017
11. Mar 1, 2015

### Simon Bridge

... which is pretty much what "we understand it" means in physics. But does that answer OPs question?

Don't get me wrong - my undergrad specialization was nuclear physics, an unpopular choice in anti-nuke NZ at the time. I know this stuff - I'm curious as to how you would answer the same question I tried to? At the level the question was asked? Presumably you would not expect someone with OPs level of understanding to wade through the Oregan state course, or follow the fermi integral. Let me see how you would explain it to the OP, not to me.

12. Mar 1, 2015

### Staff: Mentor

I was responding to one's comment that we don't know how. Well, of course, we do.

For the OP, the half-life of a radionuclide is independent of how much mass there is, whether it's a nano-gram, kilogram, or exagrams. The decay of an individual nuclide is independent from its neighbors, as far as we know.

Forming a planetary mass of a radionuclide is not something we're capable of doing, but it would certainly be noticeable over time, and we would expect the decay to be uniformly distributed in the mass, unless there would be some diffusion (chemical) process that would tend to segregate the elements.

We know that actinides have been around for millions of years, and we know some have long decayed away. Radionuclides are formed in nuclear reactions, in some cases in man-made systems such as accelerators or nuclear reactors, but also naturally, as in supernovae. As we understand nature, the actinides on earth were formed in a supernovae somewhere nearby and collected when the earth formed. The plutonium decayed long ago, because the half-lives of Pu isotopes are relatively short. Most of the U-235 decayed, but U-238 is mostly still around. Th-232 is also present in large quantities relative to other actinides.

13. Mar 27, 2015

### snorkack

10 years is a pretty short time. A planet sized mass of such short-lived isotope should get pretty hot pretty fast.

A mass of protium 150 000 km diametre would undergo fusion (as a red dwarf).
Deuterium will fuse at much lower temperatures than protium.
At which temperatures will tritium fuse (with itself or its beta decay product He-3)?
How big mass of tritium would be heated by the heat of its own beta decay to a temperature where it would undergo thermonuclear fusion with itself or He-3?