# Thread: How is Uranium Possible?

1. The decay time of uranium to lead is approximately 4.46 billion years, so the question is, if the solar system is 4.5 billion years old, how could there be any uranium left in it? In fact, if the universe is 12-14 billion years old, then how can any uranium exist anymore?

My understanding of radioactive decay is limited, so I'm sure I'm missing something here...

2.

3. The number you quote is a half life, the time it takes for half of it to decay, not all of it...

4. Originally Posted by Jason Summer
The decay time of uranium to lead is approximately 4.46 billion years, so the question is, if the solar system is 4.5 billion years old, how could there be any uranium left in it? In fact, if the universe is 12-14 billion years old, then how can any uranium exist anymore?

My understanding of radioactive decay is limited, so I'm sure I'm missing something here...
According to the Big Bang theory, when the universe was formed there was NO uranium. There were no heavy elements at all.

The heavy elements are thought to have come from synthesis in supernovae, in other words at the death of stars. So the uranium we see has to be a lot younger than the age of the universe. And of course supernovae are going on all the time, so uranium is still being synthesised.

And then there is also the half life issue, as PhDemon has pointed out.

5. Originally Posted by PhDemon
The number you quote is a half life, the time it takes for half of it to decay, not all of it...
so, does that mean 8.92 billion years for a full conversion?

6. Originally Posted by Jason Summer
Originally Posted by PhDemon
The number you quote is a half life, the time it takes for half of it to decay, not all of it...
so, does that mean 8.92 billion years for a full conversion?
No, in that time another half of what was left will be gone. Then after another 4.46 billion years, half the remainder from that will be gone. And so on.

So, for example, if you start with 128 grams of uranium, after 4.46 billion years you will have 64 grams. After another you will have 32 grams. After another 4.46 BY you will have 16 grams ...

7. What he said... He beat me to it!

8. I often wondered of Uranium is actually material from Solar Flairs...

9. No, it is dispersed in supernova explosions (as are most heavy elements). It is rare to see elements with atomic numbers above about 30 in solar flares.

10. Originally Posted by Strange
Originally Posted by Jason Summer
Originally Posted by PhDemon
The number you quote is a half life, the time it takes for half of it to decay, not all of it...
so, does that mean 8.92 billion years for a full conversion?
No, in that time another half of what was left will be gone. Then after another 4.46 billion years, half the remainder from that will be gone. And so on.

So, for example, if you start with 128 grams of uranium, after 4.46 billion years you will have 64 grams. After another you will have 32 grams. After another 4.46 BY you will have 16 grams ...
At this rate, a full conversion is going to take a while. And this looks mathematically to be an infinitely divisible process, like Zeno's paradox.

11. Originally Posted by Jason Summer
Originally Posted by Strange
Originally Posted by Jason Summer
Originally Posted by PhDemon
The number you quote is a half life, the time it takes for half of it to decay, not all of it...
so, does that mean 8.92 billion years for a full conversion?
No, in that time another half of what was left will be gone. Then after another 4.46 billion years, half the remainder from that will be gone. And so on.

So, for example, if you start with 128 grams of uranium, after 4.46 billion years you will have 64 grams. After another you will have 32 grams. After another 4.46 BY you will have 16 grams ...
At this rate, a full conversion is going to take a while. And this looks mathematically to be an infinitely divisible process, like Zeno's paradox.
It's actually an ordinary exponential decay, with the added twist of randomness. After a half-life has elapsed, you may or may not have exactly half surviving. It's an average value.

12. Originally Posted by Jason Summer
And this looks mathematically to be an infinitely divisible process, like Zeno's paradox.
Mathematically, yes. But not physically, eventually you get to one atom left ...

13. Originally Posted by Jason Summer
Originally Posted by Strange
Originally Posted by Jason Summer
Originally Posted by PhDemon
The number you quote is a half life, the time it takes for half of it to decay, not all of it...
so, does that mean 8.92 billion years for a full conversion?
No, in that time another half of what was left will be gone. Then after another 4.46 billion years, half the remainder from that will be gone. And so on.

So, for example, if you start with 128 grams of uranium, after 4.46 billion years you will have 64 grams. After another you will have 32 grams. After another 4.46 BY you will have 16 grams ...
At this rate, a full conversion is going to take a while. And this looks mathematically to be an infinitely divisible process, like Zeno's paradox.
This is a classic exponential decay curve, i.e. where the rate of decay is proportional to the amount left. It is what is used in radioisotope age determination, e.g. the well-known carbon 14 measurement of the age of organic material. By comparing the amount of the radioisotope with that of the stable isotope, you can work out how far down the exponential curve you are and hence the age of the material. There is a practical age limit, when the amount left is too small to be quantified accurately by analysis. But it's a lot longer than the half life.

14. [QUOTE=Jason Summer;607927][QUOTE=Strange;607875]
Originally Posted by Jason Summer
At this rate, a full conversion is going to take a while. And this looks mathematically to be an infinitely divisible process, like Zeno's paradox.
Once you get down to a small enough number of atoms, there are not enough to maintain the statistical average. If you look at a individual atom, there is no way to accurately predict when it will decay. All you can say is that there is a 50% chance that it will decay within the next 4.46By, a 75% chance that it will do so in 8.92By, a 87.5% chance in 13.56By and so on. It could decay in the next second or in a trillion years. The same goes if you had two atoms. You can't definitely say that one will decay in exactly 4.46By. It isn't until you get a significantly large enough sample of atoms that you can start to predict with any accuracy that 1/2 of the particles will have decayed after 4.46By.

15. [QUOTE=Janus;607952][QUOTE=Jason Summer;607927]
Originally Posted by Strange
Originally Posted by Jason Summer
At this rate, a full conversion is going to take a while. And this looks mathematically to be an infinitely divisible process, like Zeno's paradox.
Once you get down to a small enough number of atoms, there are not enough to maintain the statistical average. If you look at a individual atom, there is no way to accurately predict when it will decay. All you can say is that there is a 50% chance that it will decay within the next 4.46By, a 75% chance that it will do so in 8.92By, a 87.5% chance in 13.56By and so on. It could decay in the next second or in a trillion years. The same goes if you had two atoms. You can't definitely say that one will decay in exactly 4.46By. It isn't until you get a significantly large enough sample of atoms that you can start to predict with any accuracy that 1/2 of the particles will have decayed after 4.46By.
Okay, I think my question is answered.

But now I have a new question. If a single atom has a chance, though minimal, that it will decay within seconds, is it possible to have a large quantity like that, like a whole gram spontaneously decaying? Of course we are entering the range of near impossible probability, but "near impossible" isn't impossible, yes?

16. In theory, if you had a an entire star's worth of carbon 14, it could spontaneously, completely decay all at once. Is it likely? no. The probability is what we would considr to be effectively 0. BUT, could it happen? theoretically, yes.

Radioactive decay doesn't occur at any predefined time. It happens, or it doesn't. All we can do is measure how often it happens as an average, and notice that the rates are correlative to how much is there to begin with. that's how half-lives were discovered

17. You guys are great!

Thanks a bunch for humoring me for a bit while I figure stuff out.

18. Originally Posted by Jason Summer
Thanks a bunch for humoring me for a bit while I figure stuff out.

19. Originally Posted by Dywyddyr
Originally Posted by Jason Summer
Thanks a bunch for humoring me for a bit while I figure stuff out.
The U decayed...

20. Originally Posted by strange
Originally Posted by dywyddyr
Originally Posted by jason summer
thanks a bunch for humoring me for a bit while i figure stuff out.
the u decayed...
AaARGH!!

21. Originally Posted by Strange
Originally Posted by Dywyddyr
Originally Posted by Jason Summer
Thanks a bunch for humoring me for a bit while I figure stuff out.
The U decayed...
But that would make HumoThring.

22. you guys... T-T