Half Life -- explanation?

[EWyatt]

I've tried, but got nowhere. A kilogram of Uranium (U 235) has a half life of 700MY and decays to half its weight in that time. How is that? Let's bring it down to 4 atoms instead of 1 kg. After 700 MY do only 2 atoms degenerate? If so, what's keeping the other two at "full strength?" I understand that radioactive output may have something to do with it, but how? What am I missing with the entire "half-life" concept?

Sorry, this is a rookie question, but I've got to start somewhere. Thanks.

EW

[Sensei]

I've tried, but got nowhere. A kilogram of Uranium (U 235) has a half life of 700MY and decays to half its weight in that time. How is that?

704 million years is half-life time.

It's time needed to decay half of Uranium-235 isotope to it's daughter isotope.

https://en.wikipedia.org/wiki/Decay_product

Daugther isotope depends on decay mode.

In case of Uranium-235, it's alpha decay, that's it, atomic number is decreased by 2, and mass number is decreased by 4 (or neutron number is decreased by 2).

Z=92-2 = 90 protons.

A=235-4 = 231 mass number.

Isotope with Z=90,A=231 is Thorium-231.

Giving overall reaction:

U-235 -> Th-231 + alpha particle + 4.679 MeV energy released.

 

Thorium-231 has plentiful of mass, approximately 231.0363043 u.

 

So if you have 235 grams of U-235, after 704 million years you will have 235*0.5 = 117.5 grams of U-235, and 231*0.5 = 115.5 grams of Th-231. 117.5 + 115.5 = 233 grams.

But because Th-231 is very unstable, it's also approximation, as it'll decay already within couple hours after making it.

Edited August 15, 2015 by Sensei

[studiot]

 

and decays to half its weight in that time.

 

Yes, as Sensei said this is incorrect.

 

Due to radioactivity the uranium 'decays' into something else as described.

This something else (Thorium also has weight) so only a small amount of weight is lost during one half life.

 

Weight is not a good measure here, since the weight depends on location (Earth, Moon, Mars space).

The mass of something is the same wherever it is.

 

Finally radioactive decay is only one one many processes that half a 'half life' so is nothing special.

 

For example the voltage of a discharging capacitor follows the same law and has a half life during which the voltage falls to half its initial value.

No one asks why does the the rest of the voltage remain.

 

It's simply that many processes take time to work through. Nothing holds the undecayed atoms stable, they will all decay in the end.

[Janus]

I've tried, but got nowhere. A kilogram of Uranium (U 235) has a half life of 700MY and decays to half its weight in that time. How is that? Let's bring it down to 4 atoms instead of 1 kg. After 700 MY do only 2 atoms degenerate? If so, what's keeping the other two at "full strength?" I understand that radioactive output may have something to do with it, but how? What am I missing with the entire "half-life" concept?

Sorry, this is a rookie question, but I've got to start somewhere. Thanks.

EW

It's a statistical thing. Nothing can tell you when any particular atom of U 235 will decay. It could be in the next second or 200 billion yrs from now. All you know is that there is a 50% chance that it will decay in the next 700MY. Even if you have already been watching it for 700MY, there is still only a 50% chance that it will decay in the next 700MY.( it's like flipping a coin, every time you flip it there is a 50% chance of it coming up heads, It doesn't matter if you've already flipped it 1000 time and came up with 1000 heads in a row, the next time you flip it, the chances are still 50-50. previous flips of the coin have no effect on subsequent flips.)

Because of this, Half-life really only works when you have a large number of atoms. If you start with 10^12 atoms, you can pretty sure that will will end up with something very close to 5^12 having decayed after 700MY, just like if you flip 10^12 coins, you'll end up with 5^12 heads. On the other hand, if you just have 4 atoms, you are not as sure that you will have 2 left over after 700MY.

[ajb]

It's a statistical thing.

 

Because of this, Half-life really only works when you have a large number of atoms.

The above is really important.

[EWyatt]

It's a statistical thing. Nothing can tell you when any particular atom of U 235 will decay. It could be in the next second or 200 billion yrs from now. All you know is that there is a 50% chance that it will decay in the next 700MY. Even if you have already been watching it for 700MY, there is still only a 50% chance that it will decay in the next 700MY.( it's like flipping a coin, every time you flip it there is a 50% chance of it coming up heads, It doesn't matter if you've already flipped it 1000 time and came up with 1000 heads in a row, the next time you flip it, the chances are still 50-50. previous flips of the coin have no effect on subsequent flips.)

Because of this, Half-life really only works when you have a large number of atoms. If you start with 10^12 atoms, you can pretty sure that will will end up with something very close to 5^12 having decayed after 700MY, just like if you flip 10^12 coins, you'll end up with 5^12 heads. On the other hand, if you just have 4 atoms, you are not as sure that you will have 2 left over after 700MY.

Janus.... I think you've done it for me. Are you saying that an atom of U 235 (or quadrillions of them) will decay from it's state instantly, without a "dying (degeneration) process?" And that there is really no specific "lifespan" for a U 235 atom? If YES to both of those, then I'm good. As a bonus for me, what would you think makes that atom(s) instantly decay and not others around it?

Thanks to all who've been patient.....

[swansont]

Janus.... I think you've done it for me. Are you saying that an atom of U 235 (or quadrillions of them) will decay from it's state instantly, without a "dying (degeneration) process?" And that there is really no specific "lifespan" for a U 235 atom? If YES to both of those, then I'm good. As a bonus for me, what would you think makes that atom(s) instantly decay and not others around it?

Thanks to all who've been patient.....

 

It can decay at any time, with equal probability during any equal interval you choose. When you have a large number, this means the total will obey an exponential decrease of the parent nuclide.

[StringJunky]

As a bonus for me, what would you think makes that atom(s) instantly decay and not others around it?

Thanks to all who've been patient.....

Radioactive elements have a nuclear binding energy that is basically on the limit of just holding it all together and at some unspecifiable time an atom spontaneously decays.

[swansont]

Radioactive elements have a nuclear binding energy that is basically on the limit of just holding it all together and at some unspecifiable time an atom spontaneously decays.

 

For alpha decay it's a matter of tunneling, so I'm not sure that description works. "the limit of just holding it all together" sounds like a classical unstable equilibrium, and that's not what is going on.

[StringJunky]

 

For alpha decay it's a matter of tunneling, so I'm not sure that description works. "the limit of just holding it all together" sounds like a classical unstable equilibrium, and that's not what is going on.

Ok. I thought with the increase in the number of nucleons and the very short range of the binding force, I thought this was what was happening... never thought about the different types of decay.

[Enthalpy]

The difference is faint. Tunneling capability means that an alpha can escape the parent nucleus even if i misses some energy to do so. Consequently, nuclei that would be at the limit decay immediately, the ones we observe do have some stability.

 

If alphas don't preexist in heavy nuclei, the description of their emission must be seriously more subtle than their sticking force being tunneled from time to time. At least, it needs to group four baryons properly during the process.

[swansont]

The difference is faint. Tunneling capability means that an alpha can escape the parent nucleus even if i misses some energy to do so. Consequently, nuclei that would be at the limit decay immediately, the ones we observe do have some stability.

 

If alphas don't preexist in heavy nuclei, the description of their emission must be seriously more subtle than their sticking force being tunneled from time to time. At least, it needs to group four baryons properly during the process.

 

I disagree. The difference is between happening and not happening, which is not "faint". This is QM, and assuming a literal grouping is a classical mindset.

 

The bottom line is the Gamow/Gurney-Condon theory works pretty well. There's more to it, but it's a basic concept that works.

https://www.eng.fsu.edu/~dommelen/quantum/style_a/gamow.html