B Radioactive decay, Stability and Halflife

[A M]

Wikipedia

 

[PeterDonis]

Wikipedia

Please give a specific link.

 

[A M]

Oh that wasn't Wiki
barwinski

 

[mfb]

Alpha decay tends to have a shorter half life if the reaction releases more energy. It can be a bit more complicated but that is the general trend.

 

[PeterDonis]

The more the difference between a nucleus an its decay products, the faster it decays.

It's not always that simple. Consider a couple of examples.

First, Beryllium-8. Its mass is 8.0053051. It decays into two alpha particles; twice the alpha particle mass is 8.005204. The difference is 0.0001011 amu, which is 94.2 keV; and the Be-8 nucleus is heavier. In other words, a Be-8 nucleus is basically two alpha particles plus 94 keV--the only reason it exists at all is that it's a resonance, i.e., when two alpha particles happen to come close enough together they can briefly form this state before splitting apart again. So the "half-life" of Be-8 is really just the length of time this resonance state exists.

Second, Bismuth-209. (Note that the barwinski.net reference you gave lists this isotope as stable.) Its mass is 208.9803987. It decays into Thallium-205, which has a mass of 204.9744275; that plus the mass of an alpha particle, 4.002602, gives 208.9770295. The difference is 0.0033692 amu, or 3.138 MeV. This is a signficantly bigger difference (decay energy) than Beryllium-8, but Bismuth-209 has a much longer half-life.

However, Beryllium-8 is an extreme outlier, because its "decay product" via alpha decay is an alpha particle itself--i.e., as I said above, it's just two alpha particles close together. Of course no other alpha decay nucleus has this property. For most other alpha emitters, I would expect the general rule @mfb gave to hold, that the larger the decay energy, the shorter the half-life.

 

[mfb]

Here is a graph for half life vs. decay energy of most naturally occurring alpha emitters. Bismuth-209 is off the scale.

Edit: Here with Bi-209 drawn in:

 

[A M]

Sorry for the extremely late reply.
I don't know the reason, but the more new things I learn from Physics, the more questions are formed in my mind.
First of all, why is alpha decay much more common than other types of fission?

Beryllium-8 is an extreme outlier, because its "decay product" via alpha decay is an alpha particle itself

Why is alpha particle that special?
For example there are some nuclei with higher binding energy per nucleon. Why α?

Here is a graph for half life vs. decay energy of most naturally occurring alpha emitters.

What is wave function?
(When I want to find my answers, there are always some unfamiliar words like wave function, spin, angular momentum,... that are related to QM -about which I don't know anything!
Actually I've just entered high school and my main subject is Biology; so the only reason why I learn Physics is my great interest.)

 

[PeterDonis]

why is alpha decay much more common than other types of fission?

Alpha decay is not normally considered a type of fission. It's much more common than spontaneous fission because it's much more likely that there will be some nucleus with higher binding energy per nucleon reachable by alpha decay, than that there will be some pair of nuclei that a heavy nucleus can exactly split into by fission. Also it's much harder to split a heavy nucleus nearly in half than for just an alpha particle to come out, because many more nucleons have to se

Why is alpha particle that special?

It's not that the alpha particle itself is special in the case of Beryllium-8; it's that thinking of Beryllium-8 as "emitting an alpha particle" is a misnomer. What is really happening is that two alpha particles came together for a very short time into a resonance state called "Beryllium-8" and are now separating again. Beryllium-8 is the only nucleus for which this is the case, because it's the only nucleus that is exactly two alpha particles bound together.

That said, the alpha particle--the nucleus of Helium-4--actually is special as far as nuclei are concerned, in that its binding energy per nucleon is very high for such a light nucleus. The detailed reasons behind this are beyond the scope of this thread, but it is part of the reason that alpha particle emission is a fairly common form of radioactive decay.

What is wave function?

If you label a thread as "I" level in the quantum forum, you are expected to already know the answer to this. See further comments below.

When I want to find my answers, there are always some unfamiliar words like wave function, spin, angular momentum,... that are related to QM -about which I don't know anything!

Yes, and that means you will need to spend the time learning about it in order to have the background necessary to understand the answers. You can't expect to just ask individual questions and understand the answers without that background.

I've just entered high school

That means you have plenty of time to learn more. In particular, you have plenty of time to learn more about the basics of quantum mechanics, such as what a wave function is. It is beyond the scope of PF to give detailed explanations of basic concepts like that. The basic answer is that the wave function is how the state of a quantum system is represented mathematically in quantum mechanics; but for that answer to make sense you need to take the time to study the material on your own.

 

[A M]

it's much harder to split a heavy nucleus nearly in half than for just an alpha particle to come out, because many more nucleons have to se

That makes more sense!

Yes, and that means you will need to spend the time learning about it in order to have the background necessary to understand the answers. You can't expect to just ask individual questions and understand the answers without that background.

OK, I'll do my best to learn the background.

It is beyond the scope of PF to give detailed explanations of basic concepts like that.

As a matter of fact even much more basic explanations (like binding energy) are beyond my school lessons!

 

[PeterDonis]

As a matter of fact even much more basic explanations (like binding energy) are beyond my school lessons!

Binding energy is actually fairly easy, so I'll give you a basic pointer.

Consider a simple bound system like a hydrogen atom in its ground state. It has a binding energy of 13.6 eV. What does this mean? It means that, if you wanted to separate the proton and the electron and make them both free particles, not bound to each other at all, you would have to add 13.6 eV to the atom to do it.

In other words, the binding energy of a bound system is the energy you would have to add to the system to separate all of its constituents and make each of them a free system, not bound to any of the others at all.

 

[A M]

In other words, the binding energy of a bound system is the energy you would have to add to the system to separate all of its constituents and make each of them a free system

What is a bound state?!

 

[PeterDonis]

What is a bound state?

A state where constituents, like the proton and electron in a hydrogen atom or all of the nucleons in a nucleus, are confined to a small region of space and can't escape. This is another of those basic terms that you really need to spend some time studying quantum mechanics on your own to learn.

 

[A M]

This is another of those basic terms that you really need to spend some time studying quantum mechanics on your own to learn

A state where constituents, like the proton and electron in a hydrogen atom or all of the nucleons in a nucleus, are confined to a small region of space and can't escape.

So, I've read that according to Pauli exclusion principle, bound state of identical fermions is forbidden. (Identical fermions can't occupy the same quantum state.)
I know what fermions are, but I want to know what "the same quantum state" is.
Thank you!

 

[PeterDonis]

I've read that according to Pauli exclusion principle, bound state of identical fermions is forbidden.

No, you didn't. What you read was this:

Identical fermions can't occupy the same quantum state.

That's not the same as "bound states of identical fermions is forbidden".

I want to know what "the same quantum state" is.
Thank you!

This is one of those basic aspects of QM that you really need to take the time to study for yourself.

 

[PeterDonis]

The OP question has been answered. Thread closed.