How is rate of decay proportional to number of nuclei?

[Guest kenshi64]

Hi guys, I THINK I understand this but i'm checking.

First of is activity and rate of decay the same?

Secondly to my understanding rate of decay is how many time a nuclei breaks down in a nucleus in a given time period, so the higher the activity the more the fewer the nuclei left in the nucleus right? or have I got something wrong. (since the proportion would be inverse as per what I understand.

Thanks a kilotonne!

[Guest Apolo]

It's not number of nuclei because you're only analysing one atom. But it varies accordingly to the number of alpha particles if I'm not mistaken (I'm not of Physics... but have a pretty sure idea that it is so)

oh and relating to the doubt itself, if you see, the half-life time is a fixed number, right? So, it means that the rate of decay is constant which also means that the number of particles that suffer from decay will be equally constant. That's why it is proportional

Edited August 16, 2011 by Apolo

[Guest kenshi64]

It's not number of nuclei because you're only analysing one atom. But it varies accordingly to the number of alpha particles if I'm not mistaken (I'm not of Physics... but have a pretty sure idea that it is so)

oh and relating to the doubt itself, if you see, the half-life time is a fixed number, right? So, it means that the rate of decay is constant which also means that the number of particles that suffer from decay will be equally constant. That's why it is proportional

I don't get that, could you make a bit more clear? Thanks

[Guest Apolo]

alpha particles = Helium positively charged nuclei

Now, do you know what the half-time of an atom is? It's the time that it takes to halve its radioactivity (which is directly related to the number of alpha particles released). Now, if the halving period is a fixed number, which means that after x time, the radioactivity will have decreased by half, it necessarily means that the rate of decay is constant, right?

And since radioactivity is directly related to the number of alpha particles, if there's radioactive decay (which is constant). It will mean that the loss of alpha particles is constant too...

Because after all, it's the loss of particles that makes up the decay... :|

I gave the radioactivity as example because it's easier to understand

Wasn't this clear?? o.O

Edited August 16, 2011 by Apolo

[Drake Glau]

Activity and the rate of decay are not the same. The activity could be seen as the number of particles that have not decayed yet. The rate of decay, well there really is no "rate". Decay is all based off probabilities which is why we use Half-Lives. A single half life is the predicted time it would take for half the particles to decay. The half lives are accurate simply because it's talking about millions upon millions (probably more like trillions but whatever) of particles and as you know the more trials you have for probability the more uniform the results become.

To the above poster, radioactivity is not constant. It is very possible that after a half life there is over half the original particles. Each time a particle decayed it was based off a probability that is NOT 100% so it is completely viable that even after a single half life you have more or even less than half the original particles.

Fun lab we did to show this was with M&Ms. Imagine the side with the M&M logo to be the normal particles and the other side is the decayed particles (particle that has emitted an alpha particle). Now put them all in a bowl with the M&M facing up, put a lid on it, and then give it a small shake up and then down. Now count how many M&Ms flipped over, each "shake" can be seen as a half life and should give you a nice idea of how it's all working since the M&Ms display 50/50 chances.

Oh, right, original question, all probabilities work like this. More trials (particles) = more chances for the decay.

Continuing my M&M thing, if you have 34673458 M&Ms there is a REALLY high chance that at least one is going to flip over, now if you have 1 M&M it could take several shakes for that silly thing to flip over

Edited August 16, 2011 by Drake Glau

[Guest kenshi64]

alpha particles = Helium positively charged nuclei

Now, do you know what the half-time of an atom is? It's the time that it takes to halve its radioactivity (which is directly related to the number of alpha particles released). Now, if the halving period is a fixed number, which means that after x time, the radioactivity will have decreased by half, it necessarily means that the rate of decay is constant, right?

And since radioactivity is directly related to the number of alpha particles, if there's radioactive decay (which is constant). It will mean that the loss of alpha particles is constant too...

Because after all, it's the loss of particles that makes up the decay... :|

I gave the radioactivity as example because it's easier to understand

Wasn't this clear?? o.O

Hey I appreciate the effort , but my noodle is f*ck twisted *pulls hair* so could you make it conse ,coz you just threw a whole new bunch of terms at me and I'm like what's A and B and your explaining with the help of C and D, don't get me wrong tho, thanks

[dessskris]

the rate of decay is proportional to the number of nuclei.

try to imagine the graph?

when there are more nuclei, say 20M, if the half life is 1 month, the rate of decay is 10M/month. now, you only have 10M nuclei. with the same half life, the rate of decay would be 5M/month. and so on and so forth.

I hope my explanation is right? I'm not very sure though.