Thread: Why does radioactive material decay exponentially as opposed to at a constant rate?

Can anyone explain to me why exactly it is that radioactive material decays at an exponential rate? To make my confusion more clear, take the following example. Let's say you have 1 gram of radioactive material, and for the pure sake of argument, though I admit that I'm just pulling this number out of a hat, let's assume that 10 trillion radioactive atoms are in this gram. The half-life of this fictional radioactive material is 1 million years.

Now before I go any further, I just want to make it clear that I more or less understand the mathematics behind radioactive decay (N=N0 x e^-kt), so I don't need an explanation of that, or of how to use said formula.

Now, even though I know how to use that formula to calculate the amount left after n amount of time, I have always been completely baffled by the idea of it decaying exponentially. In other words, if you were to ask someone on the street who knew absolutely nothing about radioactive decay: "If you start with 1 gram of radioactive material, and after 1 million years it will have decayed to 0.5 grams, how long will it take for it to completely disappear?" I can almost guarantee that their answer will be 2 million years (that's what common sense would dictate), and for the life of me I have never been able to figure out why this would not be the case, because it is completely counter intuitive. Can someone explain to me what the mechanism is that makes radioactive decay an exponential process, as opposed to one that occurs at a constant rate? Do we even know?

Each atom has some probability of decaying within a certain period of time. That probability never changes.

Imagine that you have a box of dice. Every day you roll all the dice in the box and remove the ones that come up "1". After 1 day, there will be 1/6 fewer dice in the box. The next day there will be 1/6 fewer, etc., etc. Each day there are fewer dice in the box and fewer removed. If it is a big enough box of dice, so that things average out, it would closely follow an exponential decay curve.

Okay.. this is my simplified view:
1 gram divide by 2, and then divide by 2, and then divide by 2, and then divide by 2.
= So the graph looks like exponential decay...

*It just a simplified point of view

Like this pic:
http://chemwiki.ucdavis.edu/@api/dek...tive_Decay.jpg (see its divide by 2 all along!)
(from here: http://chemwiki.ucdavis.edu/Physical...ve_Decay_Rates)

Posts by Amanbir and responses moved to his thread in the Trash.

Originally Posted by Harold14370

Each atom has some probability of decaying within a certain period of time. That probability never changes.

Imagine that you have a box of dice. Every day you roll all the dice in the box and remove the ones that come up "1". After 1 day, there will be 1/6 fewer dice in the box. The next day there will be 1/6 fewer, etc., etc. Each day there are fewer dice in the box and fewer removed. If it is a big enough box of dice, so that things average out, it would closely follow an exponential decay curve.

How is it exponential if the probability stays the same lol? It's logarithmic at best. Exponential decay is only observed in chain reactions for thermonuclear explosions. Exponential decays are uncontrollable and occurs when additional neutrons or alpha particles are ejected and hit other nucleus.

Originally Posted by Oxycodone

Originally Posted by Harold14370

Each atom has some probability of decaying within a certain period of time. That probability never changes.

Imagine that you have a box of dice. Every day you roll all the dice in the box and remove the ones that come up "1". After 1 day, there will be 1/6 fewer dice in the box. The next day there will be 1/6 fewer, etc., etc. Each day there are fewer dice in the box and fewer removed. If it is a big enough box of dice, so that things average out, it would closely follow an exponential decay curve.

How is it exponential if the probability stays the same lol? It's logarithmic at best. Exponential decay is only observed in chain reactions for thermonuclear explosions. Exponential decays are uncontrollable and occurs when additional neutrons or alpha particles are ejected and hit other nucleus.

You're thinking of exponential growth. Exponential decay is exponential growth where the growth rate is negative.

Originally Posted by Oxycodone

How is it exponential if the probability stays the same lol? It's logarithmic at best. Exponential decay is only observed in chain reactions for thermonuclear explosions. Exponential decays are uncontrollable and occurs when additional neutrons or alpha particles are ejected and hit other nucleus.

You clearly do not know what an exponential is; the exponent certainly can have any sign, as has been pointed out. You should at least be aware of your ignorance so that you don't make foolish assertions, like the ones above. LOL indeed, but the derision vector is pointing at you. Laugh less, learn more. FYI, exponential decays...decay. That's hardly the signature of something that is "uncontrollable." Chain reactions for thermonuclear explosions depend on exponential growth. Think about it.

An exponential decay is the necessary logical consequence of an extremely simple thing: If a fixed percentage of atoms decay (equivalently, if the probability of a given fraction atoms decaying is fixed -- stays the same) within a given interval, you get an exponential. It's precisely the same behavior you would observe if your bank balance lost a fixed percentage every day, for example, with no replenishing of funds. This is what Harold 14370 was telling you.

Work it out mathematically, maybe with an example with specific numbers first. Start with 100 dollars, say. Suppose you lose 10% each day. So the day-by-day bank balances are in a sequence like this: 100, 90, 81, 72.90, 65.61...Plot the sequence. You will find that the points conform to those of an exponential curve.

Want the math? Here's a capsule summary: Saying that a fixed percentage of atoms decay per unit time is equivalent to saying that dN/dt is proportional to N, where N is the number of atoms. So set dN/dt = BN, where B is a constant, and solve (B will have a negative sign if you are talking about decay, and a positive sign if you are talking about growth). You can verify that an exponential is a solution to the simple equation.

Now the only difference is that, in actual fact, radioactive decay is probabilistic, so "given interval" must be interpreted stochastically. But the math is the same -- you get an exponential.

Originally Posted by Harold14370

Originally Posted by Oxycodone

Originally Posted by Harold14370

Each atom has some probability of decaying within a certain period of time. That probability never changes.

Imagine that you have a box of dice. Every day you roll all the dice in the box and remove the ones that come up "1". After 1 day, there will be 1/6 fewer dice in the box. The next day there will be 1/6 fewer, etc., etc. Each day there are fewer dice in the box and fewer removed. If it is a big enough box of dice, so that things average out, it would closely follow an exponential decay curve.

How is it exponential if the probability stays the same lol? It's logarithmic at best. Exponential decay is only observed in chain reactions for thermonuclear explosions. Exponential decays are uncontrollable and occurs when additional neutrons or alpha particles are ejected and hit other nucleus.

You're thinking of exponential growth. Exponential decay is exponential growth where the growth rate is negative.

OHHH! You're right, thank you sir! I had confused growth with decay in my head.

Originally Posted by tk421

Originally Posted by Oxycodone

How is it exponential if the probability stays the same lol? It's logarithmic at best. Exponential decay is only observed in chain reactions for thermonuclear explosions. Exponential decays are uncontrollable and occurs when additional neutrons or alpha particles are ejected and hit other nucleus.

You clearly do not know what an exponential is; the exponent certainly can have any sign, as has been pointed out. You should at least be aware of your ignorance so that you don't make foolish assertions, like the ones above. LOL indeed, but the derision vector is pointing at you. Laugh less, learn more. FYI, exponential decays...decay. Think about it.

Stfu minimod. Mad coz no tag? Here:

Untitled.jpg

You learn your math. Wtf was wrong with what I said about the exponential?

Originally Posted by Oxycodone

Stfu minimod. Mad coz no tag? Here:

Untitled.jpg

You learn your math. Wtf was wrong with what I said about the exponential?

Happy to oblige your request. Pretty much your entire post #5, which I quoted, is wrong. Here are specifics:

Originally Posted by Oxycodone

How is it exponential if the probability stays the same lol? It's logarithmic at best.

I've shown you that the math leads to an exponential if the probability stays the same. It does not lead to "logarithmic at best."

Originally Posted by Oxycodone

Exponential decay is only observed in chain reactions for thermonuclear explosions.

Here you are doubly wrong. First you are not clear on the very meaning of the word decay. Second, exponential decays (or growths) are extremely widespread in nature. They are hardly "only observed in chain reactions for thermonuclear explosions." Any undergraduate physics student will encounter many examples of exponentially growing and decaying phenomena. Indeed, (complex) exponentials are eigenfunctions of linear systems, which covers a whole lot of ground.

Originally Posted by Oxycodone

Exponential decays are uncontrollable and occurs when additional neutrons or alpha particles are ejected and hit other nucleus.

Decays are not "uncontrollable." Indeed, they are self-controlling because they are self-extinguishing. You know -- decaying. And such decays do not occur when particles "...are ejected and hit other nucleus [sic]."

So, 100% of the sentences that comprise your post #5 are wrong. You assert things strongly that you obviously have no clue about. That makes you appear ignorantly arrogant. And then responding with "STFU" when corrected merely confirms that appearance.

Originally Posted by tk421

Originally Posted by Oxycodone

Stfu minimod. Mad coz no tag? Here:

Untitled.jpg

You learn your math. Wtf was wrong with what I said about the exponential?

Happy to oblige your request. Pretty much your entire post #5, which I quoted, is wrong. Here are specifics:

Originally Posted by Oxycodone

How is it exponential if the probability stays the same lol? It's logarithmic at best.

I've shown you that the math leads to an exponential if the probability stays the same. It does not lead to "logarithmic at best."

Originally Posted by Oxycodone

Exponential decay is only observed in chain reactions for thermonuclear explosions.

Here you are doubly wrong. First you are not clear on the very meaning of the word decay. Second, exponential decays (or growths) are extremely widespread in nature. They are hardly "only observed in chain reactions for thermonuclear explosions." Any undergraduate physics student will encounter many examples of exponentially growing and decaying phenomena. Indeed, (complex) exponentials are eigenfunctions of linear systems, which covers a whole lot of ground.

Originally Posted by Oxycodone

Exponential decays are uncontrollable and occurs when additional neutrons or alpha particles are ejected and hit other nucleus.

Decays are not "uncontrollable." Indeed, they are self-controlling because they are self-extinguishing. You know -- decaying. And such decays do not occur when particles "...are ejected and hit other nucleus [sic]."

So, 100% of the sentences that comprise your post #5 are wrong. You assert things strongly that you obviously have no clue about. That makes you appear ignorantly arrogant. And then responding with "STFU" when corrected merely confirms that appearance.

exponential decay = logaritmic decrease

Got it? I just thought it was growth. Just read the post above...wtf. Why are you talking about math?

Originally Posted by Oxycodone

Why are you talking about math?

Perhaps because the question was about exponential versus constant rates; you know: math.

Originally Posted by Strange

Originally Posted by Oxycodone

Why are you talking about math?

Perhaps because the question was about exponential versus constant rates; you know: math.

Yes but my error didn't have fk all to do with math. The mod answered it and then the dude comes like a fly in the milk giving me lessons in life. So the guy with a moderator tag thought I didn't require a lesson in life, but the minimod without a tag, he thought I did. What I ask is, who the f is the minimod without a tag to think I deserve lessons in life or a math lesson? I bet now he's researching material to prove that logarithmic decrease is not equal to exponential decay, like I give a crap!

Originally Posted by Oxycodone

Originally Posted by Strange

Originally Posted by Oxycodone

Why are you talking about math?

Perhaps because the question was about exponential versus constant rates; you know: math.

Yes but my error didn't have fk all to do with math. The mod answered it and then the dude comes like a fly in the milk giving me lessons in life. So the guy with a moderator tag thought I didn't require a lesson in life, but the minimod without a tag, he thought I did. What I ask is, who the f is the minimod without a tag to think I deserve lessons in life or a math lesson? I bet now he's researching material to prove that logarithmic decrease is not equal to exponential decay, like I give a crap!

Will you calm down? You were talking nonsense and he corrected you. This is a discussion forum. That's what we do. If you don't like it, you don't have to be here. Your attitude stinks.

Originally Posted by KALSTER

Originally Posted by Oxycodone

Originally Posted by Strange

Originally Posted by Oxycodone

Why are you talking about math?

Perhaps because the question was about exponential versus constant rates; you know: math.

Yes but my error didn't have fk all to do with math. The mod answered it and then the dude comes like a fly in the milk giving me lessons in life. So the guy with a moderator tag thought I didn't require a lesson in life, but the minimod without a tag, he thought I did. What I ask is, who the f is the minimod without a tag to think I deserve lessons in life or a math lesson? I bet now he's researching material to prove that logarithmic decrease is not equal to exponential decay, like I give a crap!

You were talking nonsense and he corrected you.

He said:

"You clearly do not know what an exponential is; be aware of your ignorance so that you don't make foolish assertions, like the ones above. LOL indeed, but the derision vector is pointing at you. Laugh less, learn more. Think about it."

Can you please tell me, in your forum admin opinion, how does that correct me from a scientifically and mathematically objective point of view? What type of mathematical information does that include or suggest? Also, Could you please state elements of my original post that would require a non-mathematical and a non-objective correction, and I will be the first to accept the correction. Sir.

Like I said, this is a discussion forum. If not, he could have just posted the maths or a link to the Wiki article or something. He was giving you advice. If you don't like it, ignore it. No need to go into an extended diatribe about "how dare he".

Originally Posted by Oxycodone

Can you please tell me, in your forum admin opinion, how does that correct me from a scientifically and mathematically objective point of view?

"Wha! Mummy, nasty man on forum was horrid to me."

What are you? Ten?

Originally Posted by Strange

Originally Posted by Oxycodone

Can you please tell me, in your forum admin opinion, how does that correct me from a scientifically and mathematically objective point of view?

"Wha! Mummy, nasty man on forum was horrid to me."

What are you? Ten?

Yes, I'm 10 years old, I will write that in my personal profile. Done, wrote it below my avatar so people can see and take notice.

Originally Posted by Oxycodone

Originally Posted by KALSTER

You were talking nonsense and he corrected you.

He said:

"You clearly do not know what an exponential is; be aware of your ignorance so that you don't make foolish assertions, like the ones above. LOL indeed, but the derision vector is pointing at you. Laugh less, learn more. Think about it."

You forgot to mention the other 75% of tk421's post...

FYI, exponential decays...decay. That's hardly the signature of something that is "uncontrollable." Chain reactions for thermonuclear explosions depend on exponential growth. Think about it.

An exponential decay is the necessary logical consequence of an extremely simple thing: If a fixed percentage of atoms decay (equivalently, if the probability of a given fraction atoms decaying is fixed -- stays the same) within a given interval, you get an exponential. It's precisely the same behavior you would observe if your bank balance lost a fixed percentage every day, for example, with no replenishing of funds. This is what Harold 14370 was telling you.

Work it out mathematically, maybe with an example with specific numbers first. Start with 100 dollars, say. Suppose you lose 10% each day. So the day-by-day bank balances are in a sequence like this: 100, 90, 81, 72.90, 65.61...Plot the sequence. You will find that the points conform to those of an exponential curve.

Want the math? Here's a capsule summary: Saying that a fixed percentage of atoms decay per unit time is equivalent to saying that dN/dt is proportional to N, where N is the number of atoms. So set dN/dt = BN, where B is a constant, and solve (B will have a negative sign if you are talking about decay, and a positive sign if you are talking about growth). You can verify that an exponential is a solution to the simple equation.

Now the only difference is that, in actual fact, radioactive decay is probabilistic, so "given interval" must be interpreted stochastically. But the math is the same -- you get an exponential.

...which happens to be where he corrected you from a scientifically and mathematically objective point of view.

But hey, you know what they say, "wtf...lol...I don't give a crap".

Originally Posted by epidecus

Originally Posted by Oxycodone

Originally Posted by KALSTER

You were talking nonsense and he corrected you.

He said:

"You clearly do not know what an exponential is; be aware of your ignorance so that you don't make foolish assertions, like the ones above. LOL indeed, but the derision vector is pointing at you. Laugh less, learn more. Think about it."

You forgot to mention the other 75% of tk421's post...

FYI, exponential decays...decay. That's hardly the signature of something that is "uncontrollable." Chain reactions for thermonuclear explosions depend on exponential growth. Think about it.

An exponential decay is the necessary logical consequence of an extremely simple thing: If a fixed percentage of atoms decay (equivalently, if the probability of a given fraction atoms decaying is fixed -- stays the same) within a given interval, you get an exponential. It's precisely the same behavior you would observe if your bank balance lost a fixed percentage every day, for example, with no replenishing of funds. This is what Harold 14370 was telling you.

Work it out mathematically, maybe with an example with specific numbers first. Start with 100 dollars, say. Suppose you lose 10% each day. So the day-by-day bank balances are in a sequence like this: 100, 90, 81, 72.90, 65.61...Plot the sequence. You will find that the points conform to those of an exponential curve.

Want the math? Here's a capsule summary: Saying that a fixed percentage of atoms decay per unit time is equivalent to saying that dN/dt is proportional to N, where N is the number of atoms. So set dN/dt = BN, where B is a constant, and solve (B will have a negative sign if you are talking about decay, and a positive sign if you are talking about growth). You can verify that an exponential is a solution to the simple equation.

Now the only difference is that, in actual fact, radioactive decay is probabilistic, so "given interval" must be interpreted stochastically. But the math is the same -- you get an exponential.

...which happens to be where he corrected you from a scientifically and mathematically objective point of view.

But hey, you know what they say, "wtf...lol...I don't give a crap".

For example, someone insults your mother, calls you child of rape and then gives you a page of correct and highly important mathematical explanations. Do you listen to the mathematical explanations or do you grab something to smash his head with? Tell me brother, in front of all the forum. What would you do?

Originally Posted by Oxycodone

For example, someone insults your mother, calls you child of rape

You really equate that with a suggestion not to make foolish statements? Really? What are you? Four? Time to grow up and stop whining every time someone disagrees with you.

Originally Posted by Oxycodone

...someone insults your mother, calls you child of rape...

This happened? Where exactly?

...and then gives you a page of correct and highly important mathematical explanations. Do you listen to the mathematical explanations or do you grab something to smash his head with? Tell me brother, in front of all the forum. What would you do?

I wouldn't put myself into the position you're at in the first place. And since the question derives from what you have done, I'd say a practical answer is inapplicable.

But let's say I did do what you did... I would realize the fallacy in my supposed "correction", apologize for stating rude remarks (like lol), and take the thoroughly correct explanation offered to me. Since you simply get frustrated, ignore the criticism coming to you, and rather "find something to bash your head with", it's quite obvious what your maturity level and social attitude is on this forum.

Originally Posted by Oxycodone

For example, someone insults your mother, calls you child of rape and then gives you a page of correct and highly important mathematical explanations. Do you listen to the mathematical explanations or do you grab something to smash his head with? Tell me brother, in front of all the forum. What would you do?

Nobody said anything even close to that! This is not normal behaviour. You are overreacting.

Originally Posted by Oxycodone

Originally Posted by Strange

Originally Posted by Oxycodone

Why are you talking about math?

Perhaps because the question was about exponential versus constant rates; you know: math.

Yes but my error didn't have fk all to do with math. The mod answered it and then the dude comes like a fly in the milk giving me lessons in life. So the guy with a moderator tag thought I didn't require a lesson in life, but the minimod without a tag, he thought I did. What I ask is, who the f is the minimod without a tag to think I deserve lessons in life or a math lesson? I bet now he's researching material to prove that logarithmic decrease is not equal to exponential decay, like I give a crap!

Frigging well grow up! As Kalster says, your attitude stinks. This forum is intended for mature behaviour not the kind of crap you seem incapable of avoiding. I strongly urge a sharp and immediate change in your behaviour if you wish to stick around.

Just to be clear: in my view you require lessons in life and in maths. This one is free. The next one will be more costly.

As much as I agree with you guys, I think I'm gonna back out for now. I don't like it when a certain member, no matter how deluded or misled, receives heavy criticism from several other members at the same time. It sometimes gets to the point where we're just beating a dead horse. So unless I notice something trivial that I feel should be pointed out, I'll stay out of this discussion.

I also have a suggestion for the mods: Seeing that the OP's thread is now cluttered with personal argument, can this side-track please be separated off into its own thread?

Originally Posted by epidecus

As much as I agree with you guys, I think I'm gonna back out for now. I don't like it when a certain member, no matter how deluded or misled, receives heavy criticism from several other members at the same time. It sometimes gets to the point where we're just beating a dead horse. So unless I notice something trivial that I feel should be pointed out, I'll stay out of this discussion.

I also have a suggestion for the mods: Seeing that the OP's thread is now cluttered with personal argument, can this side-track please be separated off into its own thread?

Great idea Let's make "Oxycodone is BAD" topic and toss e-stones at him for making a mistake haha ()

Originally Posted by John Galt

Just to be clear: in my view you require lessons in life and in maths. This one is free. The next one will be more costly.

You can't cost me anything. I know your access.

Originally Posted by KALSTER

Originally Posted by Oxycodone

For example, someone insults your mother, calls you child of rape and then gives you a page of correct and highly important mathematical explanations. Do you listen to the mathematical explanations or do you grab something to smash his head with? Tell me brother, in front of all the forum. What would you do?

Nobody said anything even close to that! This is not normal behaviour. You are overreacting.

Ok sorry for whatever I done. I want to end this argument. I'll just go back to religious debates haha

Originally Posted by Oxycodone

You can't cost me anything. I know your access.

You have an amazing ability to make some of your posts sound like threats. Taking into accounts Epidecus's excellent points, but responding to them slightly differently. I am locking the thread temporarily. Anyone who wishes it to be reopened, please make a request of another member of the admin/mod team, not of me.

Originally Posted by Oxycodone

You can't cost me anything. I know your access.

Three off for threatening the operations of the forum. Don't do it again.