What causes the decay(half life) of particles and why does it follow a half life and not x type particle exists so long then decays.

Take for example 100 neutrons now first half life after 13 min would be 50 then 25 12.5(12 or 13 Im assuming not seeing a half particle :) ) etc.
now taking
2 sets of 50 each set follows 50 25 12.5
now 4 sets of 25 follow 25 12.5 6.25
now take 50 sets 2 1 what happens next here?

The more piles you have the quicker you get to not having any particles so how does having a group of the particles help maintain the structure of the particles
or does it seeing how 1 * 50 equals 12.5 * 4 and 25 * 2

then on the other extrem a pile of 1 million neutrons decay into 1/2 million in 13 minutes. Does any decable particle out there not conform to a half life?

The decay seems to be probability that within 13 minutes and halving 2 neutrons one will decay. Is this rate changable?
Its a long post that realy doesnt say much but im intresting in the decay of atoms.

What causes the decay(half life) of particles and why does it follow a half life and not x type particle exists so long then decays.

Take for example 100 neutrons now first half life after 13 min would be 50 then 25 12.5(12 or 13 Im assuming not seeing a half particle :) ) etc.


You can rewrite the decay of neutrons in other forms, but then ofcourse the "half-time" would no longer be a half-time but rather a "75%-time" or something. This is just the mathematical part.

The formula for decay is not really related to particles as such. It is typical for systems that "change" in a specific way (e.g. bacterial growth is also related to such formula). If you say that the amount of particles changes in time (= factor Δ N / Δ t ) according to the amount of particles present (=N) then you get a relation of the form:

Δ N / Δ t = - α N

where α is a constant of proportionality, and a minus sign because N decreases for decays. For very small changes, the factor Δ N / Δ t can be written as a derivative such that you get

dN/dt = - α N

This is a so-called differential equation: you are looking for a function N(t) whose derivative gives you back N(t) with a constant α in front. Such a function is the exponential function:

N(t) = N(0) exp( - α t )

Using this simple analysis you get exponential decay from an initial value N(0) to zero, with a time constant 1/α (which is related to the half-time).

Hope this gives you a small start...

Crisp

Exactly Crisp.

FNG2K4:
Why don't u try a little experiment in Excel. U will see that for any number u start out with, if u decrease the number (N) at each step by an amount 0.1*N then u will get a half life of about 7.6 (steps) approx. ALL THE TIME!!!
If u decrease it by 0.3*N then u should always get a half life of about 2.9 regardless of the initial N.

Exactly Crisp.

FNG2K4:
Why don't u try a little experiment in Excel. U will see that for any number u start out with, if u decrease the number (N) at each step by an amount 0.1*N then u will get a half life of about 7.6 (steps) approx. ALL THE TIME!!!
If u decrease it by 0.3*N then u should always get a half life of about 2.9 regardless of the initial N.

You can also decrease the number N at each step by an amount of 0.5*N, then u get a half-life of exactly 1 regardless of the initial N.

My initual question was more on the decay of the atoms why do atoms decay the way they do releasing a neutron, alpha particle,beta particle, or gamma radiation. And I was asking what properties these atoms have if they are in one pile or lots of smaller piles.

I just found it intresting that atoms decaying follow a half life scale and not a set length of time.

No, u see no individual atom has a set lifetime! Thats the whole point of quantum physics. Everything is random on such a scale including the decay process. Because an atom of a particular kind has a 'probability' of decay at a certain time it doesn't mean it WILL decay at that time. At each time point, an atom can decay or not. 2 possibilities. It is the probability that an atom will decay or not in a certain time which governs the half life of a large collection of atoms. I don't know if u understand what Im trying to say, its quite hard to explain sometimes!!! Again, experiment with it in Excel using a constrained random function or something.

My initual question was more on the decay of the atoms why do atoms decay the way they do releasing a neutron, alpha particle,beta particle, or gamma radiation. And I was asking what properties these atoms have if they are in one pile or lots of smaller piles.
consider this example:

n+ν_u-->p+e^-

what is really happening here is that one particle is approximately in one eigenstate of the weak interaction hamiltonian, but since that hamiltonian doesn't commute with the free hamiltonian, we cannot say exactly that it is one or the other. at any given time, there is a quantum probability that it can be seen in another state. i like to think of these as brought on by quantum fluctuations in the vacuum.

so anytime a decay is kinematically allowed, there is some probability (which can be calculated from first principles) that the decay will happen. we cannot predict when it will happen, only the probability that it will happen at any point in time.

I just found it intresting that atoms decaying follow a half life scale and not a set length of time.
this happens because if you have N particles, each of this has a probability of decaying of α, then averaging over many many particles, in every second, αN particles will decay, and so the total number of particles at any time will follow the differential equation that Crisp shows above.

the solution to the differential equation is an exponential decay, and these kinds of decays are conveniently described in terms of half-lives. so from some Feynman diagrams, you calculate the probability of a single decay, and then this translates directly into half-life.

It would be hard to find a collection of atoms which has EXACTLY half the number of atoms after 1 half life!

The mathematics of radioactive decay is the probabilistic mathematics used to describe coin flipping, dice throws, et cetera. It is no more mysterious than that. One can accept the statistics and not worry about what causes the decay. Alternately, one can view the process as random, as strongly implied by the data.

Suppose that you have 10²⁴ atoms of a radioactive substance with a half life of one year. That is about a kilogram of the substance (about 2.2 pounds). In a year, you expect that very close to 10²³ atoms would have decayed and 10²³ atoms would remain. If you flipped 10²⁴ true coins in a year, you would expect very close to 10²³ heads and 10²³ tails at the end of the year.

The decay rate throughout the year is not modeled by flipping coins at a constant rate. The formula is the following.Amount = InitialAmount * 2^{-Time / HalfLife}Note that for 1, 2, 3 . . . half lifes, the amount remaining is 1/2, 1/4, 1/8 . . . of the original amount. For a large number of atoms, the above formula is very precise.

The mathematics of radioactive decay in an integer number of half lifes is precisely modeled by the mathematics of coin tosses. For very short periods of time (or for a small number of atoms), I think it is modeled by Poisson probabilities with the mean calculated using the above exponential equation. This leads physicists to claim that radioactive decay is a random process. Id est: There is no deterministic mechanism which explains the decay. Causality does not seem to apply.

There are those who argue that it only seems to be probabilistic because we do not know what causes it. I expect a lot of posts by such people. There is at least one thread with many posts arguing both sides of this issue.

The belief in a deterministic mechanism for various apparently random quantum processes is like a religious belief. It is not supported by any evidence, and it is counter indicated by the data associated with such processes. Those with a scientific view are really saying that there is extremely strong evidence that radioactive decay is a random (or a-causal) process. They are willing to change their view if evidence for a causal mechanism is discovered. Until some experiment indicates otherwise, a true scientist will say that radioactive decay is a random process.

The current scientific view of radioactive decay is analogous to the view of Newtonian gravitational equations up until the development of General Relativity. Physicists from the time of Newton until about 1915-1920 said that gravity followed the laws (formulae) developed by Newton, reserving the right to change their mind if some experimental evidence indicated that another set of laws (formulae) were more precise. Anyone who disagreed without good evidence to the contrary was viewed as a fool or as having something like religious faith in anther view.

It should be noted that modern physics did not show that the Newtonian equations were incorrect, only that they could not be applied to situations unknown prior to modern times. NASA still uses Newtonian equations.

BTW: It is very difficult to imagine a causal mechanism which does not merely push the randomness down a level. Suppose that 5, 50, or 500 years from now some genius shows that a radioactive nucleus decays when one of the quarks in a nuclear particle frazzles (whatever that means). The discovery will not change the statistical nature of the data. Future physicists will say that radioactive decay is caused by the random frazzle event. Such a discovery will not restore causality, it will merely push the randomness from the atomic to the nuclear particle level.

Many people have misconceptions about probabilistic processes. Consider the following, which lists the probability of exactly half heads for various numbers of tosses. P(2) = .500 000 (or one half). Half the time you will get one head and one tail; Half the time you will get two heads or two tails. P(4) = .375 000, 37.5% of the time you will get exactly two heads & two tails. P(10) = .246 094 P(100) = .079 589 P(1000) = .025 225As the number of tosses increases, the chance of getting exactly half heads and half tails decreases, approaching zero. The ratio of heads to tails approaches one as the number of tosses increases: Id est: As the number of tosses increase, the percentage of heads approaches 50%, while the probability of exactly 50% heads decreases, approaching zero.

The following shows the probability of heads exceeding tails by ten or more or vice versa.P(10) = .001 953, which is the probability of ten heads and no tails plus the probability of ten tails and no heads. P(100) = .368 202. which is the probability of 55 or more heads plus the probability of 55 or more tails. P(1000) = .775 964, which is the probability of 505 or more heads plus the probability of 505 or more tails. As the number of tosses increases, there is an increasing chance that the absolute difference between the number of heads and tails will be ten or more. Oddly enough, for 10²⁴ coin tosses, there is a good chance that the absolute value of the difference will be one million or more, and an absolute difference of ten or more is almost guaranteed.

The above is the reason why statisticians do not think that the probability of a tail increases after a run of consecutive heads. They do not expect exactly the same number of heads and tails after a large number of flips.