# Tag Info

2

It's tempting to think of photoionisation as the photon coming in like a billiard ball and knocking out an electron. However this is a very misleading representation of the process. A gamma ray is poorly modeled as a photon or photon(s) because the energy in it is delocalised. If you wanted to use a photon description you'd have to treat the ray as a ...

4

No, Bismuth-218 forms Polonium-218 by beta decay. Assuming there aren't any nuclei big enough to fission into Bismuth-218, the only ways of forming Bismuth-218 are alpha decay, beta decay and beta plus decay. Beta plus decay would have to be Astatine-218 decaying to Polonium, but this decay mode doesn't happen (actually Polonium-218 beta decays to ...

1

You have just read reasonable answers of knowledgeable people, so now you know that "radioactive decay...- it's completely stateless (@Luaan)", "There are no patterns" (@Luboš Motl), and "Atoms are dumb" (@David Hammen). However, there is a bit more to it. Atoms may be dumb, but they happen to know quantum mechanics much better than we, mere mortals, do. So ...

1

This comes down to what you understand the initial state $|\varphi⟩$ to be, and most importantly to how you define the survival probability. In my previous answer, to keep things general I took $|\varphi⟩$ to be any square-integrable state. If you want to be more specific, however, you will run into trouble. As the Fonda paper I referenced mentions (Rep. ...

1

Is there some sort of pattern to which atoms decay at which time, or is it some miraculous property of quantum mechanics that somehow each atom knows when to decay? Atoms are dumb. They don't know anything. Radioactive decay is a memoryless process, a process that doesn't depend on history. Consider three atoms of radon 222. One was created a month ago ...

5

There are no patterns. When a particle decays, the moment when it does so is absolutely random, chosen from the distribution $$P_{\rm decay}(t\lt T\lt t+dt) = \frac{dt}{t_0}\cdot \exp(-t/t_0)$$ For $t=t_0$, the beginning of time when we knew that the particle still existed, the exponential is equal to one and we see that the "probability of the decay per ...

20

Congratulations on deriving the exponential law for yourself, one learns a great deal about science working like this. Now to your last question: If I had a group of atoms that have an 'average lifetime' of say 5 seconds, after 5 seconds has elapsed, what is the 'average lifetime' of the remaining atoms? I don't think I can arbitrarily choose some ...

11

Khalfin showed some 60 years ago that strictly exponential decay is actually incompatible with quantum theory and there must be tiny deviations both for very small and very long times. See the details and references, say, in Nature vol. 335, p. 298 (22 September 1988). There seems to be experimental confirmation as well: http://dro.dur.ac.uk/4234/1/4234.pdf ...

6

What is the "average life time"? You take the average of the life times of many identical atoms, i.e. $$T_{\text{avg}} = \frac{1}{N}\sum_{n=1}^{N} T_n$$ This is a random variable dependent on your distribution of $T_n$, which is in your case the exponential function: $p(T_n = t) = \alpha e^{-\alpha t}$ if $t\ge 0$ and zero otherwise. Knowing that, you ...

2

You are right, the average life time remains the same. In the context of your example, if you have $N$ nuclei at any arbitrary point of time $t_0$ and if $T$ is the half life of the nucleus then at time $t_0 + T$, half of them would have decayed. That $T$ is independent of when you started keeping time is the key observation in making carbon dating a ...

1

Any population whether human, animal or atomic nuclei, will with no other complications change proportional to the amount already there. Yielding a very simple differential equation. $$\frac{dP(t)}{dt} = k\,P(t)$$ where $k$ is a constant with a negative sign for exponential decay and plus sign for exponential increase. i.e. the solution is  ...

7

If you want to be very nitpicky about it, the decay will not be exponential. The exponential approximation breaks down both at small times and at long times: At small times, perturbation theory dictates that the amplitude of the decay channel will increase linearly with time, which means that the probability of decay is at small times only quadratic, and ...

0

A first principle treatment will not yield an exact exponential decay law, see e.g. here.

7

Your question drives at the definition of "true randomness", which is a deep question and not altogether resolved. But in short, in modern physics we believe the answer is yes. Indeed there is a whole body of knowledge around Bell's Theorem and the untenability of notions of countefactual reality (the notion that the outcome of a quantum measurement exists ...

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