# Tag Info

63

The right way to think about this is that, over 5,730 years, each single carbon-14 atom has a 50% chance of decaying. Since a typical sample has a huge number of atoms1, and since they decay more or less independently2, we can statistically say, with a very high accuracy, that after 5,730 years half of all the original carbon-14 atoms will have decayed, ...

41

If protons decay, then what you say is true: all atomic nuclei are indeed unstable, and a so-called "stable" nucleus simply has too long a half-life for its decay to be observed. The most tightly bound nucleus is $^{62}$Ni, with a binding energy per nucleon of 8.79 MeV [source], which is less than 1% of the mass of a nucleon. On the other hand, the decay of ...

26

Because the mass of a nucleus isn't just the sum of its parts. Positron emission obeys the nuclear mass-energy balance like all other nuclear reactions. The mass deficit is the energy of the reaction. In other words, the reaction still decreases the total mass (reactants versus products). Your observation (that a neutron is heavier than a proton) tells ...

25

The half-life of Uranium 238 is about the age of the Earth, so only about half of the original supply should have decayed by now. Also, there are some radioactive nuclei that get created by interactions with cosmic rays in the upper atmosphere (carbon-14) or decay from more stable nuclei (all of the daughter nuclei between U-238 and lead, for example).

23

We are never 100% certain of anything. The scientific method falsifies wrong theories, but it does not verify those we colloquially call "correct" or "true" If we tomorrow detect a normal oxygen atom decaying, we'll have to devise new theories to explain it. But we don't expect the things we call stable to ever decay (that's why they're called stable). We ...

22

There are two separate issues to consider. Firstly there is usually an energy barrier to decay. Radioactive decay occurs due to quantum tunnelling through the barrier, and the rate therefore depends on the barrier height. One of the very first studies of this was by George Gamow back in 1928, who studied the alpha decay of uranium-238. Even though alpha ...

22

It's also worth noting that there is nothing special about atoms. If you have any system where in every period of time an event has a certain chance of happening which only depends on internal effects of the object and no memory or communications with others - you will get the same decay curve. It's purely a matter of the statistics. If you have a ...

21

No, one doesn't need to measure the material for years - or even millions or billions of years. It's enough to watch it for a few minutes (for time $t$) and count the number of atoms $\Delta N$ (convention: a positive number) that have decayed. The lifetime $T$ is calculated from $$\exp(-t/T) = \frac{N - \Delta N}{N}$$ where $N$ is the total number of atoms ...

20

I know exactly where you're coming from. If I can put it into my own words: If it takes a sample some amount of time to decay, shouldn't a sample of half the size take half the time to decay? I have fallen into this seemingly sensical but somehow incorrect belief more than once. Here's a graph that shows what I believe you're currently thinking. The ...

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 ...

18

It's because the half life time is also incredibly long. The half-life of Uranium-238 is $4.5*10^9$ (=4.5 billion) years. Thorium-232 has $1.4*10^{10}$. Potassium-40 has $1.2*10^9$. These are all examples of primordial nuclides. Such half lives are of the order of the age of the universe. There's also the effect of having a decay chain, since decay ...

16

There is a lot of discussion about this issue on this internet, so I think this question may be worth addressing seriously. The main point of the debate seems to be the following: Over the past decades, several research groups of self-proclaimed creationist scientists have claimed discoveries of dinosaur bones that they have managed to date, using ...

15

Some elements with short half-lifes, are just decay products of those with long half-lifes.

15

This is really a comment, since I don't think there is an answer to your question, but it got a bit long to put in as a comment. If you Google for "Why is technetium unstable" you'll find the question has been asked many times in different forums, but I've never seen a satisfactory answer. The problem is that nuclear structure is much more complex than ...

14

The reason why alpha particles heavily dominate as the proton-neutron mix most likely to be emitted from most (not all!) radioactive components is the extreme stability of this particular combination. That same stability is also why helium dominates after hydrogen as the most common element in the universe, and why other higher elements had to be forged in ...

14

We can show this by thinking about what is happening. Suppose we have a set of $N$ nuclei that are all radioactive. Each of these nuclei has a chance of decaying, $\lambda$. In people lifetimes, some people live longer and some live shorter than others, but there is an average lifetime; this is what $\lambda^{-1}$ represents for nuclei. Now how many ...

14

Actually, all the atoms are identical. The time at which it is observed to decay is not an intrinsic property of a given atom, but rather an effect of quantum mechanics. For any given time bin, there is some finite amplitude for a transition to a decayed state, which in turn corresponds to a finite probability, since the particle(s) emitted will escape from ...

13

As the other answers state, the individual nuclei have a probability of decay and this happens randomly, as they sit there. You are correct though in wondering about a trigger, because at the atomic level that is exactly what happens with lasing, induced-emission = induced-decay. Spontaneous decay is random, controlled by the quantum mechanical individual ...

13

In addition to Alan's notes about keeping track of total energy in a nuclear context, it is also important to keep track of the neutrino. Even free protons can be converted to neutrons (a process called "inverse beta decay") if there is an incident anti-neutrino of sufficient energy: $$p + \bar{\nu}_e \to n + e^+ \,.$$ This is the detection mechanism that ...

11

Logically, shouldn't it take 2,865 years for the quarter to decay, rather than 5,730? Imagine that the quantity $q(n)$ of something decays as $$q(n) = Q\cdot 2^{-n}$$ where $n$ is the number of half-lifes. Initially, there is quantity $q(0) = Q\cdot 2^0 = Q$ of something. After 1 half-life, there is $q(1) = Q \cdot 2^{-1} = \frac{Q}{2}$ remaining. ...

11

One has to make clear that the watches we are using now are no longer using radium , because of radiation danger awareness. Radium dials are watch, clock and other instrument dials painted with radioluminescent paint containing radium-226. The 1900s (decade) were the peak of radium dial production, as radiation poisoning was then unknown; subsequently, ...

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 ...

11

Carbon-14 makes up about 1 part per trillion of the carbon atoms around us, and this proportion remains roughly constant due to continual production of carbon-14 from cosmic rays. The half life of carbon-14 is about 5,700 years, so if we measure the proportion of C-14 in a sample and discover it's half a part per trillion, i.e. half the original level, we ...

11

The chance for a fixed nucleus to decay doesn't depend on the number of nuclei. In a fixed amount of time all the nuclei have a certain chance to decay. Increasing the number of nuclei will increase the number of nuclei that decay, but that's really just what you'd expect. It's like rolling lots dice, the number of dice showing a certain digit will be ...

11

why is plutonium considered more dangerous than radioactive iodine? Because the press have heard of Plutonium and Pu=atomic bombs=bad Plutonium's danger is over stated, it's insoluble so hard to get into the food chain and even if ingested is going to go straight through you. Pu is only a real concern if breathed into the lungs as a fine dust. Iodine ...

10

The short half-life elements ocuring in nature come from the decay of long-half life elements. You can see examples of decay chains on this wikipedia page. For example, ²²⁴Ra (3.6 days half life) is produced by the decay of ²³²Th (14 billion years decay).

10

A more balanced approach might be to recognize that both short and long half-live materials can be serious hazards, but usually for somewhat different reasons. Also, the devil is very much in the details here, because issues such as how your body absorbs the isotopes is also very, very important. Radioisotopes with short half-lives are dangerous for the ...

10

this just pushes back the mystery back one step for me: why are nuclei with even atomic number more stable? There is no big mystery about this. There is a pairing interaction in nuclei. It's loosely analogous to the Cooper pairs in a superconductor. It's easy to construct an argument as to why, if you're looking for an element with no stable isotopes, ...

10

There really is none. Unstable elements (and unstable elementary particles) can decay into a less energetic state. However, each kind of decay depends on a quantum mechanical process, this is tunneling for $\alpha$, a virtual $W^\pm$ for $\beta$ or a transition from one nuclear shell to another for $\gamma$. Now these underlying processes can be strongly ...

9

It's not true that the atom is electrically neutral afterward. If you have a single atom, isolated in a vacuum, and all that is emitted is an alpha particle, then as you say, it has a net charge of -2e. In reality, alpha decay is a violent process that is likely to knock out some electrons as well. Furthermore, if the atom is in a solid, then electrons are ...

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