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61

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, ...


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

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 ...


23

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 ...


19

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 ...


19

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 ...


19

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 ...


15

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


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

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 ...


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 ...


11

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 ...


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

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 ...


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

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 ...


9

The short answer is no: halflives are constant. However, let's discuss a situation in which that comment might have some kind of truth behind it. If you have a parent nucleus that decays to a radioactive daughter so that there will be two (or more) decays before stability. In general there are two possibilities for this: The daughter has a shorter ...


9

Are you worried that the cables that go to the Fukushima reactors will carry radioactivity out? The answer is No. You should read up a bit on radioactivity and educate yourself, since it is one of the facts of life. In the article you will see that it is atoms that are responsible for radioactivity whereas the current in the cables is due to electrons. The ...


9

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. ...


8

The simple answer is no, though as usual in Physics things are a bit more complicated than that. There are several ways in which radionucleotides decay: alpha decay, beta decay, gamma decay, and fission. These are all mediated by the weak and strong nuclear forces, though the electromagnetic force plays some part in alpha decay and nuclear fission. There is ...


8

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 ...


8

Nuclei have energy levels just like atoms do, but while the energy level spacing in atoms is around the energy of visible light, the energy level spacing in nuclei is around the energy of gamma rays. So while an atom may relax from an excited state to the ground state by emitting visible light, when a nucleus relaxes from an excited state to a ground state ...


7

When people say that the decay rate depends critically on the $Q$ value, they're talking about alpha decays compared to other alpha decays. When you compare alpha decay to emission of other small clusters, the dependence on the atomic number $Z_c$ of the emitted cluster is much more prominent. The reason is as follows. In the Gamow model of beta decay, we ...


7

Schrödinger came up with the cat in 1935, which was relatively late in the development of quantum mechanics. Back in the 1920's there had been a lot more uncertainty. The Copenhagen school had wanted to quantize the atom while leaving the electromagnetic field classical, as formalized in the Bohr-Kramers-Slater (BKS) theory. De Broglie's 1924 thesis ...


7

Have a look at the paragraph "radioactive decay" . The half life is characteristic of each radioactive nucleus and depends on the basic interactions holding the nucleus together. It depends on the quantum mechanical probabilities of transition from one energy level to another, sometimes changing element in the periodic table. Thus, to affect the half ...


7

From: NobelPrize.org "Her continued systematic studies of the various chemical compounds gave the surprising result that the strength of the radiation did not depend on the compound that was being studied. It depended only on the amount of uranium or thorium. Chemical compounds of the same element generally have very different chemical and physical ...


7

There is nothing magical about lead for this purpose. The driving factor is the number of electrons per unit volume, which reduces (to a first approximation) to the mass density. You get very good (better than lead) shielding performance from gold, tungsten, mercury, etc; and quite reasonable performance from iron or copper. Question for the student: why ...


7

How do we know that C14 decay's exponentially compared to linear Here's an argument that might help: suppose, temporarily, that radioactive decay was linear. Let's say you started out with a sample, call it sample #1, of a billion atoms in a box, 5700 years ago (that's one half-life). By the current day, half of them would have decayed, so you'd have ...



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