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explain electron capture, to show why half-lives are ''almost always'' fixed
==Half-life==
==Half-life==
The probability of a given transformation, within a given configuration of particles, per unit time, is fixed. This means that the decay proceeds exponentially. (This is true of alpha and gamma decay also, for the same reason.) This gives every isotope a characteristic half-life. Half-lives are usually not able to be calculated on a theoretical basis; they are measured from observation. The probabilities derive from the overlap of the wave functions, leading to quantum mechanical probability. This is fixed, by the rules of quantum mechanics.
The probability of a given transformation, within a given configuration of particles, per unit time, is fixed. This means that the decay proceeds exponentially. (This is true of alpha and gamma decay also, for the same reason.) This gives every isotope a characteristic half-life. Half-lives are usually not able to be calculated on a theoretical basis; they are measured from observation. The probabilities derive from the overlap of the wave functions, leading to quantum mechanical probability. This is fixed, by the rules of quantum mechanics.
==Why neutrons are usually stable when inside a nucleus==
Neutrons, by themselves, decay. This follows from the mass difference between the neutron and the resultant proton and electron. But, when the entire nucleus is taken into account, it's often a different story.
Consider the decay of Argon-39 to Potassium-39. This is a standard beta-minus decay. The Argon atom has 18 protons, 21 neutrons, and 18 electrons, and an atomic mass of 38.964313. The Potassium atom has 19 protons, 20 neutrons, and 19 electrons, and an atomic mass of 38.963706487. The beta-plus particle (electron) ejected by the nucleus joins the electron cloud, since the atomic number has gone up by one. The mass decrease is .0006065 amu, so the decay is energetically possible, releasing .0006065 amu of equivalent energy.
Now consider the hypothetical beta-plus decay of Argon-37 to Chlorine-37. The Argon atom has 18 protons, 19 neutrons, and 18 electrons, and an atomic mass of 36.96677631. The Chlorine atom has 17 protons, 20 neutrons, and 17 electrons, and an atomic mass of 36.9659025. This would give an excess of .0008737 amu, but the decay released a positron. Furthermore, an electron was released into the atom's electron cloud. These two particles add up to .00109716 amu. So there would be an overall mass ''increase'' of .00022343 amu. This decay cannot happen.
But suppose that, instead of releasing an electron and positron, the excess electron from the atom's electron cloud simply went down into the nucleus. The nuclear transformation would be:
:<math>\begin{align}
p + \beta^- &\to n + \nu_e
\end{align}</math>
This would release .0008737 amu of mass. It is an electron capture event. This decay occurs with a half-life of 35 days.
==References==
==References==