Radioactivity occurs when an unstable
nuclei begins to emit alpha,
beta or gamma particles, in order to become more stable. When the production of nuclei lie outside the region of stable nuclei (sometimes called the belt of stability (not to be confused with the Bible Belt, or the Belt of Orion)), the ratio of protons to
neutrons are such that the nuclei become
radioactive.
For instance, when the ratio of protons to neutrons is such that the
nucleus has a surplus of neutrons, then one of the neutrons will emit an
electron or a negative beta particle, thus transforming itself into a proton. All radioactive material undergoes radioactive
decay at a certain rate regardless of external influences, such as pressure or temperature, (whereas humans undergo radioactive decay at an astronomical rate because of external influences (i.e. traffic)). The half-life of the radioactive nucleus is defined as the time it takes for one-half of the nuclei in a sample to decay. In addition, all radioactive material half-lives undergo decay according to first order kinetics and can be expressed as follows:
t-half = 0.693 /k
Wherein k represents the radioactive decay constant, and t-half is the half-life. The rate of the radioactive decay can be expressed mathematically as:
Rate = k ( Nt )
again, k is the radioactive decay constant and ( Nt ) is the number of radioactive nuclei at time t. The rate constant is representative of the radioactive nuclide, wherein each nuclide has a different value; N-zero, the nuclei at time zero, and Nt, the nuclei at time t. This expression is written as:
ln( N-zero / Nt ) = kt .
The decay constant can be obtained by counting the nuclear disintegrations over time by utilizing these equations. For instance, the original decay of Radon226 is 3.7x1010 disintegrations per second for one gram. Therefore, this one gram contains the following nuclei:
1.0 g Radon226 x (1 mol Radon226 / 226 g Radon226) x (6.022x1023 Radon226 nuclei / 1 mol Radon226) = 2.7 x 1021 Radon226 nuclei
and utilizing our second mathematical expression we have
k = (3.7 x 1010 nuclei / 2.7 x 1010 nuclei) = 1.4 x 10-11 /s.
From this value, we can thus obtain the half-life of Radon226 as follows:
t-half = (0.693 / k) = 4.95 x 1010 seconds = 1569.6 years
One instance of this would be the half-life of Carbon 14, used in archeological dating (no, we’re not talking about dating someone as old as your parents) wherein Carbon 14 decays into a stable Nitrogen 14. The half-life for carbon is 5580+-45 years, which is determined utilizing a mass spectrometer and the process of gas counting with a small amount of Carbon Dioxide in argon/alcohol gas. Other methods have been used in determining the half-lives of carbon, providing various types of half-lives. These particular measurements have been useful in equating and determining the latter stages in human evolution (yes, ladies, men HAVE evolved).
Another instance would be when the nuclei has a surplus of protons, thus emitting a positive beta particle, otherwise known as a positron, therefore transforming itself into a neutron. An example of this is also an effective dating means for archeologists and anthropologists (other than MySpace); this is Potassium-Argon dating. In this process, half the Potassium 40 isotope changes to Argon 40 with a half-life of 1.3 billion years.
Positron emission is also known as electron capture (not to be confused with Capture the Flag). As stated previously, the nucleus has a surplus of protons and correspondingly has too few neutrons. It will gain a neutron by capturing one of the negatively charged 1s electrons orbiting around the nucleus. When the electron is captured, the negative charge cancels out the positive charge on a proton in the nucleus, thus turning it into a neutron.
Gamma ray production is a product ofthis as well, and consequently, gamma rays are always produced with electron capture and positron emission, which are the same thing (you say po-TAY-to, I say po-TAH-to).
The processes just detailed show the conversion of elements, either naturally or artificially conducted. The “forced” method of converting an element to another is called nuclear transmutation and was first conducted by Rutherford in the bombardment of alpha particles into Nitrogen.
For the most part, unstable atoms, will ultimately conduct a spontaneous change in the nucleus of the atom. This nucleus will then emit a variation of either a particle with two protons and two neutrons, or an electron or a positron (or a partridge in a pear tree).
These changes, however, are not the only types of radioactivity. Radioactivity comes in a multitude of forms. In the instance of the nucleus flying apart, such as in alpha decay, there is also spontaneous fission. With spontaneous fission, no photons of particles enter the nucleus form the outside, an alpha particle is emitted and the nuclei is split into parts of equivalent mass. In the instance where at least one neutron turns itself into a proton, or vice-versa, such as in beta decay and positron emission, there is also double-beta decay and K-capture. Double-beta decay is self-explanatory. K-capture is similar to beta decay, however, the electron is captured from the K-shell of the atomic electrons (the K-shell is the shell closest to the nucleus) and a neutrino is emitted. Lastly, there is the gamma decay, wherein the nucleus internally re-configures itself (kind of like the Terminator).
More abstracts about the Radioactivity, Decay Constant and Half-Lives