Radioactive elements are elements that do not have a stable nucleus. These elements give off particles and/or rays to change their nucleus and become a stable element. Some lightweight isotopes are radioactive but, all elements that have an atomic number greater than 82 are radioactive. The process of changing the nucleus to a stable one is called radioactive decay.
Nuclear notations are used to represent the decay of one element into another. The generic formula for a radioactive element is as follows:
Some examples of nuclear decay equations are:
There are three types of natural radioactive decay. They are alpha emisson, beta emission, and gamma emission. Alpha emission results in releasing an alpha particle. An alpha particle has two protons and two neutrons, so it has a positive charge. (Since it has two protons it is a helium nucleus.) It is written in equations like this:
Beta emission is when a high speed electron (negative charge) leaves the nucleus. Beta emission occurs in elements with more neutons than protons, so a neutron splits into a proton and an electron. The proton stays in the nucleus and the electron is emitted. Negative electrons are represented as follows:
Gamma Emission is when an excited nucleus gives off a ray in the gamma part of the spectrum. A gamma ray has no mass and no charge. This often occurs in radioactive elements because the other types of emission can result in an excited nucleus. Gamma rays are represented with the following symbol.
Positron emission involves a particle that has the same mass as an electron but a positive charge. The particle is released from the nucleus.
Electron capture is when an unstable nucleus grabs an electron from its inner shell to help stabilize the nucleus. The electrons combine with a proton to form a neutron which stays in the nucleus.
Bombardment reactions involve the nucleus of the atom being bombarded (hence the name) with particles from the nucleus or an entire nucleus. Examples of the particles are neutrons and alpha particles. These reactions usually give off a different particle than the one that they were bombarded with. Here is an example equation for a bombardment reaction.
Particle accelerators are where most of the bombarding takes place. The accelerators move the particles toward each other at great speeds, to overcome the repulsive forces.
No one can say for sure when a particular nucleus will decay but one can predict how many in a given sample will decay over time. Radioactive elements have a half-life. The half life of any given element is the time that is required for one half of the sample to decay. So if you have 10 grams of a radioactive element, after one half-life there will be 5 grams of the radioactive element left. After another half-life, there will be 2.5 g of the original element left, after another half-life, 1.25 g will be left. The equation for half-life calculations is as follows:
Other variations on the half-life equation are as follows:
An example problem is if you originally had 157 grams of carbon-14 and the half-life of carbon-14 is 5730 years, how much would there be after 2000 years?
There would be 123 grams left.