## What Does it Mean to be Radioactive?

For introductory purposes, we can say that two criteria need to be met:
• The nucleus is unstable - meaning it will spontaneously decay
• There will be emission of energy and a change in mass and/or atomic number for that particle

## Half-Lives

The half-life of a radioactive isotope is the time it takes for 50% of the particles in a sample (of the same isotope) to undergo radioactive decay. Note that this says nothing about the time it will take one individual particle to decay. Since radioactive isotopes are decaying at every moment, the half-life defines the time interval when the first 50% of a sample have decayed. It is important to notr that after two half-live, 25% of the original sample (one-half of one-half) remains. After three half-lives, the percentage is down to 12.5%, or one-eighth, equivalent to one-half of one-half of one-half. Given the half-life of an isotope, the amount of an isotope that remains after a certain interval of time can be calculated using the formula below:

## Half-Life Problems - How Much Remains?

If a 100. g sample of thorium-230 is analyzed, how much is left after 3.2×105 years?

First, find the half-life of the thorium-230. If this information is not given in the problem, it must be found in a table. Next, make sure the half-life's units of time agree with the length of time given in the problem. In this case, both are given in years, so there is no conversion necessary. If this is not the case, one value must be converted into the other's unit of time. For converting days to years, it is strongly recommended that 365.25 days be used as the equivalent for one year. Although it may seem negligible, the accumulation of many years may result in the loss of a multitude of days. Be sure to plug in the initial mass into A0, as the subscript 0 indicates it represents initial mass. The variable A represents the mass that remains.

## Half-Life Problems - How Much Has Decayed?

How much iron-55 will decay if a 112.4 g sample is left to decay for 225.3 days?

The trick to a problem that asks for hiow much has decayed is to realize that you are not done after you have solved for A. The difference between A0 (the initial mass) and A (the final mass) is equal to the mass that has decayed.