# Half life

Figure 1. A chart showing the decay of a radioactive nucleus over time. The time that it takes the mass or activity of the source (the number of decay events per second) to fall to the 50% mark is the half life. The half life in this image is 1 year.[1]

Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay. Additionally, one half life is the time that it takes for the activity of a source to fall to half its original value.[2] The second law of thermodynamics, specifically the disorder statement can be used to help understand why radioactive decay occurs. This statement says that the entropy of a closed system can never decrease, meaning that things must fall further into disorder, not order. This helps to clarify why matter breaks down into a less and less organized state over time - this process is known as "decay". Part of this process includes certain types of atoms which break down into new, different types of atoms at some measurable rate - this is radioactive decay.

All radioactive materials have unstable nuclei within them. Additionally, there are also some nuclei within the substance that are already in their stable state - the proportion of stable to unstable nuclei in a sample can vary. The stable nuclei in the sample are unchanging (and in a stable energetic state), but the unstable nuclei will undergo some sort of nuclear decay over time to become stable.[3] This results in an emission of some form of radiation. Since half life is a measure of time, the half life is a value that determines how long this reduction to a more stable energy state will take.[2]

Different substances experience a loss of their radioactivity more quickly than others. Some radioactive elements can have half of their unstable nuclei decay in less than one second. For example, krypton-101 has a half life of about a ten millionth of a second.[4] In contrast, some elements have extraordinarily long half lives and take billions of years to decay. Uranium-238 has a half life of 4.51 billion years.[2] This means that it would take billions of years for uranium-238 to decay into a ratio of half uranium-238 and half thorium-234.[4] Uranium-235 (another naturally occurring isotope of uranium) has a shorter half life than uranium-238, that's only ~700 million years.[4]

## Equation

There is an equation that is frequently used to determine how much of a certain radioactive substance remains after a given time has passed. This is determined from properties such as the half life of the substance, and how much of the substance there was initially. The equation used is:

$N = N_o \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}$

where:

• $N$ is the amount of substance after time has passed
• $N_o$ is the initial amount of substance
• $t$ is the amount of time that has passed
• $t_{1/2}$ is the half life of the substance

Additionally, a similar equation can be used to show how the activity of the substance diminishes over time. When this is being expressed, the equation takes the form:

$A = A_o \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}$

where:

• $A$ is the activity of the substance after time has passed
• $A_o$ is the initial activity of the substance
• $t$ is the amount of time that has passed
• $t_{1/2}$ is the half life of the substance

The graph shown in Figure 1 is a visual representation of these equations above. It is important to note that regardless of the actual length of the half-life (whether it is millions of years or a few nanoseconds) the shape of the graph will be the same.

Knowledge of half lives is part of how geologists date rocks with radioisotopic dating.

## References

1. Created internally by a member of the Energy Education team
2. GCSE Physics. (July 23, 2015). Half Life [Online]. Available: http://www.gcsescience.com/prad16-half-life.htm
3. HyperPhysics. (July 23, 2015). Radioactive Half-Life [Online]. Available; http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli.html
4. Chart of the nuclides. (July 24, 2015). Half-Life [Online]. Available; http://www.nndc.bnl.gov/chart/reCenter.jsp?z=92&n=143