The radioactive half-life (Nave, 2000) for a given radioisotope is a measure of the tendency of the nucleus to “decay” or “disintegrate”.

Radioactive decay is a totally random event that is based purely upon probability.

The video explaining radioactive half-life should give you a good start to understanding the concept of radioactive half-life.

__Alpha, Beta and Gamma Rays Radioactive Decay and Half-Life__

Half-Life is the time it takes for half of a given sample to decay into stable components. This disintegration of the radioactive sample is via the release of radioactive particles (Deer, 2015, November 30) such as Alpha, Beta and Gamma rays.

Check out this video explaining Alpha, Beta and Gamma rays

__Geiger Counters and radioisotopes__

Different radioactive isotopes or radioisotopes (Encyclopædia Britannica, 1990) have different half-lives:

- 5,715 years for carbon-14
- 20 minutes for francium-223

The half-life of a radioactive sample is measured via using a Geiger-Muller counter (Deer, 2015, February 28). The half-life is a measure of time (GCSE Bitesize, 2014) and can be determined from:

- Time taken for radioisotope nuclei in a sample to halve
- Time taken for count rate from a radioactive isotope to fall to half

The video above explains how Radioisotopes decay.

__Alpha, Beta and Gamma Decay Equations__

As the element decays, it converts from one substance to another.

For example, Radium-219 decays to Polonium-215, emitting an alpha particle, which is basically a high energy Helium nuclei in the process. The Radium-219 is said to have undergone radioactive Alpha particle decay. The equation is a shown below.

Carbon-14 decays (Wikipedia, 2016) to Nitrogen-14 emitting a beta particle (Whatisnuclear, 2015) and is said to undergoe radioactive beta decay. In radioactive Beta particle decay, a neutron turns into a proton and releases an electron or beta particle. The equation is a shown below.

After witching the video explaining Carbon-14 decay, this concept should become easier to understand.

__Half Life Graphs and how to calculate Half-life__

Radioactivity decreases with time and can be measured on a graph (GCSE Bitesize, 2014) showing the count rate decrease as each half-life period passes as shown below.

The time take for the count rate on the graph (y-axis) to fall to half of its value is the half-life and can be read from the x-axis, which is calibrated in time.

After watching this video, you should understand how to using Graphs to solve Half-Life.

__Half-life Calculations using Logarithmic relations__

You can also solve worded problem to solve for half life or the amount of a sample remaining, using the below equation:

(1/2)^{n} = R_{f}

Where

n = number of half-lives

R_{f }= fraction of radioisotope remaining relative to original amount

__Worked Example of Half-Life Calculation__

Example #1: How many years will it take for 88.0 grams of tritium to decay to an 11.0 gram sample? (The half-life of tritium is 12.3 years.)

Solution:

First find the ratio R_{f }between the original sample (ChemTeam, 2001) and the final amount of tritium left after some of it has decayed.

11.0 g / 88.0 g = 0.125

Then plug this into the equation:

(1/2)^{n} = 0.125

Using log then work out the value of n:

n log 0.5 = log 0.125

n = log 0.125 / log 0.5

n = 3

So the total time is calculated thus:

half-life x n = 12.3 years x 3 = 36.9 years

__How to calculate the Half-Life for any sample__

Using this equation, you can also calculate the half-life of any sample.

Example #2: A 208 g sample of sodium-24 decays to 13.0 g of sodium-24 in 60.0 hr. What is the half-life of this radioactive isotope?

Solution:

Determine the decimal amount remaining:

13.0 g / 208 g = 0.0625

Determine the number of half-lives:

(1/2)n = 0.0625; n log 0.5 = log 0.0625; n = 4

Determine the length of the half-life:

60.0 hr / 4 = 15.0 hr

This is similar to using the Half-Life Graph (GCSE Bitesize, 2014) by looking visually for the sample count going down to half.

__Uses of Radioisotopes__

Radioisotopes are used (Kentchemistry, 2015) in various fields:

- Detection of Disease
- Tracing Chemical
- Geological Dating
- Archaeological Dating
- Process Control in manufacturing
- Food Irradiation
- Smoke Detectors

This video above shows the uses of Radioactive Isotopes

__Radioisotopes in Medicine – Imaging__

The most commonly known use of Radioisotopes in medicine is in making X-rays. The x-ray machine (GCSE Bitesize, 2014) uses a hot cathode that emits electrons that are attracted to a tungsten anode. Some of the kinetic energy of the electrons is converted to x-rays as shown below.

Skin and bone absorb x-rays and varies depending on the thickness and density of these parts of the body. The X-rays that pass through form the images that you see in X-ray images. Radiation from Gamma Rays is also used to sterilize equiptment (GCSE Bitesize, 2014).

__Radioisotopes in Medicine – Tracers__

Radioisotopes are also used as tracers in the body (GCSE Bitesize, 2014) to detect various (Kentchemistry, 2015) cancers.

- Iodine-131, a beta emitter, in sodium iodide in drinking water to detect thyroid cancer
- Sodium-24 injected into the bloodstream to study blood circulation and detect impaired circulation
- Thallium-201 compound injected into the bloodstream to detect damage in heart tissue
- Technetium-99m a decay product of molybdenum-99, is used for locating brain tumors and damaged heart cells

__Radioisotopes in Industry – Broken Pipes to Carbon Dating__

Radioisotopes are also used in tracing leaks in pipes (GCSE Bitesize, 2014) as well as in smoke detectors using Americium-241 (Kentchemistry, 2015).

Carbon-14, with half life of 5700 years is used in Archaeology (Kentchemistry, 2015) to determine the age of objects containing Carbon. U-238 is used for dating rocks and has a half life of 4.5 billion years.

See the graphs below (GCSE Bitesize, 2014) to get an idea of the half-lives of Carbon-14 and U-238.

__Resources for Radioisotopes for further reading__

Click on the following resources to learn more about the various uses of Radioisotopes in these fields:

GCSE Bitesize Uses of radioisotopes

GCSE Bitesize Radiation Treatment

Kent Chemistry Use of Radioisotopes

Chemwiki Uses of Radioisotopes

__Conclusion__

Half-Life calculations are easy to master once you understand the concepts of what a half-life represents both on a graph as well as in doing worded questions and mathematical calculations.

The best way to be comfortable with Half-life calculations is to practice many questions as often as possible.

Radioisotopes have many varies uses, from medical to sterilizing our food all of which are beneficial to mankind, with Nuclear War being a consequence of Nuclear Energy.

Even more beneficial is the use of Radioisotopes as a potential long-lasting form of Alternative Energy that is cheaper and safer than coal.

Thorium-90 is plentiful on the earth and may potentially power not only our homes but also our vehicles and even our smartphones in the future.

__References:__

- ChemTeam. (2001).
*Radioactivity: Half-Life*. http://www.chemteam.info/Radioactivity/Radioactivity-Half-Life.html - Deer, L. (2015, February 28).
*US$436 @RadiumBLE Geiger-Muller Counter – How a Pancake Tube makes a Portable Geiger-Muller Radiation Detector*. Retrieved from http://mythoughtsontechnologyandjamaica.blogspot.com/2015/02/us436-radiumble-geiger-muller-counter.html - Deer, L. (2015, November 30).
*What is Radioactivity and what are alpha, Beta and Gamma Particles*. Retrieved from https://lindsworthdeer.wordpress.com/2015/11/30/what-is-radioactivity-and-what-are-alpha-beta-and-gamma-particles/ - Encyclopædia Britannica. (1990).
*Radioactive isotope*. Retrieved from http://www.britannica.com/science/radioactive-isotope - GCSE Bitesize. (2014).
*More radioactive dating – higher tier only*. Retrieved from http://www.bbc.co.uk/schools/gcsebitesize/science/add_gateway_pre_2011/radiation/radioisotopesrev4.shtml - GCSE Bitesize. (2014).
*Radiation treatment*. Retrieved from http://www.bbc.co.uk/schools/gcsebitesize/science/add_ocr_gateway/radiation/treatmentrev1.shtml - GCSE Bitesize. (2014).
*Radiation treatment*. Retrieved from http://www.bbc.co.uk/schools/gcsebitesize/science/add_ocr_gateway/radiation/treatmentrev3.shtml - GCSE Bitesize. (2014).
*Radiation treatment*. Retrieved from http://www.bbc.co.uk/schools/gcsebitesize/science/add_ocr_gateway/radiation/treatmentrev4.shtml - GCSE Bitesize. (2014).
*Uses of radioisotopes*. Retrieved from http://www.bbc.co.uk/schools/gcsebitesize/science/add_gateway_pre_2011/radiation/radioisotopesrev3.shtml - GCSE Bitesize. (2014).
*What is radioactivity?*. Retrieved from http://www.bbc.co.uk/schools/gcsebitesize/science/add_ocr_gateway/radiation/radioactivityrev1.shtml - Kentchemistry. (2015).
*Uses of Radioisotopes*. Retrieved from http://www.kentchemistry.com/links/Nuclear/radioisotopes.htm - Nave, R. (2000).
*Radioactive Half-Life*. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli2.html - Whatisnuclear. (2015).
*What is radiation? What is radioactivity?*. Retrieved from http://www.whatisnuclear.com/articles/radioactivity.html - Wikipedia. (2016, 3 March).
*Carbon-14*. Retrieved from https://en.wikipedia.org/wiki/Carbon-14