What is Half-life (Radioactive Decay)?

Half life radioactive decay

Half-life decay (t1⁄2) is the time required for a quantity to reduce to half of its initial value. This is actually described as a probability, as illustrated below. In nuclear physics this demonstrates how quickly unstable isotopes undergo radioactive decay. It also shows the nature of exponential or non-exponential decay. This model is extensively used in medical, physics and chemistry to predict lifetimes of substances, radioactive elements and concentrations of observed liquids.

What is Half-life (radioactive decay)?

The half-life is the time taken for an entity to reduce to half of its original value and is used to illustrate how unstable atoms undergo radioactive decay. It also describes exponential or non-exponential decay, such as the biological half-life of pharmaceutical drugs in the body.

Rutherford’s discovery of the concept in 1907, namely half-life period, was subsequently shortened to half-life in the 1950s. He successfully used the principle of a radioactive element’s e.g. Radium’s half-life to determine the age and decay to liberate Lead 206. Half-life is constant over the lifetime of an exponentially decaying quantity.

 

Half-life of example materials and elements

oxygen 16 infinite
uranium 238 – 4,460,000,000 yrs
uranium 235 – 713,000,000 yrs
carbon 14 – 5,730 yrs
cobalt 60 – 5.27 yrs
silver 94 – 0.42 seconds

Half-life formula and related equations

The half-life is actually defined as a probability. Specifically, it is the time for exactly half of the entities to decay, on average. The probability of a radioactive atom decaying within its half-life is 50%.

In a random simulation of many identical atoms undergoing radioactive decay, after one half-life there are not exactly half of the atoms left, linked to the random variation in the process. However, with a large sample, the law of large numbers suggests that it is a very good approximation to say that half of the atoms will remain.

In a chemical reaction, the half-life is related to the time it takes for the concentration to fall to half of its initial value. In a first-order reaction the half-life of the reactant is ln(2)/λ, where λ is the reaction rate constant. An exponential decay can be described below:

 

 

 

where N0 is the initial quantity of the substance that will decay, N(t) is the quantity and has not yet decayed after a time t, t1⁄2 is the half-life of the decaying quantity, τ is the mean lifetime of the decaying quantity, λ is the decay constant of the decaying quantity.

The three parameters t1⁄2τ, and λ are all directly related in the following way:

 

 

where ln(2) is the natural logarithm of 2 (approximately 0.693)

 

 

Radioactive decay by +2 processes

Some quantities decay by two exponential-decay processes simultaneously and the actual half-life T1⁄2 can be related to the half-lives t1 and t2 that the quantity would have if each of the decay processes acted in isolation:

 

 

For +3 the analogous formula is:

 

 

What happens to the mass in half-life decay?

As an example, if the half-life is 10 yrs, its highly probable that half of the radioactive atoms will decay, however, there will not be a significant change in mass.

 

 

Half-life usage within Radiotherapy and Biology

An example in Radiotherapy, the isotope cobalt-60 has a half-life of 5.26 years. After this time period, if the original quantity contained 16 g, it would now contain only 8 g of cobalt-60. After 10.52 years, the sample would be 4 g etc. The newly formed nickel-60 nuclei remain with the undecayed cobalt-60.

A biological half-life is the time for a substance (drug, radioactive nuclide) to lose one-half of its pharmacologic activity. This may also describe the time that it takes for the concentration in blood plasma to reach one-half of its steady-state. The understanding of biological and plasma half-lives can be complicated, linked to factors including accumulation in tissues and receptor interactions.

A radioactive isotope decays according to first order kinetics, where the rate constant is a fixed number. However, the elimination of a substance from an organism follows more complex chemical kinetics.  In epidemiology, the concept of half-life can refer to the length of time for the number of incident cases in a disease outbreak to drop by half.

An example of a drug administrated to the body:

A 1000 mg dose of an intravenous drug with a half-life of 30 minutes as an example.

  • 30 minutes after the drug is injected, 500 mg of the drug is abundant in the body.
  • 60 mins, 250 mg evident
  • 120 mins, 125 mg evident
  • 240 mins, 62.5 mg evident

 

Non-exponential half-life decay

In a decay that isn’t exponential, the half-life will change during the decay. It is unusual to describe half-life in this scenario, however, it can be used to describe the decay in terms of its first half-life, second half-life and so on. The first half-life is defined as decay to 50%, the second half-life is from 50% to 25% etc.

Half-life calculator

Please see a link to a half-life calculator. Note this is a third party website and we are not responsible for the content on it.

https://www.calculator.net/half-life-calculator.html

 

 

Recent category posts

References

  1.  John Ayto, 20th Century Words (1989), Cambridge University Press.
  2. ^ Muller, Richard A. (April 12, 2010). Physics and Technology for Future PresidentsPrinceton University Press. pp. 128–129. ISBN 9780691135045.
  3. ^ Chivers, Sidney (March 16, 2003). “Re: What happens during half-lifes [sic] when there is only one atom left?”. MADSCI.org.
  4. ^ “Radioactive-Decay Model”. Exploratorium.edu. Retrieved 2012-04-25.
  5. ^ Wallin, John (September 1996). “Assignment #2: Data, Simulations, and Analytic Science in Decay”. Astro.GLU.edu. Archived from the original on 2011-09-29.
  6. Jump up to:a b Rösch, Frank (September 12, 2014). Nuclear- and Radiochemistry: Introduction1Walter de GruyterISBN 978-3-11-022191-6.
  7. ^ Jonathan Crowe; Tony Bradshaw (2014). Chemistry for the Biosciences: The Essential Concepts. p. 568. ISBN 9780199662883.
  8. ^ Lin VW; Cardenas DD (2003). Spinal cord medicine. Demos Medical Publishing, LLC. p. 251. ISBN 978-1-888799-61-3.
  9. ^ Pang, Xiao-Feng (2014). Water: Molecular Structure and Properties. New Jersey: World Scientific. p. 451. ISBN 9789814440424.
  10. ^ Australian Pesticides and Veterinary Medicines Authority (31 March 2015). “Tebufenozide in the product Mimic 700 WP Insecticide, Mimic 240 SC Insecticide”. Australian Government. Retrieved 30 April 2018.
  11. ^ Fantke, Peter; Gillespie, Brenda W.; Juraske, Ronnie; Jolliet, Olivier (11 July 2014). “Estimating Half-Lives for Pesticide Dissipation from Plants”Environmental Science & Technology48 (15): 8588–8602. Bibcode:2014EnST…48.8588Fdoi:10.1021/es500434pPMID 24968074.
  12. ^ Balkew, Teshome Mogessie (December 2010). The SIR Model When S(t) is a Multi-Exponential Function (Thesis). East Tennessee State University.
  13. ^ Ireland, MW, ed. (1928). The Medical Department of the United States Army in the World War, vol. IX: Communicable and Other Diseases. Washington: U.S.: U.S. Government Printing Office. pp. 116–7.
  14. https://en.wikipedia.org/wiki/Half-life

https://www.britannica.com/science/half-life-radioactivity

https://atomic.lindahall.org/what-is-meant-by-half-life.html

https://spark.iop.org/does-mass-halve-half-life#gref

https://www.news-medical.net/health/What-is-the-Half-Life-of-a-Drug.aspx