Chapter 3: Unit 5. Half life
Half Life
Radioactive atoms are unstable. They become stable through decays. The half life is the time it takes for one half of a radioactive sample to decay. Knowing the half life and amount of radioactive substance, one can calculate how much sample remains after a period of time. The half life of an isotope is a physical property. The value can be from fractions of a second to billions of years. Half life values are constant. There is no way to speed up or slow down this natural process.
The diagram below shows the exponential plot of percentage of radioactive isotopes versus remaining vs. number of half lives.
If a radioactive nucleus starts with 100 g or 100 molecules ( 100%) amount, after each half-life the amount gets decreased to half.
100% to 50% to 25% to 12.5%
1st half life 2nd half life 3rd Half life
Theoretically, a radioactive substance should emit radiation for infinite period of time. As evident from the figure above. In reality, radiation decays to 0.01% after ten half lives.
Here is the table of common radioisotopes and their half lives:
We can determine the amount of a radioactive isotope remaining after a given number half-lives by using the following expression:
amount remaining=initial amount×(1/2)n
where n is the number of half-lives. This expression works even if the number of half-lives is not a whole number.
The half life of a radioisotope is independent of temperature and pressure and only characteristic properties of that isotope. It only gives us information about how slow or how fast c chemical reaction occurs. Radioactive isotopes with shorter half lives are preferred in medical field due to less harmful side effects.
Application of half life: Radioactive dating:
Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon. The method was developed in the late 1940s by Willard Libby, who received the Nobel Prize in Chemistry for his work in 1960.
Radiocarbon, or carbon 14, is an isotope of the element carbon that is unstable and weakly radioactive. The stable isotopes are carbon 12 and carbon 13.
Carbon 14 is continually being formed in the upper atmosphere by the effect of cosmic ray neutrons on nitrogen 14 atoms. It is rapidly oxidized in air to form carbon dioxide and enters the global carbon cycle.
Plants and animals assimilate carbon 14 from carbon dioxide throughout their lifetimes. When they die, they stop exchanging carbon with the biosphere and their carbon 14 content then starts to decrease at a rate determined by the law of radioactive decay.
Try this out
https://teachchemistry.org/periodical/issues/march-2017/half-life-investigation
Activity:
Go to the above simulation and click on the Element X. Then click on “Decay Sample”.
Notice the graph of half life.
What is the half life of element X?
Watch this out!
Questions:
- If the half life of Iodine-131 is 8.0days, how much of a 100. mg sample of Iodine-131 remains after 40 days?
Ans: 3.13mg