Radioactive elements have a **half-life**. Half-life occurs naturally in some of the radioactive elements while it could be artificially stimulated in some other elements.

**The half life of any given element is the time that is required for one half of the sample to decay. **

For example: If you have 10 grams of a radioactive element to start with….. after one half-life there will be 5 grams of the radioactive element left.

After another half-life, there will be 2.5 g of the original element left, after another half-life, 1.25 g will be left.

Number ofhalf-lives elapsed | Fractionremaining | Percentageremaining | |

0 | ^{1}/_{1} | 100 | |

1 | ^{1}/_{2} | 50 | |

2 | ^{1}/_{4} | 25 | |

3 | ^{1}/_{8} | 12 | .5 |

4 | ^{1}/_{16} | 6 | .25 |

5 | ^{1}/_{32} | 3 | .125 |

6 | ^{1}/_{64} | 1 | .563 |

7 | ^{1}/_{128} | 0 | .781 |

… | … | … | |

n | 1/(2)^{n} | 100/(2)^{n} |

Each and every radioactive element has its own half-life. For instance, ^{238}U has a half-life of 4.5billion years.

**Example**

A radioactive substance has a half-life of 20 minutes. If we begin with a 500 g sample, how much of the original sample remains after two hours?

Two hours is 120 minutes -> six half-lives. At the end of the stated time period, 7.8 g remains.

500 g -> 250 g -> 125 g -> 62.5 g -> 31.25 g -> 15.625 g -> 7.8125 g

**7.8 g remains**

Another interesting fact is half-life of ^{14}C is 5730 years and this is very helpful in geological dating of any archaeological material. (CARBON DATING)

**CARBON DATING**

The ratio of normal carbon (carbon-12) to carbon-14 in the air and in all living things at any given time is nearly constant. At this moment, your body has a certain percentage of carbon-14 atoms in it, and all living plants and animals have the same percentage.

As soon as a living organism dies, it stops taking in new carbon. The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample. By looking at the **ratio of carbon-12 to carbon-14 **in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely.

Three types of natural radioactive decay include alpha radiation, beta radiation and gamma radiation.

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