The half-life of a radioactive isotope is defined as the amount of time it takes for half of the radioactive particles to decay.  Consider a container with 128 unstable nuclei.  Over time, some of the nuclei decay, forming daughter nuclei and related decay particles.  Eventually, half of the nuclei will have decayed into daughter nuclei.  In this example, after a certain amount of time had passed, 64 nuclei decayed to daughter nuclei, leaving 64 of the original parent nuclei.


Half-life: the time it takes for half the radioactive nuclei in a sample to decay


The half-life of one substance may differ from a second substance.  For example carbon-14, which is used to date organic material, has a half-life of 5730 years.  Iodine-131, however, has a half-life of 192 hours. Iodine-131 is used in the medical diagnosis of thyroid problems.


Simulation: Half-Life
This simulation demonstrates the rate of radioactive decay and the concept of half-life.  Open the Half-life simulation and use the controls on the right to begin.  When done, complete the self-check questions in the simulation.


Example Problem

A radioactive sample has an activity of 3.2 × 103 Bq.  The isotopes in the sample have a half-life of 24 hrs.  What is the activity of this sample after five days have passed?

 

Given 

 

Required

the amount of activity after five days

 

Analysis and Solution 

Determine the number of half-lives that have elapsed.

 

Determine the amount remaining.

 

Paraphrase

After five days, the sample will have an activity of 1.0 × 102 Bq.