# Half-Life

All radioactive elements do not decay at the same pace. They have drastically different rates of decay. The radioactive decay time is expressed in terms of half-life period. The half-life of a radioactive substance is the time required for the decay of half the substance present in a sample of that substance. Regardless of the amount of a particular radioactive substance we have, it takes the same time (half-life) to complete the decay of half the number of nuclei in that sample.

The half-life of a radioactive substance is the time required for the complete decay of exactly half the amount of that substance.

Example

Calculate the amount of time (in years) it takes for the decay of 75% of a given sample of carbon-14. Carbon-14 has a half-life of approximately 5700 years.

Solution

After the first 5700 years of decay, 50% of the original sample is left. After 5700 more years, 50% of that sample will have decayed, which means that there is now 25% of the original intact sample. This is the amount of time that the question is asking for. To be clear about our analysis, let's rephrase what we have said. We have 25% of the original sample left at this point. Thus the decay of 75% of the original sample is complete. So the answer is 5700 x 2 = 11400 years.

Table: Summary of changes in the parent nucleus due to different decay modes.

M = mass number of the parent nucleus undergoing decay.

Z = atomic number of the parent nucleus undergoing decay.