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# Examine the model of half-life in radioactive decay and make quantitative predictions about the activity or amount of a radioactive sample

The rate of decay of an radioactive isotope is measured by its half life.

**Half life **: It is the time required for radioactive isotope to reduce to half of its initial value.

- It has been found that the rate at which radioactive isotopes decay , is directly proportional to the number of atoms present. The rate can be expressed as :
- (where is the decay constant , with units
*s*)^{-1}

- (where is the decay constant , with units
- This equation can be integrated to give the following result :
- where,
*N*is the number of atoms present at time_{o}*t = 0**N*is the number of atoms present at time_{t}*t*

- where,

- Using the definition of half life , we can find
- is when the number of atoms are half the original amount, i.e.
- Thus ,
- rearranging we get ,
- Thus if we can measure the half life, we can calculate the decay constant.

Extract from *Physics Stage 6 Syllabus *© 2017 NSW Education Standards Authority (NESA)