Question

A student wants to measure the half-life of a radioactive isotope. He is told the isotope has a half-life of between 10 and 20 minutes. Illustrating your answers as appropriate, describe: a) What measurements should he take? b) How should he use the measurements to arrive at an estimate of the half-life for the isotope?

Answer 1

To measure the half-life of a radioactive isotope, a student should record the initial activity and then measure the count rate at regular intervals until the activity reaches half of its initial value. This time defines the half-life. Graphing the results can help determine the half-life more precisely.

Step-by-step explanation:

Measuring Radioactive Half-life

To measure the half-life of a radioactive isotope, a student should follow a systematic approach to collect and analyze data accurately. Here are the steps:

1. Begin with a known quantity of the radioactive isotope, ensuring that the initial activity is measured using a device like a Geiger counter.
2. Record the initial count rate (in counts per minute or cpm) at the very start of the measurement. This is the activity level of the isotope when time equals zero.
3. Measure the count rate at regular intervals (e.g., every minute) over a period that exceeds the expected half-life range (10-20 minutes in this case).
4. Continue recording the activity until at least one instance where the count rate falls to half of the initial value.
5. Identify the time it took for the activity to reduce to half of its original value. This time is the estimated half-life of the isotope.

To verify the estimate, the student should observe if the activity continues to fall to half of each preceding value after every consistent duration approximating the measured half-life. Graphing the decay curve, where count rate is plotted against time, can provide a visual representation to aid in the determination of half-life.

Calculating the Half-life

Using the measurements taken, the half-life is calculated by finding the time span where the count rate reaches half of the initial count rate. This process is repeated to see if the same time span results in further halving of the activity. By plotting a decay curve, one can more precisely determine the half-life by finding the time it takes for the activity to decay from full to half on the graph.

The equation for determining the amount of remaining radioactive material after a given number of half-lives is: Final amount = Initial amount * (0.5)^n, where 'n' is the number of half-lives elapsed.