A Geiger counter placed next to a radioactive sample produces 200 counts per minute.One hour later,the Geiger counter reads 180 counts per minute.What is the half-life of the radioactive sample?

Question

Quizplus · Accepted Answer

The half-life of a radioactive substance is the time it takes for half of the radioactive atoms to decay. The decay rate is proportional to the number of radioactive atoms present. To find the half-life, we can use the formula $N = N_0 \times (1/2)^{t/T}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life.Given that the count drops from 200 to 180 in 1 hour, we can see that the substance has not halved, and thus, the half-life is longer than 1 hour. We can estimate the half-life by understanding that a small decrease (from 200 to 180) over an hour suggests a relatively long half-life. Among the given options, 6.6 hours is a reasonable estimate that aligns with the slow decay rate observed. Precise calculation would require using logarithms and the decay formula, but given the options and the information, 6.6 hours is the best estimate.

A Geiger Counter Placed Next to a Radioactive Sample Produces