Video Transcript
Examine the count rate results from
a Geiger counter used to measure the radioactivity of a sample for three
minutes. What is the approximate half-life
of the sample? (A) Between zero and 30
seconds. (B) Between 120 and 150
seconds. (C) Between 30 and 60 seconds. (D) Between 90 and 120 seconds. Or (E) between 60 and 90
seconds.
To determine the half-life of the
sample, we need to figure out how much time it takes for half of the sample to decay
away. When half of the sample decays
away, the count rate will decrease by half. This means we need to determine the
amount of time for the count rate to decrease by half using our data. From the table, we can look at the
time steps for the sample to decay. In the first 30 seconds, the count
rate decreases by 70, which is much less than half of 300. This means that the half-life must
be longer than 30 seconds. The same is true of 60 seconds. In the first 90 seconds, the count
rate decreases from 300 to 142, which is approximately half.
Note that radioactivity is a random
process. So there is some variation. This means that the half-life is
somewhere around 90 seconds, but perhaps a little under 90 seconds since more than
half the sample decayed away. Thus, the answer to the question
“What is the approximate half-life of the sample?” is (E) between 60 and 90
seconds.
