A radiation detector on a laboratory bench is switched on when there are no radioactive samples in the laboratory. The count rate displayed by the detector is 24 counts per minute. A radioactive sample is now placed next to the detector and the count rate displayed is 248 counts per minute. The sample is left next to the detector for 48 hours, after which time the count rate displayed is 31 counts per minute. Based on this information, what is the half-life of the sample?
Answer:
7) D
When no radioactive sample was present, the count was 24 per minute. Therefore, the background radiation = 24 counts per minute.
When the sample was placed next to the detector, count rate = 248 counts.
To calculate the sample’s radioactive count, we need to subtract the background radiation. Sample’s radioactive count = 248-24 = 224 counts per minute.
After 48 hours, displayed count rate = 31 counts
Activity of sample after 48 hours 31-247 counts per minute
Therefore, the count rate of the sample only decreased from 224 to 7
Number of half lives = number of times 224 is divided by 2 until it reaches 7.
224 / 2″ = 7
224/2″=7
32 =2n
n=5
Number of half lives = 5
In 48 hours, the sample underwent 5 half lives. Half-life of sample 48 ÷ 5 = 9.6 hours
