The count rate of a radioactive material is 800 count/min. If the half-life of the material is 4 days, what would the count rate be in 16 days later

Answer Details

Radioactive decay is a process in which the unstable nucleus of a radioactive atom breaks down into a more stable nucleus and emits radiation in the form of particles or waves. The rate at which a radioactive substance decays is measured in terms of its half-life, which is the time taken for half of the original sample to decay. In this problem, the count rate of a radioactive material is 800 count/min and its half-life is 4 days. This means that in 4 days, the count rate will be halved to 400 count/min, and in another 4 days, it will be halved again to 200 count/min, and so on. Therefore, if we want to know what the count rate will be in 16 days later, we need to find out how many half-lives have occurred in that time. Since the half-life of the material is 4 days, there are 4 half-lives in 16 days. This means that the count rate will be halved 4 times, which is equivalent to dividing the initial count rate (800 count/min) by 2 four times. So, the count rate in 16 days later would be: 800 count/min ÷ 2 ÷ 2 ÷ 2 ÷ 2 = 50 count/min Therefore, the answer is 50 count / min.