After decaying for 48 hours, 1/16 of the original mass of a radioisotope sample remains unchanged. What is the half life of this radioisotope
The correct answer and explanation is:
Correct Answer: 12 hours
To determine the half-life of the radioisotope, we must understand how radioactive decay works. A half-life is the time it takes for half of a radioactive substance to decay. Every time a half-life passes, only half of the remaining substance is left.
In this problem, we are told that after 48 hours, only 1/16 of the original mass remains. This implies that the substance has gone through multiple half-lives because the mass keeps halving with each one. Let’s figure out how many half-lives are required to reach 1/16 of the original amount.
We start with 1 (the whole original mass):
- After 1 half-life: 1/2 remains
- After 2 half-lives: 1/4 remains
- After 3 half-lives: 1/8 remains
- After 4 half-lives: 1/16 remains
So, it takes 4 half-lives to decay to 1/16 of the original amount. We are told this process took 48 hours.
To find the half-life, divide the total time by the number of half-lives:
48 hours ÷ 4 = 12 hours
Therefore, the half-life of the radioisotope is 12 hours.
This method of calculation relies on exponential decay, which is common for radioactive substances. Each half-life reduces the amount of material to half of what it was in the previous period. This consistent halving leads to a geometric sequence, where the remaining fraction after n half-lives is (1/2)^n. By recognizing the pattern and matching it to the elapsed time, we can accurately calculate the half-life of any radioactive sample using this approach.