When dealing with radioactive decay, the concept of half-life is crucial. The half-life of a radioactive substance is the time it takes for half of the radioactive atoms in a sample to decay.
Here's how you can calculate the fraction of a given sample that remains after four half-lives:
1. After the first half-life, half of the sample will decay, and half will remain. So, after the first half-life, you will have 1/2 of the original sample left.
2. After the second half-life, half of what remains will decay, leaving 1/2 of 1/2, which is 1/4 of the original sample.
3. After the third half-life, half of what remains will decay, leaving 1/2 of 1/4, which is 1/8 of the original sample.
4. After the fourth half-life, half of what remains will decay, leaving 1/2 of 1/8, which is 1/16 of the original sample.
Therefore, after four half-lives, 1/16 of the original sample of the radioactive nuclide will remain.
