The half-life of cesium-137 is 30.2 years. If the initial mass of a sample of cesium-137 is 1.00 g, how much will remain after 30.2 years?
The half-life is the amount of time it takes for a given sample to lose half of the original amount.
In this case, the original amount is 1.00 grams.
The half-life is 30.2 years.
The elapsed time is 30.2 years.
Thus, one half-life has elapsed. Therefore you have lost half the original mass. You have 0.500 grams remaining.
Note that after another 30.2 years you will not lose the remaining amount! Instead, you will lose half of the original amount, so you will lose another 0.250 grams, leaving 0.250 grams behind.