Question

If you began with 200g of a parent isotope, you would have 50g of that isotope after two half-lives. How many grams are left after 4 half-lives? (Show Your Work!)

Answer 1

Begin with 200g of a parent isotope, after two half-lives you have 50g. Following the pattern of decay, after four half-lives, you will have 12.5 grams remaining.

Step-by-step explanation:

The question involves understanding radioactive decay and calculating the amount of a parent isotope remaining after a certain number of half-lives.

For the given problem, if you start with 200g of a parent isotope, after two half-lives you're left with 50g. A half-life is the period it takes for half of the isotope to decay into daughter elements. After one half-life, you would have half of 200g, which is 100g. Following two half-lives, you would have half of that amount, which is 50g. Continuing this, after three half-lives you would have half of 50g, so 25g. Finally, after four half-lives, you would have half of the 25g, which would be 12.5 grams.

Therefore, after four half-lives, you would have 12.5 grams of the parent isotope remaining.