the half life of a certain element is 100 days. how many half-lives will it be before only one-fourth of this element reamains

200 Days

Explanation:

Usually not so good in chemistry, but this is math!

Half life means in this time half goes away. What happens when two half lives pass? half of what was remaining goes away. Maybe an example will make it more clear.

Say we start with 100 grams. After the amount of time for the half life to pass completes, we have 50, or half of the original amount. The half life time passes again and THAT gets cut in half to 25 grams. this is 1/4 of the original (Hey, what we're looking for.) Just to make it clear what is happening after another half life 1/8 remains, so it goes from The starting amount to 1/2 to 1/4 to 1/8 and so on, it keeps getting cut in half.

So how many times do we have to cut 1 in half until we get to 1/4? Twice as was shown before. Now, two half lives for this element is what? 100+100 days. So 200 Days.