14C has a half-life of 5,730 years. If we start with 70 grams of 14C at time zero how many grams of14C will be left after three half-lives?_________
(1/2)(1/2)(1/2) = 1/8
so
70/8 grams
To find out how many grams of 14C will be left after three half-lives, we can use the formula for radioactive decay:
Amount remaining = Initial amount * (1/2)^(number of half-lives)
Given that the half-life of 14C is 5,730 years and we start with 70 grams of 14C, let's calculate the remaining amount after three half-lives.
First, we need to determine the number of years that have passed after three half-lives. Since each half-life is 5,730 years, three half-lives would be 3 * 5,730 = 17,190 years.
Now, we can substitute the values into the formula:
Amount remaining = 70 grams * (1/2)^(17,190 / 5,730)
Simplifying:
Amount remaining = 70 grams * (1/2)^3
= 70 grams * (1/8)
= 8.75 grams
Therefore, after three half-lives, there will be 8.75 grams of 14C remaining.