The half-life of carbon-14 is 5730 years. If we start with 10 grams of carbon-14, after 5730 years, we will have _____ of carbon-14 left.
hint: it's called a half-life for a reason.
To solve this problem, we can use the formula for exponential decay:
N(t) = N0 * (1/2)^(t / T)
Where:
- N(t) is the amount of carbon-14 remaining after time t
- N0 is the initial amount of carbon-14 (10 grams in this case)
- t is the time elapsed (5730 years in this case)
- T is the half-life of carbon-14 (5730 years in this case)
Plugging in the values, we can calculate the amount of carbon-14 remaining:
N(t) = 10 * (1/2)^(5730 / 5730)
Simplifying the term (1/2)^(5730 / 5730) gives us:
N(t) = 10 * (1/2)^1
And simplifying further gives us:
N(t) = 10 * (1/2)
Calculating the result gives us:
N(t) = 5
Therefore, after 5730 years, we will have 5 grams of carbon-14 left.
To find out how much carbon-14 would be left after 5730 years, we need to recognize that the half-life is the time it takes for half of a radioactive substance to decay. In this case, the half-life of carbon-14 is 5730 years.
If we start with 10 grams of carbon-14, after 5730 years, half of it would have decayed. That means we would have 5 grams remaining.
After another 5730 years, half of the remaining 5 grams would decay, leaving us with 2.5 grams.
This process continues as time goes on. So, after 2 half-lives (5730 years x 2), we are left with 2.5 grams.
Therefore, after 5730 years, we will have 5 grams of carbon-14 left.