if a sample of rock starts out with 32 atoms of carbon-14 how much carbon-14 would be left after 5,700 years
To determine how much carbon-14 would be left after 5,700 years, we need to understand the concept of carbon-14 decay and its half-life.
Carbon-14 is a radioactive isotope that undergoes decay over time. The half-life of carbon-14 is approximately 5,730 years, meaning that half of the original amount of carbon-14 will decay in that time.
To calculate the amount of carbon-14 remaining after a certain time, we can use the following formula:
N(t) = N(0) * (1/2)^(t / T)
Where:
N(t) = the amount of carbon-14 remaining after time t
N(0) = the initial amount of carbon-14
t = the elapsed time
T = the half-life of carbon-14
In this case, we start with 32 atoms of carbon-14 and want to find the amount remaining after 5,700 years.
Using the formula, we substitute the values:
N(t) = 32 * (1/2)^(5,700 / 5,730)
Calculating this expression, we find:
N(t) ≈ 16 atoms
Therefore, after 5,700 years, approximately 16 atoms of carbon-14 would be left.