Final Answer:
After 10 seconds, there will be 6.25 mg of C-15 remaining.
Step-by-step explanation:
Radioactive decay is a first-order process, which means that the rate of decay is proportional to the amount of radioactive material remaining. The half-life of a radioactive isotope is the time it takes for half of the original amount to decay.
The formula for radioactive decay is:
N(t) = N0 * e^(-kt)
where:
N(t) is the amount of radioactive material remaining at time t
N0 is the initial amount of radioactive material
k is the decay constant
t is the time
The decay constant for a radioactive isotope can be calculated using the following equation:
k = ln(2) / t1/2
where:
t1/2 is the half-life of the isotope
Plugging in the values for carbon-15, we get:
k = ln(2) / 2.5 s = 0.277 s^-1
Now we can use the formula for radioactive decay to calculate the amount of C-15 remaining after 10 seconds:
N(10 s) = 100 mg * e^(-0.277 s^-1 * 10 s) = 6.25 mg
Therefore, after 10 seconds, there will be 6.25 mg of C-15 remaining.