The strontium-87 isotopes stores in the body and decays by the process shown below. The half-life is 2.80hr. Suppose that 0.766 millicuries got into the body. How many mc will remain after 8.40 hr?
k = 0.693/t1/2
Then
ln(No/N) = kt
No = 0.766
N = solve for this
k from above
t = 8.40 hr
2.30
To determine the amount of strontium-87 isotopes that will remain after 8.40 hours, we can use the concept of radioactive decay and the given information.
First, let's understand what is meant by "half-life." The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life of strontium-87 is 2.80 hours.
To solve this problem, we can use the following formula for radioactive decay:
N(t) = N₀ * (1/2)^(t / Tₕₑₖ)
Where:
N(t) is the amount of substance remaining after time t
N₀ is the initial amount of substance
t is the time that has elapsed
Tₕₑₖ is the half-life of the substance
Using the given data:
N₀ = 0.766 millicuries (initial amount)
Tₕₑₖ = 2.80 hours (half-life)
t = 8.40 hours (time that has elapsed)
Let's substitute these values into the formula to calculate N(8.40):
N(8.40) = 0.766 * (1/2)^(8.40 / 2.80)
Now, let's evaluate this expression:
N(8.40) = 0.766 * (1/2)^3
Calculating (1/2)^3:
(1/2)^3 = 1/8 = 0.125
Now, substitute this value back into the equation:
N(8.40) = 0.766 * 0.125
N(8.40) ≈ 0.09575
Therefore, approximately 0.09575 millicuries of strontium-87 isotopes will remain in the body after 8.40 hours.