a sample of radioactive iodine (half life=3 days) originally weighed 10 g, but now weighs 0.625 g. How old is the sample?
0.625 = 10 (1/2)^(t / 3)
log(0.625 / 10) = (t / 3) log(1/2)
or ... 10 , 5 , 5/2 , 5/4 , 5/8
0.625 = 10 * (1/2)^n
0.00625 = .5^n
log 0.00625 = n log 0.5
n = log 0.00625 / log 0.5
n is the number of 3 day periods
time in hours = n * 3 * 24
To determine the age of the radioactive iodine sample, we can use the concept of the half-life. The half-life is the time it takes for half of the radioactive material to decay.
In this case, the half-life of the radioactive iodine is given as 3 days. This means that after 3 days, half of the radioactive iodine will decay, and only half of the original amount will remain.
We are given that the original weight of the sample was 10 g, and the current weight is 0.625 g.
First, we need to determine the number of half-lives that have passed. Since each half-life is 3 days, we can calculate this by dividing the elapsed time by the half-life (3 days).
Elapsed time = (current weight / original weight) x half-life
Plugging in the numbers we have:
Elapsed time = (0.625 g / 10 g) x 3 days
Calculating this, we find:
Elapsed time = 0.0625 x 3 days
Elapsed time = 0.1875 days
So, approximately 0.1875 days have passed since the radioactive iodine sample originally weighed 10 g.