Answer: The decay of iodine-131 into xenon-131 can be represented by the following nuclear equation:
^131I -> ^131Xe + e-
Given that the half-life of iodine-131 is 8 days, we can use the following equation to determine the amount of iodine-131 remaining after a certain time (t):
N = N0 * (1/2)^(t/T1/2)
where N is the amount of iodine-131 at time t, N0 is the initial amount of iodine-131 (1.000 g in this case), and T1/2 is the half-life of iodine-131 (8 days).
a) After 16 days:
Using the equation above, we can calculate the amount of iodine-131 remaining after 16 days:
N = 1.000 g * (1/2)^(16/8) = 0.500 g
Therefore, the amount of iodine-131 remaining after 16 days is 0.500 g.
b) After 24 days:
Using the same equation, we can calculate the amount of iodine-131 remaining after 24 days:
N = 1.000 g * (1/2)^(24/8) = 0.250 g
Therefore, the amount of iodine-131 remaining after 24 days is 0.250 g.
c) The time required for 99.9% of the iodine-131 to decay:
We can use the same equation to determine the time required for 99.9% of the iodine-131 to decay. We can set N/N0 equal to 0.001 (since we want to know when only 0.1% of the original amount remains):
0.001 = (1/2)^(t/8)
Taking the natural logarithm of both sides:
ln(0.001) = (t/8) ln(1/2)
t = -8 ln(0.001) / ln(1/2)
t = 69.3 days (approx.)
Therefore, the time required for 99.9% of the iodine-131 to decay is approximately 69.3 days.