Question

After t days, 6 grams of iodine -131 decays to a mass y (in grams ) given by y = 6 (1)/(2)ᵗ / (8), t >= 0. How much of the initial mass remains after 180 days?

Answer 1

To find out how much iodine-131 remains after 180 days, use the provided decay function with t = 180. After the calculations, it's found that approximately 0.000000498 grams of the original 6 grams of iodine-131 remains after this period.

Step-by-step explanation:

To determine how much of the initial mass of iodine-131 remains after 180 days, we can apply the given decay function y = 6(1/2)t/8, where t is the time in days. The half-life of iodine-131 is known to be 8 days. Iodine-131 decays following a first-order reaction, with a decay constant of 0.138 d−1, though this constant is not needed for this specific calculation.

To find the remaining mass after 180 days:

1. Plug the value of t (180 days) into the decay equation.
2. Calculate y = 6(1/2)180/8.
3. Simplify the exponent: 180/8 = 22.5.
4. Calculate the remaining mass: y = 6(1/2)22.5 ≈ 6 x 0.000000083.
5. Compute the final value: y ≈ 6 x 0.000000083 ≈ 0.000000498 grams.

Thus, after 180 days, approximately 0.000000498 grams of the initial 6 grams of iodine-131 remain.