Iodine-131 has a half-life of eight days. A sample that originally contained 10 grams of iodine-131 now contains 1 gram. How much time elapsed between the two measurements?

Question

Quizplus · Accepted Answer

Using the formula for half-life decay:

Nt = N0 * (1/2)^(t/T)

where Nt is the final amount, N0 is the initial amount, t is the time elapsed, and T is the half-life.

Plugging in the given values:

1 = 10 * (1/2)^(t/8)

Taking the logarithm of both sides:

log(1) = log(10) + (t/8) * log(1/2)

0 = 1 - (t/8) * 0.301

Solving for t:

t = (1/0.301) * 8

t ≈ 26.6 days

Therefore, the answer is C.

Iodine-131 Has a Half-Life of Eight Days