Iodine-123,used in thyroid therapy,has a half-life of 13.27 hours.How many half-lives are required for a 160 mg sample of iodine-123 to decay to 5.0 mg?

Question

Quizplus · Accepted Answer

To find the number of half-lives required for a 160 mg sample of iodine-123 to decay to 5.0 mg, we use the formula for exponential decay: $N = N_0 \times (1/2)^{n}$, where $N$ is the final amount, $N_0$ is the initial amount, and $n$ is the number of half-lives. Rearranging the formula to solve for $n$, we get $n = \log(N/N_0) / \log(1/2)$. Plugging in the values $N = 5$ mg and $N_0 = 160$ mg, we find $n = \log(5/160) / \log(1/2)$. This calculation simplifies to finding how many times 160 needs to be halved to get to 5, which is 5 half-lives.

Iodine-123,used in Thyroid Therapy,has a Half-Life of 13