A 12.6-mg supply of iodine-131, used in hospitals in the treatment of hyperthyroidism, was stored for 24.06 days (d). If the half-life of iodine- 131 is 8.021 days, how many mg remain? Be sure your answer has the correct number of significant figures.
To find the amount of iodine-131 remaining after 24.06 days, we can use the radioactive decay formula:
\[ \text{Amount remaining} = \text{Initial amount} \times (1/2)^{(\text{time elapsed} / \text{half-life})} \]
Plugging in the values:
\[ \text{Amount remaining} = 12.6 \, \text{mg} \times (1/2)^{(24.06 \, \text{days} / 8.021 \, \text{days})} \]
\[ \text{Amount remaining} = 12.6 \, \text{mg} \times (1/2)^{2.99987} \]
\[ \text{Amount remaining} = 12.6 \, \text{mg} \times 0.125025 \]
\[ \text{Amount remaining} = 1.57515 \, \text{mg} \]
Therefore, about 1.58 mg of iodine-131 remain after 24.06 days, when keeping the correct number of significant figures.