Question

Iodine-131 is used to destroy thyroid tissue in the treatment of an overactive thyroid. The half-life of iodine-131 is 8 days. If a hospital receives a shipment of 200 grams, how much would remain after 32 days? Round to the nearest tenth.

Answer 1

Given:

a,) The half-life of iodine-131 is 8 days.

b.) A hospital receives a shipment of 200 grams.

c.) Determine how much would remain after 32 days.

We will be using the following formula:

`\text{ N}_t\text{ = N}_0((1)/(2))^{\frac{t}{t_{(1)/(2)}}}`

Where,

`\begin{gathered} \text{ N}_t\text{ = Quantity of the substance remaining} \\ \text{ N}_0\text{ = Initial quality of the substance = 200 grams} \\ \text{ t = Time elapsed = 32 days} \\ \text{ t}_{(1)/(2)}\text{ = Half life of the substance = 8 days} \end{gathered}`

We get,

`\text{N}_t\text{ = N}_0((1)/(2))^{\frac{t}{t_{(1)/(2)}}}`
`\text{ N}_t\text{ = \lparen200\rparen\lparen}(1)/(2))^{(32)/(8)}`
`\text{ N}_t\text{ = 200\lparen}(1)/(2))^4`
`\text{ N}_t\text{ = 200\lparen}(1)/(16))\text{ = }(200)/(16)`
`\text{ N}_t\text{ = 12.5 grams}`

Therefore, in 32 days, only 12.5 grams of Iodine-131 will remain.