Question

Polonium-210 is a radioactive substance with a half-life of 138 days. If a nuclear facility is handling 190 grams of polonium-210, then how many grams of polonium-210 will be left in 230 days.

Answer 1

We have been given that Polonium-210 is a radioactive substance with a half-life of 138 days. A nuclear facility is handling 190 grams of polonium-210. We are asked to find the grams of polonium-210 will be left in 230 days.

We will use half-life formula to solve our given problem.

`A=A_0\cdot ((1)/(2))^{(t)/(h)}`, where,

`A` = Final amount,

`A_0` = Initial amount,

t = Time,

h = Half life.

Upon substituting our given values in half-life formula, we will get:

`A=190\cdot ((1)/(2))^{(t)/(138)}`

To find the grams of polonium-210 will be left in 230 days, we will substitute
`t=230` in our formula as:

`A=190\cdot ((1)/(2))^{(230)/(138)}`

`A=190\cdot (0.5)^{(5)/(3)}`

`A=190\cdot (0.31498026247)`

`A=59.84624986`

Upon rounding to nearest hundredth, we will get:

`A\approx 59.85`

Therefore, approximately 59.85 grams of polonium-210 will be left in 230 days.