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.

$A=A_0\cdot (\frac{1}{2})^{\frac{t}{h}}$, 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:

$A=190\cdot (\frac{1}{2})^{\frac{t}{138}}$

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

$A=190\cdot (\frac{1}{2})^{\frac{230}{138}}$

$A=190\cdot (0.5)^{\frac{5}{3}}$

$A=190\cdot (0.31498026247)$

$A=59.84624986$

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.