Question

Polonium-210 is a radioactive substance with a half-life of 138 days. If a nuclear facility is handling 255 grams of polonium-210, then how many grams of polonium- 210 will be left in 250 days. Round your answer 4 decimal places and remember to use labels.

Your Answer:

Answer units:

Answer 1

We know that radioactivity follows first order chemical kinetics.

Half life =138 days

For 1st order kinetics

We know rate constant (k) = 0.693/half life

K = 0.693/138

K= 0.00502 days^​​​-1

Now initial amount of polonium (A​​​​​​0​​​​​) = 255 g

Time taken (t) = 250 days

Amount left (A) = ?

We know for 1st order

(A) =(A_{​​​​​​0}​​​)e^​​-kt

(A) = 255×e^{-0.00502×250}

(A) = 255× e^{​​​​​​-1.26}

^{​(A) = 255 × 0.2837}

^{(A) = 72.3435g}

^​​​​​​​​Hence 72.3435 g of sample was left.