'Polonium-210 is a radioactive substance with a half-life of 138 days. If a nuclearfacility is handling 310 grams of polonium-210, then how many grams of polonium-210 will be left in 330 days. Round your answer 4 decimal places and remember touse labels.
Accepted Solution
A:
Answer:59.0891 g (rounded to 4 decimal places)Explanation:Half-life time of a radioactive substance is the time for half of the substance to decay.Thus, the amount of the radioactive substance that remains after a number n of half-lives is given by:[tex]A=A_0\cdot (1/2)^n[/tex]Where:A is the amount that remains of the substance after n half-lives have elapses, andA₀ is the starting amount of the substance.In this problem, you have that the half-live for your sample (polonium-210) is 138 days and the number of days elapsed is 330 days. Thus, the number of half-lives elapsed is: 330 days / 138 days = 2.3913Therefore, the amount of polonium-210 that will be left in 330 days is:[tex]A=310{g}\cdot (1/2)^{2.3913}=59.0891g[/tex]