Question

'Polonium-210 is a radioactive substance with a half-life of 138 days. If a nuclear

facility 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 to
use labels.

Answer 1

• 59.0891 g (rounded to 4 decimal places)

Step-by-step 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:

• 
  `A=A_0\cdot (1/2)^n`

Where:

• A is the amount that remains of the substance after n half-lives have elapses, and

• A₀ 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 = 2.3913

Therefore, the amount of polonium-210 that will be left in 330 days is:

• 
  `A=310{g}\cdot (1/2)^(2.3913)=59.0891g`