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'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.

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Edufirst

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, 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:

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

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