In a lab, you produce a quantity of the radioactive isotope thorium-234. Over the course of several weeks, the unstable isotope decays, and you measure the amount of thorium-234 remaining in the sample. You obtain the following data. What is the half life of Thorium-234? How much Thorium 234 will there be after two half lives? Days Elapsed Grams of Thorium 234 Remaining
0 16
12 11
24 8
36 6
a. 36 days
b. 12 days
c. 24 days / 4 grams

Option C. 24 days / 4 grams

Explanation:

From the question given above, the following data were obtained:

Days Elapsed >>>> Mass Remaining

0 >>>>>>>>>>>>>>> 16

12 >>>>>>>>>>>>>>> 11

24 >>>>>>>>>>>>>>> 8

36 >>>>>>>>>>>>>>> 6

A. Determination of the half-life of Thorium-234.

To determine the half-life, it is important to know the definition of half life.

Half-life is defined as the time taken for a substance to reduce to half its original mass.

From the table given above, we can see that the original mass of the isotope is 16 g (i.e at 0 day). By day 24, the mass of the isotope is 8 g (i.e half the original mass). Thus, the half-life of the isotope is 24 days.

B. Determination of the mass of the isotope remaining after 2 half lives.

Original amount (N₀) = 16 g

Number of half-lives (n) = 2

Amount remaining (N) =?

N = 1/2ⁿ × N₀

N = 1/2² × 16

N = 1/4 × 16

N = 4 g

Thus, 4 g of the isotope is remaining after 2 half lives.

Summay:

Half-life = 24 days

Amount remaining after 2 half-lives = 4 g

Option C gives the correct answer to the question.

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