The isotope has a half-life of 21 hours. If a sample initially contains exactly 10000 atoms of , approximately how many of these atoms will remain after one week?
A) 1250
B) 78
C) 39
D) 0
E) none of the above

Question

The isotope  has a half-life of 21 hours. If a sample initially contains exactly 10000 atoms of  , approximately how many of these atoms will remain after one week?
A) 1250 
B) 78 
C) 39 
D) 0 
E) none of the above

Quizplus · Accepted Answer

First we need to determine the number of half-lives that occur in a week. There are 24 hours in a day, so in one week there are 24*7 = 168 hours. Since the half-life of the isotope is 21 hours, there will be 168/21 = 8 half-lives in one week.

After each half-life, the number of remaining atoms is halved. Therefore, after 8 half-lives, the number of remaining atoms is:

10000 / (2^8) ≈ 39

Therefore, approximately 39 atoms of the isotope will remain after one week. The correct answer is C.

The Isotope Has a Half-Life of 21 Hours