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 these choices are correct.

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 these choices are correct.

Quizplus · Accepted Answer

One week is equal to 7 days or 168 hours. If the half-life is 21 hours, then the number of remaining atoms after 7 days is approximately (1/2)^(168/21) times the initial number of atoms. Simplifying this equation, we get (1/2)^8, which is equal to 1/256. Multiplying this fraction by the initial number of atoms (10000) gives us approximately 39, which is the closest choice to our calculated value. Therefore, the best choice is C, 39.

The Isotope Has a Half-Life of 21 Hours