The number of radioactive nuclei in a particular sample decreases to one-eighth of its original number in 9 days.What is the half-life of these nuclei?
A)9/8 days
B)2 days
C)3 days
D)8 days
E)10 days

Question

Quizplus · Accepted Answer

The time taken for the number of nuclei to decrease to half its original number is the half-life.
Let the original number of nuclei be N.
After one half-life, the number of nuclei remaining is N/2.
After two half-lives, the number of nuclei remaining is N/4.
After three half-lives, the number of nuclei remaining is N/8, which is the final number.
From the problem, we know that it takes 9 days for the number of nuclei to decrease to one-eighth of the original number.
Therefore, 3 half-lives (or 3 times the half-life) have passed in 9 days.
So, the half-life is 9/3 = 3 days.
Hence, the correct answer is C.

The Number of Radioactive Nuclei in a Particular Sample Decreases