The half-life of a certain radioactive isotope is 32 hours.What fraction of the sample would remain after 16 hours?(a)0.50(b)0.25(c)0.62(d)0.71
N=N(initial)(.5)^(t/half-life)
(N/N(initial))= (.5)^(16/32)
= .707
= 70.7% of original
not understood
0.71
I can easily understood ,thank you
To determine the fraction of the sample that remains after a given time, we need to understand the concept of the half-life of a radioactive isotope.
The half-life is the time it takes for half of the original sample of a radioactive isotope to decay. In this case, the half-life of the radioactive isotope is 32 hours.
To find the fraction of the sample remaining after 16 hours, we need to consider how many half-lives have passed.
Since the half-life is 32 hours and we want to know what fraction remains after 16 hours, we need to find out how many times 16 fits into 32. Dividing 32 by 16, we find that it fits exactly two times (32 รท 16 = 2).
Since two half-lives have passed, the fraction remaining after 16 hours would be half of half, or (1/2) * (1/2) = 1/4.
Therefore, the answer is (b) 0.25.