A certain radioactive isotope decays to one fourth of its original amount in 4.0 hours.What is its half life?

Question

Quizplus · Accepted Answer

The half-life is the time it takes for half of the original amount of the isotope to decay. Since the isotope decays to one fourth of its original amount in 4.0 hours, we can set up the equation:
(original amount) * (1/4) = (original amount) * (1/2)^n, where n is the number of half-lives.
Simplifying, we get:
1/4 = (1/2)^n
Taking the logarithm base 2 of both sides, we get:
log2(1/4) = n
n = -2
Therefore, it takes 2 half-lives for the isotope to decay to one fourth of its original amount. Since we know it takes 4.0 hours for this to happen, each half-life must be:
4.0 hours / 2 = 2.0 hours
So the answer is B.

A Certain Radioactive Isotope Decays to One Fourth of Its