A radioactive material initially is observed to have an activity of 1600 decays/sec.If six hours later it is observed to have an activity of 400 decays/sec,what is its half-life?

Question

Quizplus · Accepted Answer

The formula for calculating half-life is:
activity = initial activity x (0.5)^(time/half-life)
Let's plug in the given values:
400 = 1600 x (0.5)^(6/half-life)
Dividing both sides by 1600:
0.25 = (0.5)^(6/half-life)
Taking the logarithm of both sides (using any base):
log(0.25) = (6/half-life) x log(0.5)
Solving for half-life:
half-life = 6 / [log(0.25) / log(0.5)]
half-life ≈ 3 hours
Therefore, the answer is B because the half-life of the radioactive material is 3 hours.

A Radioactive Material Initially Is Observed to Have an Activity