The number of a certain radioactive nuclide present in a sample decays from 160.to 20.in 39 minutes.What is the half-life of this radioactive species?

Question

Quizplus · Accepted Answer

The half-life of a radioactive nuclide is the time it takes for half of the initial amount to decay.

Using the formula N=N0 (1/2)^(t/t1/2), where N is the final amount, N0 is the initial amount, t is the time passed, and t1/2 is the half-life:

N = 20
N0 = 160
t = 39 minutes

20 = 160(1/2)^(39/t1/2)

Divide both sides by 160:

1/8 = (1/2)^(39/t1/2)

Take the logarithm of both sides (base 2):

-3 = -39/t1/2

Solve for t1/2:

t1/2 = 13 minutes

The Number of a Certain Radioactive Nuclide Present in a Sample