You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 66.7 minutes, what is the half-life of this substance? Express your answer with the appropriate units.

Answer: 33.35 minutes

Explanation:

A (t) = A (o) * (.5) ^[t / (t1/2) ] ... equ1

Where

A (t) = geiger count after time t = 100

A (o) = initial geiger count = 400

(t1/2) = the half life of decay

t = time between geiger count = 66.7 minutes

Sub into equ 1

100=400 (.5) ^[66.7 / (t1/2)

Equ becomes

.25 = (.5) ^[66.7 / (t1/2) ]

Take log of both sides

Log 0.25 = [66.7 / (t1/2) ] * log 0.5

66.7 / (t1/2) = 2

(t1/2) = (66.7/2) = 33.35 minutes