Question

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 63.6 minutes , what is the half-life of this substance?

Answer 1

we have:

[A]o = 400 count

[A] = 100 count

t = 63.6 min

use integrated rate law for 1st order reaction

ln[A] = ln[A]o - k*t

ln(100) = ln(400) - k*63.6

4.6052 = 5.9915 - k*63.6

k*63.6 = 1.3863

k = 2.18*10^-2 min-1

we have:

k = 0.0218 min-1

use relation between rate constant and half life of 1st order reaction

t1/2 = (ln 2) / k

= 0.693/(k)

= 0.693/(2.18*10^-2)

= 31.8 min

Answer: 31.8 min