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

Answer 1

For a first order reaction rate constant , k = ( 2.303 /t )x log ( M_o / M)

Where

M_o = initial activity = 400 counts

M= activity after time t = 100 counts

t = time = 37.8 min

Plug the values we get k = ( 2.303 /37.8 )x log ( 400/100)

                                     = 0.0367 min^-1

Half-life =0.693 / k

          = 0.693 / (0.0367 min^-1)

          = 18.9 min