Question

With the following data, estimate the half-life of an unknown, and suggest what isotope it is (see a table for a list of possible isotopes) (the correct answer is 1.82 h , argon-41. I just do not know how to get it. thank you)

time (s)	counting rate (counts/s)
0	200
1000	182
2000	162
3000	144
4000	131

Answer 1

Let the concentration be C1 at time t1 and C2 at time t2

Then according to the equation we can write

       ------ (i)

   ------- (ii)

Divide equation 1 by equation 2 we get

Taking ln both sides we get

Now coming back to part (b) of the equation

b) Using the table we can write

Hence Lambda * No = 200

Now we can write the other equation

182 = 200 * e^(-1000*lambda)

ln(200/182) = 1000 * lambda

lambda = 9.431 * 10^(-5)

100 = 200 * e^(-t*9.431*10^(-5))

ln2 = t * 9.431 * 10^(-5)

t = 7348.21 seconds