Question

Example: The radioactive isotope decays by electron capture with a half –life of 272 days. •(a) Find the decay constant of the lifetime. •(b) If you have a radiation source containing , with activity 2.00µCi, how many radioactive nuclei does it contain? •(c) What will be the activity of this source after one year?5

Answer 1

a) Radioactive decay is a statistical process which depends upon the instability of the particular radioisotope. If there are N radioactive nuclei at a time t, then the number ΔN which would decay in a time interval Δt would be proportional to N:

Where the decay constant is the probability of the nucleus decaying in the next unit of time. If we take the limit when the time interval goes to cero and solve the differential equation we get:

With this equation we can get the fraction of undecayed nuclei after a time t. This proportion is not only valid for the count of nuclei N, the same is true for mass and for activity. Half-life , is defined as the time it takes for this proportion to be 1/2:

Replacing with the given value of half-life of our isotope:

b) The number of decays per second, this is, activity, is proportional to the number of radioactive nuclei present in the sample, and the proportionality constant is the decay constant . Activity (A) is usually measured in Becquerels (Bq). One decay per second equals one Bq. An older unit is the Curie (Ci), one Ci is approximately the activity of 1 g of Radium and equals exactly 3,7 x 10¹⁰ Bq. Or what is the same 1 Bq = 2,703 x 10^-11 Ci  

If we have a source with activity of 2 x 10^-6 Ci = 74000 Bq, then:

c) Finally, as we stated before the following is true:

The initial activity of the source is 2 micro Ci. After 1 year = 365 days, the activity of the source will be: