Question

A sample contains a mixture of ²³⁹Pu and ²⁴⁰Pu in unknown proportions. The activity of the mixed sample was found to be 4.35 x 10⁷ dpm for a sample of 0.125 mg of Pu. Calculate the weight % of each Pu isotope present

Answer 1

Ans:

• a mixture of 239Pu and 240Pu has a activity of 4.35 x 10⁷ dpm for a sample of 0.125mg of Pu.
• the half-lives of the isotopes are 2.44 x 10⁴ and 6.58 x 10³y, respectively

• calculate the isotopic composition

• number of seconds in a year is [A=kN; k=0.693/t1/2 = 0.693/7.6x1011s = 9.11 x10-13s -1 N=(1.0g)/(239g/mol)*(6.02x1023mol-1)= 2.5 x1021 atom A=(9.11 x10-13s -1)( 2.5 x1021 atom) = 2.27x10⁹ disintegrations/sec]

In disintegration per minute ie. in dpm

• for 239Pu: A = 2.27 x10⁹/s  g = 2.27 x10⁹/1/60  g = 2.27 x10⁹ x 60/m  g = 1.362 x 10¹¹ /m x g

• for 240Pu: A = 8.37 10⁹/s  g = 8.37 10⁹/1/60  g = 8.37 10⁹/s  g = 5.022 x 10¹¹/m x g

• let the fraction of 239Pu = x; then the fraction 240Pu = 1 - x

• (1.362 x 10¹¹ )x+(1 – x)(5.022 x10¹¹) = 4.35 x 10⁷ dpm/0.000125g = 3.48 x 10¹¹

  (5.022 x10¹¹) – (3.66 x 10¹¹) x = 3.48 x 10¹¹

3.66 x 10¹¹ x =   1.542 x 10¹¹   

• x = 0.42 = 42% 239Pu

• 1-x = 0.58 = 58% 240Pu