A source contains two phosphorous radionuclides 3215P (T1/2 = 14.3d) and 3315P(T1/2 = 25.3d). Initially, 10% of the decays come from 3315 P. How long one must wait until 90% do so?
Let the number of atoms of 1532P be N1 and atoms of 1533P be N2. The decay constants of two atoms be λ1 and λ2 respectively. The initial activity of 1533P is 91 times that of 1532P. Therefore, we can write the decay constants as: N1λ1=9N2λ2 ___(i) Let after time t the activity of 1533P be 9 times that of 1532P N1λ1e−λ1t=9N2λ2e−λ2t ___(ii) Now. Divide equation (ii) by (i) and taking the natural log of both sides we get λ1t=ln 81−λ2t t=λ2−λ1ln 81 where λ2=0.048/day and λ1=0.027/day t=0.048−0.0274.394=209.2 days t comes out to be 209.2 days
