Isotopes of oxygen with mass number less than 16 undergo beta plus emission. Assuming an equi molar mixture of O14 and O15, find a) the ratio of nucleide at the end of 1 Hr and b) at what time will the ratio of O14 nuclei to O15 nuclei be equal to 0.25.? Given that t1/2 for O14=71sec and t1/2 for O15= 124 sec.

Hi Kiran,

O¹⁴ ----> N¹⁴         λ1

O¹⁵-----> N¹⁵         λ2

λ1=0.693/71=0.00976

λ2=0.693/124=0.00589

[A]₀₁=[A]₀₂

λ1* t=ln{ [A]_01/[A]_t1}----1

λ2* t=ln{ [A]_02/[A]_t2}-----2

After 1 hr=60*60 sec

a)from 1 and 2 :  e^λ1*t/e^λ2*t=[A]t2/[A]t1=e^(λ1-λ2)*t=e^{0.00387*60*60}=e^13.932

b)[A]t2/[A]t1=e^(λ1-λ2)*t=e^0.00387*t=1/0.25

   0.00387*t = ln 4=2.303*2*0.3010 =1.386

   t= 1.386/0.00387 =358.14 sec