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 t_1/2 for O¹⁴=71sec and t_1/2 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