JEE Main202125 Feb 2021Morning ShiftPhysicsNuclear PhysicsActual
Two radioactive substances X and Y originally have N 1 and N 2 nuclei respectively. Half life of X is half of the half life of Y . After three half lives of Y , number of nuclei of both are equal. The ratio N 1 N 2 will be equal to :
Options
- A1 3
- B8 1
- C3 1
- D1 8
Correct answer
B. 8 1
Step-by-step solution
T x = t ; T y = 2 t 3 T y = 6 t , N 1 ' = N 2 ' N 1 e - λ 1 6 t = N 2 e - λ 2 6 t N 1   N 2 = e λ 1 - λ 2 6 t = e 1 t - 1 2 t × 6 t ln 2 = e ln 2 3 = e ln 8 = 8