JEE Main202126 Feb 2021Evening ShiftPhysicsNuclear PhysicsActual
A radioactive sample is undergoing α decay, At any time t 1 , its activity is A and another time t 2 , the activity is A 5 . What is the average life time for the sample ?
Options
- Aln 5 t 2 - t 1
- Bln t 2 + t 1 2
- Ct 2 - t 1 ln 5
- Dt 1 - t 2 ln 5
Correct answer
C. t 2 - t 1 ln 5
Step-by-step solution
Let initial activity be A 0 A = A 0 e - λ t             . . . 1 A 5 = A 0 e - λ t 2           . . . 2 1 ÷ 2 5 = e λ t 2 - t 1 λ = ln 5 t 2 - t 1 = 1 τ τ = t 2 - t 1 ln 5