JEE Main20207 Jan 2020Evening ShiftPhysicsNuclear PhysicsActual
The activity of a radioactive sample falls from 700 s - 1 to 500 s - 1 in 30 minutes. Its half life is close to:
Options
- A72 m i n
- B62 m i n
- C66 m i n
- D52 m i n
Correct answer
B. 62 m i n
Step-by-step solution
From equation of radioactivity. A t = A 0 e - λ t ln A 0 A t = λ t ⇒    ln 700 500 = λ ( 30 min ) ------ 1 also ⇒    ln 2 = λ t 1 / 2 -------- 2 ( ii ) / ( i ) ⇒    ln 2 ln ( 7 / 5 ) = t 1 / 2 ( 30 min )    ⇒    ( 2 . 06004 ) 30 = t 1 / 2 = 61 . 8 min ≈ 62 m i n