JEE Main202310 Apr 2023Evening ShiftPhysicsNuclear PhysicsActual
The half life of a radioactive substance is T . The time taken, for disintegrating 7 8 t h part of its original mass will be:
Options
- A2 T
- B3 T
- CT
- D8 T
Correct answer
B. 3 T
Step-by-step solution
It is given that t 1 2 =   T . After disintegration of 7 8 t h part, 1 8 t h part is only left. Using the decay formula, N = N 0 1 2 t t 1 2 ⇒ N 0 8 = N 0 1 2 t T ⇒ - ln 8 = - t T ln 2 ⇒ 3 ln 2 = t T ln 2 ⇒ t = 3 T