MHT CET202617 April 2026Morning ShiftPhysicsNuclear PhysicsActual
The half-life of the isotope ₁₁ Na ²⁴ is 15 hr. How much time does it take for ( 7 8 )^ th of a sample of this isotope to decay ?
Options
- A45 hour
- B60 hour
- C75 hour
- D90 hour
Correct answer
A. 45 hour
Step-by-step solution
Fraction of the sample decayed is 7 8 . Fraction of the sample remaining is 1 - 7 8 = 1 8 . The amount of substance remaining after time t is given by N = N₀ ( 1 2 )^ t T_ 1/2 . Substituting the values, we get 1 8 = ( 1 2 )^ t 15 . ( 1 2 )^3 = ( 1 2 )^ t 15 t 15 = 3 t = 45 hr. Answer: 45 hour