JEE Main202523 Jan 2025Morning ShiftPhysicsNuclear PhysicsActual
A radioactive nucleus n₂ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n₁ . If initial number of both nuclei are the same, what is the ratio of number of nuclei of n₂ to the number of nuclei of n₁ , after one half-life of n₁ ?
Options
- A1 / 8
- B8
- C4
- D1 / 4
Correct answer
D. 1 / 4
Step-by-step solution
aligned & N ₂= N ₀ e ^ -3 t & ~N ₁= N ₀ e ^ - t & N ₂ ~N ₁ = e ^ -2 t & t _ half lifeofN t & t = 2 _ n 1 & ~N ₀ 2 = N ₀ e ^ - t aligned aligned & t = 2 & t = 2 & = e ^ -2 2 & ~N ₂ ~N ₁ = 1 4 aligned