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MHT CET202122 Sep 2021Evening ShiftPhysicsNuclear PhysicsActual

Two radioactive materials X ₁ and X ₂ have decay constants ' 5 ' and ' ' respectively. Initially, they have the same number of nuclei. After time ' t ', the ratio of number of nuclei of X₁ to that of X₂ is 1 e . Then t is equal to

Options

  1. A2
  2. Be
  3. C1 4

Correct answer

3

Step-by-step solution

Let N₁ be the number of X₁ and N₂ be the number of nuclei of X₂ after time t. aligned & N ₁= N ₀ e ^ -5 t and N ₂= N ₀ e ^ - t & N ₁ ~N ₂ = e ^ -5 t e ^ - , t = 1 e ^ 4 t = 1 e & 4 t =1 & t = 1 4 aligned

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