Two radioactive materials X1 and X2 have decay constants

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Two radioactive materials X₁ and X₂ have decay constants 5λ and λ respectively. If initially they have the same number of nuclei,
then the ratio of the number of nuclei of X₁ to that of X₂ will be 1/e after a time

1. λ
2. 1 λ
  2
3. 1
  4λ
4. e
  λ

Correct Option: C

Let the required time be t. Then
N₁ = N₀e^-λ₁t ; N₂N₀e^-λ₂t
Where
N₁ = number of nuclei of X₁1 after time t
N₂ = number of nuclei of X₂ after time t
N₀ = initial number of nuclei of X₁ and X₂ each.

Now,	N₁	=	N₀e^-λ₁t
	N₂		N₀e^-λ₂t

Here	N₁	=	1
	N₂		e

λ₁ = 5λ ; λ₂ = λ

∴	1	=	e^-5λt
	e		e^-λt

⇒ e^-1 = e^-4λt ⇒ 44λt = 1

∴ t =	1
	4λ