Two radioactive substances A and B have decay constants

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Two radioactive substances A and B have decay constants 5 λ and λ respectively. at t = 0 they have same number of nulei. The ratio of number of nuclei of A to those of B will be (1/e)² after a time interval

λ_A = 5λ and λ_B = λ
At t = 0, (N₀)_A = (N₀)_B
Given,

	N_A	=		1		²
	N_B			e

According to radioactive decay,

	N	= e^λt
	N₀

	N_A	= e^λ_At ....(i)
	(N₀)_A

	N_B	= e^λ_Bt ....(ii)
	(N₀)_B

From (1) and (2),

	N_A	= e^{-(5λ - λ)t}
	N_B

⇒		1		²	= e^-4λt		1		^4λt
		e					e

⇒ 4λt = 2

∴ t =	1	.
	2λ