The half life of a radioactive nucleus is 50 days. The time

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The half life of a radioactive nucleus is 50 days. The time interval (t₂ – t₁ ) between the time t₂ when 2/3 of it has decayed and the time t₁ when 1/3 of it had decayed is :

N₁ = N₁ e^–λt

N₁ =	1	N₀
	3

	N₀	= N₀e^{- λt₂}
	3

	1	= e^{- λt₂} ....(i)
	3

N₂ =	2	N₀
	3

	2	N₀ = N₀e^{- λt₁}
	3

	2	= e^{- λt₁}
	3

Dividing equation (i) by equation (ii)

	1	= e^{- λ(t₂ - t₁)}
	2

λ(t₂ - t₁) In 2

t₂ - t₁ =	In 2	= T_1/2 = 50 days
	λ