In a radioactive material the activity at time t1 is R1

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In a radioactive material the activity at time t₁ is R₁ and at a later time t₂, it is R₂. If the decay constant of the material is λ, then

1. R₁ = R₂e^{λ(t₁ - t₂)}
2. R₁ = R₂e^{λ(t₁/ t₂)}
3. R₁ = R₂
4. R₁ = R₂e^{λ(t₁ + t₂)}

Correct Option: D

Let at time t₁ & t₂, number of particles be N₁ & N₂. So,

R₁ =	dN₁	= -λN₁; R₂ =	dN₂	= -λ N₂
	dt		dt

	R₁	=	λN₁	=	N₁	= e^{-λ(t₂ - t₁)}
	R₂		λN₂		N₁e^{-λ(t₂ - t₁)}

R₁ = R₂e^{λ(t₂ - t₁)} = R₂e^{-λ(t₂ - t₁)}