Consider a chain of radioactive decays 1 --> 2 --> 3 with nuclei of type 3 being stable (decay constants are $\displaystyle \lambda$ ₁ and $\displaystyle \lambda$ ₂).

(a) Assuming that at t = 0, N₁ = N₀ and N₂ = N₃ = 0, find N_i(t), I = 1, 2, 3.

(b) Examine N_i, I = 1, 2, 3 at small t, keeping only linear terms, and interpret the results

(c) Find the limits of N_i, I = 1, 2, 3 as t --> $\displaystyle \infty$ and interpret.

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Consider a chain of radioactive decays 1 --> 2 --> 3 with nuclei of type 3 being stable (decay constants are $\displaystyle \lambda$ ₁ and $\displaystyle \lambda$ ₂).

(a) Assuming that at t = 0, N₁ = N₀ and N₂ = N₃ = 0, find N_i(t), I = 1, 2, 3.

(b) Examine N_i, I = 1, 2, 3 at small t, keeping only linear terms, and interpret the results

(c) Find the limits of N_i, I = 1, 2, 3 as t --> $\displaystyle \infty$ and interpret.

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