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Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N 0 nuclei of the element

Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N0 nuclei of the element

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Hello Student,
Please find the answer to your question
(a) Let at time ‘t’ number of radioactive are N.
Net rate of formation of nuclei of A.
dN /dt = α – λ N or dN / α – λN = dt
or \int_{N_0}^{N}\frac{dN}{\alpha - \lambda N } = \int_{0}^{t} dt
Solving this equation, we get
N = 1 / λ [α – (α – λN0)e-λt] …..(1)
(b) Substituting α = 2λN0 and
t = t1/2 = 1n(2) / λ in equation (1),
we get, N = 3/2 N
(ii) Substituting α = 2λ N0 and t ⟶ ∞ in equation (1), we get
N = α / λ = 2 N0
Thanks
Navjot Kalra
askIITians Faculty

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