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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 N₀ nuclei of the element

Amit Saxena

12 Years agoGrade upto college level

1 Answer

Navjyot Kalra

12 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 = t_1/2 = 1n(2) / λ in equation (1),

we get, N = 3/2 N₀

(ii) Substituting α = 2λ N₀ and t ⟶ ∞ in equation (1), we get

N = α / λ = 2 N₀

Thanks
Navjot Kalra
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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 N0 nuclei of the element

Amit Saxena

1 Answer

Navjyot Kalra

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