Modern Physics> Nuclei of a radioactive element A are bei...

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 , 10 Years ago

Grade upto college level

1 Answers

Navjyot Kalra

Last Activity: 10 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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Modern Physics> Nuclei of a radioactive element A are bei...

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 , 10 Years ago

Navjyot Kalra

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