A radioactive isotope is being produced at a constant rate A. The isotope has a half life T. Initially, there are no nuclei and after a time, t>>T, the number of nuclei becomes a constant. The value of this constant is:

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$\frac{A}{T} I n (2)$

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$A T I n (2)$

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$\frac{A T}{I n (2)}$

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Solution

The correct option is D
$\frac{A T}{I n (2)}$

$\frac{d N}{d t} = A - λ N$

After time t >> T, the number of nuclei becomes a constant, so net rate of change in the number of nuclei, $\frac{d N}{d t} = 0$

which gives, $N = \frac{A}{λ}$

Substituting $λ = \frac{l n (2)}{T}$ , we get $\frac{A T}{I n (2)}$

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A radioactive isotope is being produced at a constant rate A. The isotope has a half life T. Initially, there are no nuclei and after a time, t>>T, the number of nuclei becomes a constant. The value of this constant is:

The correct option is D ATIn(2) dNdt=A−λN After time t >> T, the number of nuclei becomes a constant, so net rate of change in the number of nuclei, dNdt=0 which gives, N=Aλ Substituting λ=ln(2)T, we get ATIn(2)