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  • A radioactive isotope is being produced at a constant rate X. Half-life of the isotope is Y. After sometime, number of radioactive nuclei becomes constant. This constant number is:<div c

A radioactive isotope is being produced at a constant rate X. Half-life of the isotope is Y. After sometime,
number of radioactive nuclei becomes constant. This constant number is:

Option: 1

X Y / \ln 2


Option: 2

XY


Option: 3

X Y \ln 2


Option: 4

\mathrm{X} / \mathrm{Y}


Answers (1)

best_answer

The total number of nuclei is constant if \mathrm{X}=\lambda \mathrm{N}. 

\text { or } \quad \mathrm{X}=\frac{\ln (2) \mathrm{N}}{\mathrm{Y}} \quad\left(\because \lambda=\frac{\ln (2)}{\mathrm{T}_{1 / 2}} \text { and } \mathrm{T}_{1 / 2}=\mathrm{Y}\right)

\Rightarrow \mathrm{N}=\mathrm{XY} / \ln (2)

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vinayak

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