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Standard XII

Chemistry

Law of Radioactivity

Two radioacti...

Question

Two radioactive materials $X_{1}$ and $X_{2}$ have decay constants 10 $λ$ and $λ$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $X_{1}$ to that of $X_{2}$ will be 1/e after a time $\frac{1}{x λ}$ . The value of x is ___ .

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Solution

$\frac{N x_{1} (t)}{N x_{2} (t)} = \frac{1}{e}$ or $\frac{N_{0} e^{- 10 λ t}}{N_{0} e^{- λ t}} = \frac{1}{e}$

(Initially both have same number of nuclei say $N_{0}$ )

or $e = \frac{e^{-} λ t}{e^{- 10 λ t}}$

or $e = e^{9 λ t}$

or $9 λ t = 1$

or $t = \frac{1}{9 λ}$

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Two radioactive materials X1 and X2 have decay constants 10 λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that of X2 will be 1/e after a time 1xλ. The value of x is ___ .

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Two radioactive materials $X_{1}$ and $X_{2}$ have decay constants 10 $λ$ and $λ$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $X_{1}$ to that of $X_{2}$ will be 1/e after a time $\frac{1}{x λ}$ . The value of x is ___ .

$\frac{N x_{1} (t)}{N x_{2} (t)} = \frac{1}{e}$ or $\frac{N_{0} e^{- 10 λ t}}{N_{0} e^{- λ t}} = \frac{1}{e}$

(Initially both have same number of nuclei say $N_{0}$ )

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or $e = e^{9 λ t}$

or $9 λ t = 1$

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