A radioactive sample consists of two distinct species having the equal number of atoms initially- The mean-life time of one species is - and that of the other is 5- The decay products in both cases are stable- A plot is made of the total number of radioactive nuclei as a function of time- Which of the following figure best represent the form of this plot -

When a radioactive sample decays simultaneously with different processes, nbsp; The effective decay constant is goven by, nbsp; λ=λ_1+λ_2 By law of radio ...

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Standard XII

Chemistry

Law of Radioactivity

A radioactive...

Question

A radioactive sample consists of two distinct species having the equal number of atoms initially. The mean-life time of one species is $τ$ and that of the other is $5 τ$ . The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time. Which of the following figure best represent the form of this plot ?

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Solution

The correct option is A
When a radioactive sample decays simultaneously with different processes,

The effective decay constant is goven by,

$λ = λ_{1} + λ_{2}$

By law of radioactivity,

$N = N_{0} e^{- λ t}$

Therefore, total number of nuclei decrease exponentially with time as represented by option $(A)$

The total number of nuclei neither remains constant, as in option $(B)$ nor can ever increase, as in option $(C)$ and $(D)$ .

Hence, option $(A)$ is correct.

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