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At time \mathrm{t=0 \, N_1} nuclei of decay constant \mathrm{\lambda _{1}} and \mathrm{N _{2}} nuclei of decay constant \mathrm{\lambda _{2}} are mixed. The decay rate of the mixture is

Option: 1

\mathrm{N_1 N_2 e^{-\left(\lambda_1+\lambda_2\right) t}}


Option: 2

\mathrm{\frac{N_1}{N_2} e^{-\left(\lambda_1-\lambda_2\right)t}}


Option: 3

\mathrm{N_1 \lambda_1 e^{-\lambda_1 t}+N_2 \lambda_2 e^{-\lambda_2 t} }


Option: 4

\mathrm{N_1 \lambda_1 N_2 \lambda_2 e^{-\left(\lambda_1+\lambda_2\right)} \cdot t}


Answers (1)

best_answer

At time \mathrm{t}, number of nuclei is of 1 \mathrm{N_1^{\prime}=N_1 \cdot e^{-\lambda_1 t}}

At time \mathrm{t_{2}} number of nuclei is of 2 \mathrm{N_2^{\prime}=N_2 e^{-\lambda_2 t}}

Rate of decay = Rate of decay of 1 + Rate of decay of 2

\mathrm{ =\lambda_1 N_1^{\prime}+\lambda_2 N_2^{\prime}}
\mathrm{ =\lambda_1 N_1 \cdot e^{-\lambda_1 t}+\lambda_2 N_2 e^{-\lambda_2 t}}.

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