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Two radioactive materials $\mathrm{A}$ and $\mathrm{B}$ have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $\mathrm{B}$ to that of $\mathrm{A}$ will be $\mathrm{"e"}$ after a time $\mathrm{\frac{1}{a \lambda}}$ . The value of $\mathrm{ a}$ is___________.
Option: 1
9

Option: 2
-

Option: 3
-

Option: 4
-

Answers (1)

best_answer

$\mathrm{\lambda_A =25 \lambda }$

$\mathrm{\lambda_B =16 \lambda }$

$\mathrm{\frac{N_B}{N_A} =\frac{N_0 e^{-\lambda_B t}}{N_0 e^{-\lambda_A t}}=e }$

$\mathrm{e^{\left(\lambda_A-\lambda_B\right) t}=e}$

$\mathrm{but\: \: t=\frac{1}{a \lambda} (\text { Given }) }$

$\mathrm{\left(\lambda_A-\lambda_B\right) t =1 }$

$\mathrm{t =\frac{1}{\left(\lambda_A-\lambda_B\right)}=\frac{1}{a \lambda} }$

$\mathrm{\lambda_A-\lambda_B =a \lambda }$

$\mathrm{a \lambda =a \lambda }$

$\mathrm{a =9 }$

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