Question

Q ​Two radioactive subtances A and B have decay constants 5$\lambda and\lambda$ and respectively At t = O they havethe same number of nuclei. The ratio of number Of nuclei of A to those of B will be ${\left(\frac{1}{e}\right)}^2$ after a time interval

1. 1/4
2. 4$\lambda$
3. 2$\lambda$
4. 1/2

Answer 1

Dear student,

$$\begin{gathered} Decayequationisgivenby: \\ N=N_0{e}^{-\lambda t} \\ FornucleiA \\ {N}_A=N_o{e}^{-5\lambda t} \\ forB \\ {N}_B=N_o{e}^{-\lambda t} \\ where{N}_{0}isthenoofnucleiatt=0 \\ \frac{N_A}{N_B}=\frac{N_o{e}^{-5\lambda t}}{N_o{e}^{-\lambda t}} \\ \frac{1}{e^2}=e^{-4\lambda t} \\ {e}^{-2}=e^{-4\lambda t} \\ t=\frac{1}{2\lambda } \end{gathered}$$
So check the options may be in option 1 and 4 lambda is missing.
Regards