Radioactive material 'A' has decay constant '8 $\lambda$'  and material 'B' has decay constant '$\lambda$'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A  will be e ?

detailed solution

Correct option is A

The number of radioactive nuclei ‘N’ at any time t is given as N(t)=N0e-λtwhere N0 is number of radioactive nuclei in the sample at some arbitrary time t = 0 and λ is the radioactive decay constant. Given: λA=8λ,λB=λ,N0A=N0B=N0∴  NBNA=e-λte-8λte=e-λte8λt=e7λt⇒1=7λt or t=17λ NOTE:-     in original question paper the question was  "Radioactive material 'A' has decay constant '8 λ'  and material 'B' has decay constant 'λ'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A  will be1e ? "with this data value for  t we get after solving we get t = -17λ Negative value of time is not possible. So given ratio in question should be NBNA=e