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# Two radioactive materials A & B have decay constants 12X & X respectively . If initially they have same no.of nuclei , then ratio of no. of nuclei of A to B will be $\;\large\frac{1}{e}\;$ after a time

$(a)\;1/12 X\qquad(b)\;1/11X\qquad(c)\;1/32X\qquad(d)\;1/224X$

Answer : (b) $\;\large\frac{1}{11X}$
$\large\frac{N_{A}}{N_{B}}=\large\frac{1}{e}\;$ or
$\large\frac{N_{0} e^{-12Xt}}{N_{0} e^{-Xt}}=\large\frac{1}{e}$
or $\;e=\large\frac{e^{-Xt}}{e^{-12Xt}}$$=e^{11Xt}$
$11Xt=1$
$t=\large\frac{1}{11X}\;.$