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

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Answer : (b) $\;\large\frac{1}{11X}$

Explanation :

$\large\frac{N_{A}}{N_{B}}=\large\frac{1}{e}\;$ or

$\large\frac{N_{0} e^{-12Xt}}{N_{0} e^{-Xt}}=\large\frac{1}{e}$

Initially both have same no . of nuclei say no .

or $\;e=\large\frac{e^{-Xt}}{e^{-12Xt}}$$=e^{11Xt}$

$11Xt=1$

$t=\large\frac{1}{11X}\;.$

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