# NEET Physics Nuclei Questions Solved

Two radioactive materials ${\mathrm{X}}_{1}$ and ${\mathrm{X}}_{2}$ have decay constants $10\mathrm{\lambda }$ and $\mathrm{\lambda }$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of ${\mathrm{X}}_{1}$ to that of ${\mathrm{X}}_{2}$ will be 1/e after a time

(a) $1/\left(10\mathrm{\lambda }\right)$                   (b) $1/\left(11\mathrm{\lambda }\right)$
(c) $11/\left(10\mathrm{\lambda }\right)$                 (d) $1/\left(9\mathrm{\lambda }\right)$

(d) ${\mathrm{N}}_{1}={\mathrm{N}}_{0}{\mathrm{e}}^{-10\mathrm{\lambda t}}$ and ${\mathrm{N}}_{2}={\mathrm{N}}_{0}{\mathrm{e}}^{-\mathrm{\lambda t}}$

$⇒\frac{{\mathrm{N}}_{1}}{{\mathrm{N}}_{2}}=\frac{1}{\mathrm{e}}={\mathrm{e}}^{-1}={\mathrm{e}}^{\left(-10\mathrm{\lambda }+\mathrm{\lambda }\right)\mathrm{t}}={\mathrm{e}}^{-9\mathrm{\lambda t}}⇒\mathrm{t}=\frac{1}{9\mathrm{\lambda }}$

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