# NEET Physics Nuclei Questions Solved

Watch Physics > Nuclei Videos If 10% of a radioactive material decays in 5 days, then the amount of original material left after 20 days is approximately
(a) 60%              (b) 65%
(c) 70%              (d) 75%

(b) $\mathrm{N}={\mathrm{N}}_{0}{\mathrm{e}}^{-\mathrm{\lambda t}}$

....(i)

and ${\mathrm{xN}}_{0}={\mathrm{N}}_{0}{\mathrm{e}}^{-\mathrm{\lambda }×20}⇒20\mathrm{\lambda }={\mathrm{log}}_{\mathrm{e}}\left(\frac{1}{\mathrm{x}}\right)$            ....(ii)

Dividing (i) and (ii) , we get

$\frac{1}{4}=\frac{{\mathrm{log}}_{\mathrm{e}}\left(1/0.9\right)}{{\mathrm{log}}_{\mathrm{e}}\left(1/\mathrm{x}\right)}=\frac{{\mathrm{log}}_{10}\left(1/0.9\right)}{{\mathrm{log}}_{10}\left(1/\mathrm{x}\right)}=\frac{{\mathrm{log}}_{10}0.9}{{\mathrm{log}}_{10}\mathrm{x}}\phantom{\rule{0ex}{0ex}}⇒{\mathrm{log}}_{10}\mathrm{x}=4{\mathrm{log}}_{10}0.9⇒\mathrm{x}=0.658=65.8%$

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