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Q.
$90 \%$ of the active nuclei present in a radioactive sample are found to remain undecayed after $1$ day. The percentage of undecayed nuclei left two days will be:
Nuclei
Solution:
Using $N=N_{0}(2)^{-t / T}$
at $t=1$ day
$0.9 N_{0}=N_{0}(2)^{-t / T}$
$\Rightarrow \frac{1}{T}=\frac{\log \left(\frac{10}{9}\right)}{\log (2)}$
at $t=2$ days
$N=N_{0}(2)^{-2/T}$
$\Rightarrow \frac{\log \left(\frac{N_{0}}{N}\right)}{\log (2)}-2 \frac{\log \left(\frac{10}{9}\right)}{\log (2)}$
$\Rightarrow \frac{N_{0}}{N}=\frac{100}{81}$
$\Rightarrow N = 0.81 \,N_0$