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13.Nuclei
medium
$90\%$ of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the initial sample will decay in a total time $2t$ : ..............$\%$
A
$20$
B
$19$
C
$40$
D
$38$
Solution
Given that $90 \%$ is left un-decayed after time $t$.
Hence, $10 \%$ decays in time $t$
Initially assume that the amount of substance is $'x'$
After time $t^{\prime} 10 \%$ is decayed.
i.e. Amount of substance left $=0.9 x$
After further time $t^{\prime}$ another $10 \%$ is decayed.
i.e. $0.1 \times 0.9 x$ is decayed
Leaving behind $0.81 x$.
Hence after time $2 t$ we see that $0.19 x$ has decayed, which is $19 \%$
Standard 12
Physics
