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$90 \%$ of a radioactive sample is left undecayed after time $t$ has elapsed . what percentage of the initial sample will decay in a total time $2t$ :
Option: 1
$20 \%$

Option: 2
$19 \%$

Option: 3
$40 \%$

Option: 4
$38 \%$

Answers (1)

best_answer

Let initial number $\mathrm{=}$ $\mathrm{=N_{0}}$

$\mathrm{after \, time\, t \, N=0.9\, \mathrm{No}=N_0 \cdot e^{-\lambda t}}$

$\mathrm{\Rightarrow e^{-\lambda t}=0.9 -(1)}$

$\mathrm{after \, time\, 2t \,, N^{1}=N_{0}\,\: e^{-2\lambda\, t}}$

$\mathrm{N^1=N_0 \times(0.9)^2=0.81 \, N_0 \text {. }}$

$\mathrm{\Rightarrow \%\text{\, of sample decayed} }$
$\mathrm{=\frac{0.19 N 0}{N_{0}} \times 100 \%=19 \%}$ .

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