First slide

Radio activity

Question

After a time t has elapsed, 90% of a radioactive sample is undecayed. The percent that will decay in a time 2t is

Easy

A

19 %
B

81 %
C

20 %
D

40 %

Solution

$0.9 N_{0} = N_{0} e^{- λt}$
$\Rightarrow λ = \frac{1}{t} \ln (\frac{10}{9})$
$N' = N_{0} e^{- λ . 2 t} = N_{0} {(\frac{9}{10})}^{2} = \frac{81 N_{0}}{100}$
$∴$ decayed = 19%.

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