Question 203: Atoms & Nuclei

Question

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

Accepted Answer

$${T_{1/2}} = 20 \Rightarrow {{\ln 2} \over \lambda } = 20$$ min
$$ \Rightarrow \lambda  = {{\ln 2} \over {20(\min )}}$$
$$ \because $$ $${N_t} = {N_0}{e^{ - \lambda t}}$$
$${{{N_t}} \over {{N_0}}} = {e^{ - \lambda {t_1}}} \Rightarrow 0.67 = {e^{ - \lambda {t_1}}}$$
$$ \Rightarrow \ln (0.67) =  - \lambda {t_1}$$
$$ \Rightarrow \ln \left( {{{100} \over {67}}} ight)  = \lambda {t_1}$$
$$ \Rightarrow {t_1} = {{\ln \left( {{{100} \over {67}}} ight) 	imes 20(\min )} \over {(\ln 2)}}$$
Similarly, $${t_2} = {{\ln \left( {{{100} \over {34}}} ight) 	imes 20(\min )} \over {(\ln 2)}}$$
$${t_2} - {t_1} = 19.57$$ min $$ \approx 20$$ min.

Answer

40 minutes

Answer

60 minutes

Answer

13 minutes

Answer

20 minutes

Atoms & Nuclei

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

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