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  • For a certain radioactive substance, it is observed that after 4 hours, only of the original sample is left undecayed. If follows that<di

For a certain radioactive substance, it is observed that after 4 hours, only 6.25 \% of the original sample is left undecayed. If follows that

Option: 1

the half life of the sample is 2 hour


Option: 2

the mean life of the sample is  \frac{1}{\ln 4}  hour 

 


Option: 3

the decay constant of the sample is 2 \ln 2 \text { hour }^{-1}


Option: 4

after a further 4 hours, the amount of the substance left
over would by only 0.39% of the original amount


Answers (1)

best_answer

We have 6.25 \%=\frac{6.25}{100}=\frac{1}{16}

The given time of 4 hours thus equals 4 half lives so that the half
life is 1 hour.

\text { Since half life }=\frac{\ln 2}{\text { decay constant }} \text { and }

\text { mean life }=\frac{1}{\text { decay constant }}

after further 4 hours, the amount left over would by \frac{1}{2^4} \times \frac{1}{2^4}

\text { i.e. } \frac{1}{256} \text { or } \frac{100}{256} \text { or } 0.39 \%  of original amount.

Posted by

manish painkra

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