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A radioactive isotope X has a half-life ...

A radioactive isotope X has a half-life of 3s. At t = 0 s, a given sample of this isotope X contains 8000 atoms. Find the time `t_(1)`, when 1000 atoms of isotope X remains in the sample.

Text Solution

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a) `lamda=(0.693)/(T_(1//2))=(0.693)/3=0.231s^(-1)`
b) `N=N_(0)^(-lamdat_(1))` (or)
`t_(1)=1/lamdalog_(e)""N_(0)/N`
`=1/(0.231)log_(e)""(8000)/1000`
= 9 sec
`|(dN)/(dt)|_(t=t_(1))=lamdaN=0.231xx1000=231 s^(-1)`
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