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For a radioactive material, half-life pe...

For a radioactive material, half-life period is 600s. If initially there are 600 number of molecules, find the time taken for disintegration of 450 molecules and the rate of disintegration.

Text Solution

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The initial number of molecules, `N_(0)=150`
The final number of molecules, N = 150
`N/N_(0)=(1/2)^(n)or150/600=(1/2)^(n)`
`(1/2)^(2)=(1/2)^(n)orn = 2=t/T_(1//2)`
`t=2xx600s=1200s`
Best of disintegration,
`R=(dN)/(dt)=-lamdaN`
= `(0.693)/T_(1//2)xx150`
= `0.693/600xx150=0.173`
disintegration/second at the instant when 150 molecules were remaining.
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