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A radioactive nucleus X converts into st...

A radioactive nucleus X converts into stable nucleus Y. Half-life of X is 50 years. Calculate the age of radioactive sample when the ratio of X and Y is 1 : 15.

Text Solution

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Let initial number of nuclei X = `N_(0)`
Number of nuclei of X left at any time `t=N_(X)`
Number of nuclei of Y at any time t = `N_(0)-N_(X)=N_(Y)`
Now, `N_(X)=N_(0)e^(-lamdat)`
`N_(Y)=N_(0)-N_(X)=N_(0)-N_(0)e^(-lamdat)=N_(0)(1-e^(-lamdat))`
It is given that `N_(X)/N_(Y)=1/15`
`(N_(0)e^(-lamdat))/(N_(0)(1-e^(-lamdat)))=1/15or16e^(-lamdat)=1`
`e^(-lamdat)=16`
`lamdat=log_(e)2^(4)=4xxlog_(e)2=4xx0.693`
`t=4xx(0.693)/lamda`
`t=4xxT_(1//2)" "=4xx50=200`years.
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