Write the expression for the half life of a radioactive element.

Explanation

After one half life
`t=T_(1//2) rArr N= N_(0) //2`
Using the relation `N= N_(0) e^(-lambda t)`
`rArr N_(0) //2 = N_(0) e^(- lambda T_(1//2) )`
`rArr 1//2 = e^(-lambda T_(N))`
`rArr lambda T_(1//2) = log_(n) 2`
`rArr lambda T_(1//2) = 0.693 `
Arriving at `T_(1//2) = (0.693)/(lambda) `