The half-life period of a radioactive element is `1.4 xx 10^(10)` years. Calculate the time in which the activity of the element is reduced to 90% of its original value.

Explanation

`t_(1//2) = 0.693/k or k=0.693/t_(//2)= 0.693/(1.4 xx 10^(10)`years
`t=2.303/k log N_(0)/N_(t) = 2.303/(0.693 // 1.4 xx 10^(10) years) xx log 100/90`
`= 2.303/0.693 xx 1.4 xx 10^(10) xx 0.4558` years = `2.13 xx 10^(9)` years.