If in 3160 years, a radioactive substance becomes one-fourth of the original amount, find it’s the half-life period.

Explanation

Given that `(N)/(N_(0)) = (1)/(4)`
We know that `N = ((1)/(2))^(n) N_(0)`
or `(N)/(N_(0)) = ((1)/(2))^(n)`
Equating Eqs. (i) and (ii), we get
`(1)/(4) = ((1)/(2))^(n)`
`implies ((1)/(2))^(2) = ((1)/(2))^(n)`
`:.n = 2`
Total time `(T) = n xx t_(1//2)`
or `t_(1//2) = (3160)/(2) = 1580` year