A radioactive substance has half-life `T_(1/2)` and number of radioactive nuclides present initially was `N_(0)`. What is the number of radioactive nuclides at time t ?

Explanation

We know that number of radioactive nuclides left intact after a time `T_(1/2)` is `N = N_(0)/2` ,
Thus, after another time equal to `T_(1/2)` (i.e., after 2 half-lives) value `N =1/2(N_(0)/2)=N_(0)(1/2)^(2)`. It follows that after a time equal to n half-lives, the number of radioactive nuclides left intact will be `N=N_(0)(1/2)^(n)`
For time t, `n=t/T_(1/2)` and hence, `N=N_(0)(1/2)^(t/T_(1/2)`.