Explanation

When a radioactive element undergoes decay, the number of atoms decreases by half every half-life. So, after "n" half-lives, the number of atoms left behind is:

No × (1/2)^n

Where:

No = initial number of atoms

n = number of half-lives

This is because the decay process follows a geometric progression with a common ratio of 1/2.

So, after "n" half-lives, the number of atoms left is (1/2)^n times the initial number, which is:

(1/2)^n No