I was studying types of nuclear decay, and I came across the concept of "half-life". And I started wondering why does nuclear matter decay in half-lives? In other words, why does the rate of nuclear decay decrease as a function of time?

Is it because as more atoms decay, the surface area of the radioactive matter decreases, and the number of atoms "exposed" decrease? Does the outer layer of atoms somehow "shield" the inner atoms and stabilize them, preventing them from decay?

Or is there another mechanism at play?