tunneling in particle decays
Roll a ball toward a hill. If it does not have enough energy to reach the top, it rolls back down — it cannot get to the other side, end of story. A quantum particle facing such a barrier behaves differently. Because it is described by a wave, a small part of that wave can leak through to the far side even when the particle lacks the energy to go over the top. Sometimes the particle simply appears on the other side, as if it had bored a tunnel straight through. This is quantum tunneling.
Tunneling follows from the wave nature of matter. A particle's wavefunction does not stop dead at a barrier; it decays smoothly inside the forbidden region and, if the barrier is thin or low enough, emerges with a small but nonzero amplitude on the other side. Squaring that surviving amplitude gives the probability of getting through. The dependence is dramatic: the wider or taller the barrier, the more brutally the chance drops, so tunneling rates can span an enormous range. This is why some processes happen in a fraction of a second while others take billions of years — a small change in the barrier translates into a vast change in the rate.
In particle and nuclear physics tunneling is everywhere. Alpha decay is a classic case: an alpha particle is trapped inside a nucleus by a barrier it does not have the energy to climb, yet it occasionally tunnels out, and the steep dependence of the tunneling probability on energy explains why nuclear half-lives range from microseconds to billions of years. The same mechanism lets atomic nuclei fuse in the Sun despite their electric repulsion, and it governs the rates of many unstable particle and nuclear transitions. Tunneling is also the working principle of devices like the scanning tunneling microscope. The key idea: in the quantum world, classically forbidden does not mean impossible, only improbable.
Uranium-238 lives about four and a half billion years because the alpha particle inside its nucleus can only escape by tunneling through a barrier — a rare event, but the steep barrier dependence makes the half-life immense.
Forbidden but not impossible: tunneling sets decay rates that span from microseconds to eons.
Tunneling does not violate energy conservation; the particle never has more energy than it started with, it simply has a small probability of being found beyond a barrier it could not classically cross.