Well, I wonder if that didn't add to the confusion. Let's dig in!
He gets the simplified atom description and the strong nuclear force correct. He's right that it's all probabilistic (the probability of decay is called the decay constant, and this is related to the half-life).
His description of the strong nuclear force applied primarily to alpha decay and spontaneous fission. In the nucleus the protons have an electric charge repulsion for each other (the electromagnetic force, e-m force), but at close ranges they also experience the strong nuclear force (snf) which is stronger than the e-m force. The snf drops off very fast with distance compared to the e-m force, so in large atoms, a proton experiences the e-m force from all the other protons, but only the snf force from its close neighbors.
At very short ranges, the snf shifts to repulsive because the quarks which make up the protons and neutrons can't be in the same space at the same time (Pauli exclusion principle).
Beta particle decay is associated with the weak nuclear force (wnf), which can change one type of quark into another. This change causes a particular nuclear particle to change into the other, with the emission of beta particles and neutrinos. The weak nuclear force doesn't produce a bound state like the other forces (gravity, e-m, & snf).
Gamma decay follows alpha or beta decay if the daughter nucleus is left in an excited nuclear state. The daughter achieves stability by losing energy (gamma radiation).
What I've described above are the fundamental forces acting on the nuclear particles leading to the decay of a nucleus. The half-life tells us how long it will take to go from some initial number of radioactive atoms (N) to half the original amount (N/2).
But it still doesn't tell us why a particular atom decays today and another one of the exact same type decays some time in the future. The forces apply a sort of stress, that renders the atoms susceptible to decay, but something else must be triggering the decay. A common analogy is that of the conditions of a mountainside just prior to an avalanche. Something triggers the unstable state to decay to a lower potential energy state.
We think it is the perturbations in the quantum vacuum which trigger the decay. The quantum vacuum is what remains if you could remove all the energy and matter from a volume of space. The resultant "nothing" itself is unstable, it contains fleeting quanta of energy that pop into and out of existence. And these trigger the
Music, please Maestro: