 In this video we will discuss unstable nuclei and how they can decay towards more stable nuclei. Whether a system is stable depends on the energy of the system. Take the example of a ball sitting on the side of a hill. Is this a static system? Will the ball stay on the hill? No. We know that the ball will move to a lower energy state on the hill, gaining kinetic energy in the process. There are two important points regarding this situation. First, the motion of the ball is in a loud process, since gravity can pull the ball down the hill. Second, the kinetic energy given to the ball is a result of the work done by this gravitational force. The stability of nuclei is governed by similar considerations, with one very important extra point. That is the equivalency between mass and energy that was first formulated by Einstein in 1905. This is perhaps his most famous equation, equals mc2. Let's look at some particular cases of nuclear decay. Consider three atoms that all have 40 nucleons in their respective nuclei. These are potassium-40 with 19 protons and 21 neutrons, calcium-40 with 20 protons and 20 neutrons, and scandium-40 with 21 protons and 19 neutrons. Each of these atoms have a mass that can be measured, and the measured masses and kilograms are shown. While they are very similar, calcium-40 is very slightly lower in mass than both of its neighbouring mass-40 atoms. Since e equals mc2, if there is an allowed physical process that could convert potassium-40 into calcium-40, this change could lower the energy of the system, and the process might be spontaneously possible. Similarly, there could be an allowed physical process that converts scandium-40 into calcium-40, lowering the energy of the system. Note that the total energy still has to be conserved, so such a process must emit something that carries away the loss of nuclear energy, similar to the ball on a hill that ends up with kinetic energy.