Slide 10 of 13
This is a little like the story of the Three Little Pigs. Houses of straw are unstable, meaning it doesnít take much work (energy) to blow them apart into individual straws, but a house made of brick is much more stable because it would require much more energy to separate it into its constituent elementary pieces.
Itís the same thing with the nucleus, except that Einsteinís famous mass-energy relation lets you figure out in advance how much energy would be required to break it apart into individual nucleons -- all you have to do is weigh the nucleus accurately. Thatís easy with a mass spectrograph, which nuclear physicists invented long before it became a standard tool in analytic chemistry.