This question probably shows my obvious ignorance in this topic. Huzzah for asking questions!

When a radioactive isotope decays, part of it's mass is converted into energy. (It emits alpha particles, beta particles, or gamma rays). If a radioactive isotope (lets call it X) emits, say, an alpha particle, then the total mass of the system is represented by:

Mass of X=Mass of Y + Mass Alpha Particle,

where Y is the next element in the decay series, with mass equal to Mass X minus Mass Alpha particle.

According to my understanding of the concept, when this occurs a portion of the mass is converted into energy, and this is where the energy for nuclear reactors and nuclear devices is derived from. Where does the mass come from? According to the probably over-simplified equation above, all the mass is conserved, unless somehow Mass X > Mass Y + Mass Alpha Particle.