Conservation of matter

The law of conservation of mass, also known as principle of mass / matter conservation is that the mass of a closed system (in the sense of a completely isolated system) will remain constant over time. The mass of an isolated system cannot be changed as a result of processes acting inside the system. A similar statement is that mass cannot be created/destroyed, although it may be rearranged in space, and changed into different types of particles. This implies that for any chemical process in a closed system, the mass of the reactants must equal the mass of the products.

Definition provided by Wikipedia

Don't Buy into the Idea of Conservation of matter!!!!

In the real world matter is "disappearing" all the time.  Anytime matter interact and binds with other matter matter disappears, anytime matter "falls" apart (like in alpha and beta decay) matter is "created".   For most chemical process we don't consider what is going on in the nucleus, it is solely electron / electron interaction (most of undergraduate chemistry classes is based on electron electron interactions).

The Conservation of matter and energy

Einstein's Mass Energy Equivalence states that matter can be exchanged for energy,  and in nuclear physics this exchange occurs when a positively charged proton bonds with a charge neutral neutron.  Two particles that, using the classical ideas of mechanics, have no reason to form a bond.  This bond that is created this way turns out to be one of the strongest forces in the known universe.  Take the nucleus of a helium atom, two protons (from coulombs law) have a very, very strong repulsion to each other, so what keeps them together?.  Each  neutron (the two of them) has one bond to each proton, and collectively these bonds are strong enough to overcome the repulsive nature of the protons.  When considering the strength of these types of bonds we tend not to look at them as forces (there is most certainly is a force there) but as binding energy.

What it looks like for us

How do we solve nuclear reaction problems?

The first step in solving nuclear energy problems consider everything in the problem to be energy.  Mass according to Einstein is energy, every proton every neutron is a packet of energy.  Now, every electronvolt has  be accounted for during the reaction, so take all of the initial mass and subtract the final mass, you get whats called the mass defect (Mass initial - Mass final = Mass defect).  If the mass defect is positive, this is the amount of matter that is converted into energy in the reaction (a portion of the matter in the reaction in converted into energy).   If the mass defect is negative, this is the amount of energy that is needed to create the reaction (During the reaction one of the particle needs to have this amount of kinetic energy in order for the reaction to happen).  Once the mass defect is calculated use Einstein's equation to solve for E (energy).