“What Einstein's theory predicts is that the 'binding energy' which is added to the system will be measurable as an increase in mass of the two resulting particles such that the sum of the two particles is greater than the initial mass of the helium atom.”
Just to be sure I understand—isn’t the sum of the two particles less than the initial mass of the helium atom, due to the loss of the binding energy?
Hmm...
I tried to side step this a little, hoping to keep the picture simpler.
In the case of a helium atom, the binding energy is negative. That is one way of saying that energy is released during the process of binding. That is why one can use "fusion" as a source of energy. That energy has to be added back in order to "un-fuse" the atom, so the separated particles end up having more mass than the original helium atom.
Fission of uranium exhibits the opposite case. It takes just a little energy to cause the uranium atom to separate into smaller particles. As the separation occurs, much stored energy is released. The mass of all the particles at the end is less than the mass of the original atom.
The fission example is like a compressed spring with a string tied to keep the spring compressed. If a little energy is added to break the string, the spring can release its stored energy.