In beta plus decay proton gets converted to neutron-- where does the extra mass come from? Beta plus decay seems to be violating law of conservation of mass-energy-- when a proton changes to neutron a very small quantity of Mass is added to the right side of equation -- but where does this mass come from?
 A: You must remember that in special relativity, which is necessary when studying nuclear reactions , the is no conservation of mass, just conservation of energy and momentum .
The mass of a particle is the "length" of the four vector, and the mass of a system of particles is the mass of the vector sum of their four momenta. In Nuclear Physics this has been registered statistically for the nuclei with the nuclear binding energy curve, and the curve tells us if a nucleus has enough energy to allow for the transition of proton to neutron and the eventual decay nucleus and products.
A: You need to remember that mass and energy are the same thing in different forms, so for example, the mass of the electron is 500,000 electron volts. You can't violate the 1st Law of Thermodynamics (mass/energy can neither be created nor destroyed), which is an inviolable law. When a proton is converted into a neutron, it has to acquire mass/energy from somewhere because the neutron is 3 mass units heavier than a proton. The answer is simple: the necessary mass/energy can be acquired from a collision with another massive particle or, on rarer occasions, by absorbing the energy of a neutrino or gamma photon. In order to become a neutrino, the proton also needs to acquire some negative charge so that the neutron can be neutral. It is impossible to create negative charger without creating an equal quantity of positive charge, so this unwanted positive charge is emitted as a positron, which also adds another mass unit to the equation. The kinetic energy of the particles involved must also be taken into account.
