# Binding Energy and Energy Mass Equivalence

Consider a neutral atom. An external force acts on one of its valence electron so that it brings this valence electron to infinity away from the rest of the atom. The electron's kinetic energy does not change during this process. In other words, at every instant of time the external force is equal (or infinitesimally equal) and opposite to the attraction force of the rest of the atom on the electron.

If we do this, the final sum of mass of the electron at infinity and the mass of the rest of the atom will be larger than the initial mass of the atom. Does this mean that at every instant of time, when the external force is applied on the electron, the mass of the electron increases? But then the net force on the electron is zero so why will its mass change?

• How did you detach the electron from the atom in the first place? You had to do work on the electron. You cannot ignore binding energy. Also, how did you accelerate the electron away from the atom after detaching it? Again, you did work. Your assumptions about the KE not changing are false. – Bill N Nov 15 '18 at 18:23
• You can re-phrase this question in the classical domain by lifting a satellite out of orbit and off to infinity. – JEB Nov 15 '18 at 19:06