Accepting Einstein’s General Relativity Theory, that the changes in gravitational field can propagate at the speed of light, it is proposed here that: before an electron in an atom emits a photon, the energy (h f0) of the photon was a part of total energy of the atom; contributing to establishing the gravitational-field around the atom. As soon an electron in that atom emits a photon of energy h f0 , and the photon starts moving away from the atom, the gravitational-field around the atom partly reduces, proportional to the photon’s energy h f0 , and this wave of ‘reduced gravitational field’ propagates radially-outwards at the speed of light. And a part of energy of the photon gets spent in “filling” the ‘gravitational potential-well’ produced by its energy, when it was a part of energy of the atom. From the derivation presented here we find that the energy spent by the photon to “fill” the ‘gravitational potential-well’, during its inter-galactic journey manifests as the ‘cosmological red-shift’.