No, atoms do not decrease their mass after emitting photons. When an atom emits a photon, it releases energy in the form of electromagnetic radiation. This energy comes from transitions of electrons between different energy levels within the atom. However, the mass of the atom itself remains unchanged.
According to the theory of relativity, mass and energy are equivalent and related by Einstein's famous equation, E=mc², where E is energy, m is mass, and c is the speed of light. This equation implies that mass can be converted into energy and vice versa. In processes such as nuclear reactions, mass can be converted into energy, but in the case of emitting photons, the energy released does not result in a decrease in the atom's mass.
Instead, the atom experiences a change in its energy state, but the total mass of the atom, which is determined by the combined mass of its protons, neutrons, and electrons, remains constant.