The question requires us to identify the type nuclear decay that releases a photon of light energy and does not change the atom's mass or atomic number.
As we are talking about a nuclear decay that doesn't provoke a change in the atom's mass or atomic number, we can rule out both alpha and beta decay. Remember that an alpha particle contains two protons and two neutros, therefore an alpha decay changes both mass and atomic number. Similarly, the emission of an beta particle also changes the atomic number.
Then, we can analyze the remaining options: gamma decay and electron capture decay.
Electron capture decay is i process in which a proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, causing the change of a proton to neutron and causes the emission of a neutrino.
Gamma decay, on the other side, an atomic nucleus changes from a higher energy-state to a lower energy-state through the emission of electromagnetic radiation (a photon). Since it doesn't occur the emission of a particle, there is no change to the number of protons or neutrons and the atom's mass and atomic number remains unchanged.
Therefore, the best option would be letter A, "Gamma decay".