Spontaneous transition depends ona.Energy of input photonsb.Lifetime of excited statec.Number of atoms in ground state

Spontaneous transition in quantum mechanics refers to the process by which an atom, molecule, or nucleus in an excited state spontaneously returns to its ground state. Here's how each of the factors you mentioned affects this process:

a. Energy of input photons: The energy of the input photons determines the initial excited state of the atom. The higher the energy of the photon, the higher the excited state. However, once the atom is in an excited state, the spontaneous transition to the ground state does not depend on the energy of the input photons.

b. Lifetime of excited state: The lifetime of the excited state is the average time the atom spends in the excited state before it spontaneously returns to the ground state. The longer the lifetime, the longer it takes for the spontaneous transition to occur on average. So, the rate of spontaneous transition is inversely proportional to the lifetime of the excited state.

c. Number of atoms in ground state: The number of atoms in the ground state does not directly affect the rate of spontaneous transition of an individual atom. However, in a large collection of atoms, if more atoms are in the ground state, then there are more atoms available to be excited and subsequently undergo spontaneous transition. So, the total rate of spontaneous transitions in the collection of atoms is proportional to the number of atoms in the ground state.