An "allowed" atomic excited state has a lifetime, meaning the expected time before the excited state returns to the ground state by photon emission. Allowed state lifetimes depend on a complex formula for energy difference, wave function overlap, and quantum state parameters. For example, the calculated hydrogen 2p -> 1s allowed transition lifetime is about 1.6 nanoseconds. The hydrogen 2s-> 1s transition on the other hand, is not an allowed transition (called "forbidden"), and takes much longer to return to the 1s state. The quantum numbers are n, l, s, and m. Transition lifetimes from higher level hydrogen states are longer: 5p->1s is about 24 nanoseconds. These are all calculated and tabulated in Bethe and Salpeter, "Quantum Mechanics for One and two Electron Atoms", page 266. For higher Z hydrogen-like atoms, the lifetimes are shorter. Often, transitions with lifetimes over some arbitrary value, like 100 nanoseconds, are called metastable, even thought they may be "allowed"..
Sometimes, an atomic or molecular state is conditionally stable, but will decay to the ground state if it collides with another atom that stimulates the transition (like in a gas).
Bob S
