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A metastable state is an excited energy state of an atom that has a significantly longer lifetime than typical excited states. These states are characterized by a forbidden energy transition, making it more difficult for an electron to decay back to a lower energy state, thus increasing its lifetime. On the other hand, a normally allowed energy state is an energy level of the atom that electrons can occupy as allowed by quantum mechanical principles. Electrons can easily transition between these states by emitting or absorbing photons, and the excited states have relatively short lifetimes.

The differences between metastable states and normally allowed energy states can be broken down into the following points: 1. Lifetime: Metastable states have significantly longer lifetimes compared to normally allowed energy states. 2. Energy transitions: Metastable states involve forbidden energy transitions, meaning that it is highly unlikely for an electron to decay back to a lower energy state. In contrast, energy transitions between normally allowed energy states are more likely to occur. 3. Radiative decay: Since metastable states involve forbidden energy transitions, radiative decay (emission of a photon) is less likely. In normally allowed energy states, radiative decay occurs more frequently.

Metastable states play a crucial role in the operation of laser systems. Laser systems work on the principle of stimulated emission, where an incoming photon causes an excited electron to drop to a lower energy state and emit a second, identical photon. This process amplifies the light, resulting in a coherent, intense beam of light. For a laser to function efficiently, a population inversion is required, where there are more atoms in an excited state than in the ground state. Metastable states play a critical role in achieving population inversion due to their long lifetimes. Since metastable states decay less frequently than normal energy states, they essentially "trap" electrons, allowing a higher number of atoms to remain in excited states for an extended period. This makes it easier to create a population inversion, ensuring the efficient operation of the laser system.