Rami Arieli: "The
Laser Adventure" Chapter 2.7 page 1

**Atoms stay in an excited level only for a short
time (about 10 ^{-8} [sec]), and then they return to a lower energy
level by spontaneous emission.**

Every energy level has a **characteristic
average lifetime**, which is the time after which only
1/e (about 37%) of the excited atoms still remain in the excited state.
Thus, this is the time in which 67% of the excited atoms returned to a
lower energy level.

According to the quantum theory,** the transition
from one energy level to another is described by statistical probability**.
**The probability of transition from higher
energy level to a lower one is inversely proportional to the lifetime of
the higher energy level.**

In reality, the probability for different transitions is a characteristic
of each transition, according to selection rules (For an **explanation
about
selection rules click here**).

When the transition probability is low for a specific transition, the
lifetime of this energy level is longer (about 10^{-3} [sec]),
and this level becomes a "**meta-stable**"
level. In this meta-stable level a large population of atoms can assembled.
As we shall see, this level can be a candidate for lasing process.

When the population number of a higher energy level is bigger than the
population number of a lower energy level, a condition of "**population
inversion**" is established.

If a population inversion exists between two energy levels, the probability
is high that an incoming photon will **stimulate**
an excited atom to return to a lower state, while emitting another photon
of light. The probability for this process depend on the match between
the energy of the incoming photon and the energy difference between these
two levels (comment...).