Rami Arieli: "The
Laser Adventure" Chapter 2.8 page 2
Conclusion:
If at specific moment (t=0) the number of atoms in the excited
state E2 is N2(0), then when we leave
the system without external influence, the number of atoms in the
excited state will decay exponentially according to the equation
in previous page.
Pay attention that in
spontaneous emission, the population number (N1) of the lower
energy level
(E1) is unimportant.