Rami Arieli: "The
Laser Adventure" Chapter 2.8 page 1

**(Advanced level only, need to know first order
differential equations).**

**For simplicity we shall assume**:

- 1. The material is composed of many identical atoms.

2. Each atom has only two energy levels: **E _{1}** and

3. The only decay mechanism of energy level **E _{2}** is
spontaneous emission.

4. At time t **N _{1}** atoms are in energy level

This equation defines the **lifetime**
**t _{2}** of energy level

(For a reminder about the solution for a differential
equation of this kind, **Click
here**)

The solution to the rate (differential) equation is:

check by substitution that the solution is valid.