Lasers

In a steady state, the rate of excitation from level 0 to level 2 equals the rate of de-excitation from level 2 to level 1. This can be expressed as: where:
- and are the populations of levels 1 and 2, respectively.
From the problem statement, the total excitation rate is given as , so the population at level 2 is: Using the steady state condition: Solving for : Thus, the value of is 2.

In a three-level laser system, to achieve sustained lasing action, certain conditions must be met to maintain the population inversion between the energy levels. 1. Condition (A): The lifetime of energy level 1 should be greater than that of energy level 2. This ensures that level 1 can accumulate more population before the system decays to level 0. If the lifetime of level 1 is too short, it will not effectively contribute to the population inversion needed for lasing. 2. Condition (B): The population of the particles in level 1 should be greater than that of level 0. For lasing to occur, there must be a population inversion, meaning that more particles should occupy the higher energy level (level 1) than the lower energy level (level 0). This condition is necessary for the laser to emit light. Thus, the necessary conditions for lasing are (A) and (B).