Quantum Mechanics - Laser

The electronic energy levels of atoms of a certain gas are given by E_n = E₁ n², where n = 1, 2, 3, ... Assume that transitions are allowed between all levels. If one wanted to construct a laser from this gas by pumping the n = 1 → n = 3 transitions, which energy level or levels would have to be metastable? 

A. n = 1 only
B. n = 2 only
C. n = 1 and n = 3 only
D. n = 1, n = 2, and n = 3
E. None  

(GR9677 #99)

Solution:

 

LASER = Light Amplified Stimulated Emission Radiation.

There are 3 energy levels involved: Short-lived state, Metastable state, Ground State.

Fundamental principle of laser is population inversion (there are more atoms in the excited state than ground state).

To achieve population inversion:
1. Atoms in E₁ are pumped to E₃ by external source of energy.
2. The atom then decays quickly to E₂
3. The transition from E₂ to E₁ must be forbidden, for example, by a  Δl = ± 1 selection rule. Then, the state with energy E₂ is said to be metastable (its lifetime must be long compared with the usually short lifetimes of excited states).

Therefore, a large number of atoms can exist for a relatively long time at E₂, where they are just waiting for a photon to come along and stimulate the transition to E₁.

In this the case, stimulated emission will occur before spontaneous emission.  

Answer: B